Multipole Refinement Research Articles

Electron density changes accompanying high-pressure phase transition in AlOOH

Abstract An attempt to compare and describe the differences in the electron density distribution between two phase structures of AlOOH has been made. High-resolution, high-pressure experiments with α-AlOOH diaspore were conducted using single-crystal synchrotron X-ray diffraction data. A multipole model of experimental electron density in the α-AlOOH single crystal was refined. Simultaneously, similar multipole refinement was conducted for another phase of diaspore (δ-AlOOH), this time based on a previously published data set. Both results were compared and supported by density functional theory (DFT) calculations. Although the results are affected by the limited quality of the data, it is clear that the phase transition caused significant changes in the shape and arrangement of the atomic basins. Atomic basins are a much better tool to present subtle electron density distribution changes than traditional polyhedra. Straightforward comparison of datasets available in older scientific papers and current datasets is challenging because of differences in data quality and collection parameters. However, augmenting experimental data with computational results can help reveal important information in even incomplete datasets.

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.

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.

High-resolution structural study on pyridin-3-yl ebselen and its N-methylated tosylate and iodide derivatives.

The crystal structure of the pyridine-substituted benzisoselenazolinone 2-(pyridin-3-yl)-2,3-dihydro-1,2-benzoselenazol-3-one (C12H8N2OSe, 2), related to the antioxidant ebselen [systematic name: 2-phenyl-1,2-benzoselenazol-3(2H)-one, 1], is characterized by strong intermolecular N...Se(-N) chalcogen bonding, where the N...Se distance of 2.3831 (6) Å is well within the sum of the van der Waals radii for N and Se (3.34 Å). This strong interaction results in significant lengthening of the internal N-Se distance, consistent with significant population of the Se-N σ* antibonding orbital. Much weaker intermolecular O...Se chalcogen bonding occurs between the amide-like O atom in 2 and the less polarized C-Se bond in this structure. Charge density analysis of 2 using multipole refinement of high-resolution data allowed the electrostatic surface potential for 2 to be mapped, and clearly reveals the σ-hole at the extension of the Se-N bond as an area of positive electrostatic potential. Topological analysis of the electron-density distribution in 2 was carried out within the Quantum Theory of Atoms in Molecules (QTAIM) framework and revealed bond paths and (3,-1) bond critical points (BCPs) for the N...Se-N moiety consistent with a closed-shell interaction; however, the potential energy term is suggestive of electron sharing. Analysis of the electron localization function (ELF) for the strong N...Se and the weak O...Se chalcogen-bonding interactions in the structure of 2 suggest significant electron sharing in the former interaction, and a largely electrostatic interaction in the latter. Conversion of 2 to its N-methylated derivatives by reaction with methyl iodide [1-methyl-3-(3-oxo-2,3-dihydro-1,2-benzoselenazol-2-yl)pyridin-1-ium iodide, C13H11N2OSe+·I-] and methyl tosylate [1-methyl-3-(3-oxo-2,3-dihydro-1,2-benzoselenazol-2-yl)pyridin-1-ium toluenesulfonate trihydrate, C13H11N2OSe+·C7H7O3S-·3H2O] removes the possibility of N...Se chalcogen bonding and instead structures are obtained where the iodide and tosylate counter-ions fulfill the role of chalcogen-bond acceptors, with a strong I-...Se interaction in the iodide salt and a weaker p-Tol-SO3-...Se interaction in the tosylate salt.

Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB2.

Case studies of 1T-TiSe2 and YBa2Cu3O7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB2 in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the Tc of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB2 samples─a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB2 to form non-stoichiometric Mg1-xB2 phases (1 - x ∼ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen-Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg1-xB2 phases during HT synthesis.

New refinement strategies for a pseudoatom databank – toward rapid electrostatic interaction energy estimations

Pseudoatom databanks, collections of parameters from the multipole model of electron densities for various atom types, are used to replace the Independent Atom Model with the more accurate Transferable Aspherical Atom Model (TAAM) in crystal structure refinements. The databanks are also employed to reconstruct the electron density of a molecule, crystal or biomacromolecular complex in a fast yet accurate way and compute various properties such as the energy of electrostatic interactions, for example. A even faster but similarly accurate model for estimations of electrostatic energy exists called aug-PROmol [Bojarowski, Kumar & Dominiak (2016). ChemPhysChem, 17, 2455–2460]. A model analogous to aug-PROmol cannot be built from the current pseudoatom databanks, as they perform badly when truncated to the monopole level. Here, new strategies for multipole model refinements were sought, leading to better parametrization at the monopole level. This would allow the creation of a pseudoatom databank in a single route of model parametrization, which would be suitable for both crystal structure refinement and rapid electrostatic energy calculations. Here it is shown that the cumulative approach to multipole model refinements, as opposed to simultaneous or iterative refinements of all multipole model parameters (Pv , κ, Plm , κ′), leads to substantially different models of electron density. Cumulative refinement of two blocks of parameters, the first with Pv and κ and then the second with Plm and κ′, leads to the P v κ|P lm κ′ model having promising properties. The P v κ|P lm κ′ model is as good as the University at Buffalo DataBank (UBDB) in X-ray structure TAAM refinements and electrostatic energy estimations, especially for less polar molecules. When truncated to the monopole level, the P v κ model has a chance to replace aug-PROmol in fast yet accurate electrostatics energy calculations, although some improvements in κ parametrization for polar functional groups are still needed. The P v κ model is also a source of point charges which behave similarly to restrained electrostatic potential (RESP) charges in electrostatic interaction energy estimations.

Origin of the low formation energy of oxygen vacancies in CeO2

Oxygen vacancies play a crucial role in determining the catalytic properties of Ce-based catalysts, especially in oxidation reactions. The design of catalytic activity requires keen insight into oxygen vacancy formation mechanisms. In this work, we investigate the origin of oxygen vacancies in CeO2 from the perspective of electron density via high-energy synchrotron powder x-ray diffraction. Multipole refinement results indicate that there is no obvious hybridization between bonded Ce and O atoms in CeO2. Subsequent quantitative topological analysis of the experimental total electron density reveals the closed-shell interaction behavior of the Ce–O bond. The results of first-principles calculation indicate that the oxygen vacancy formation energy of CeO2 is the lowest among three commonly used redox catalysts. These findings indicate the relatively weak bond strength of the Ce–O bond, which induces a low oxygen vacancy formation energy for CeO2 and thus promotes CeO2 as a superior catalyst for oxidation reactions. This work provides a new direction for design of functional metal oxides with high oxygen vacancy concentrations.

Back Cover: Trapping X‐ray Radiation Damage from Homolytic Se−C Bond Cleavage in BnSeSeBn Crystals (Bn=benzyl, CH2C6H5) (Angew. Chem. Int. Ed. 26/2022)

Radiation damage in the form of radical formation by homolytic Se−C bond cleavage was trapped by high-resolution X-ray and EPR experiments, as reported by Dietmar Stalke et al. in their Communication (DOI: 10.1002/anie.202203665). Orange dibenzyldiselenide single crystals are X-ray exposed with various intensities and the benzyl radical formation is monitored by multipole refinement and quantum/molecular mechanics. In any interpretation of selenium containing structures, particularly in life science experiments from synchrotrons, it is important to consider those radical-induced processes.

Si-H···Se Chalcogen-Hydride Bond Quantified by Diffraction and Topological Analyses.

The Si-H···Se contact in 1-mesitylselanyl-8-(dimethylsilyl)naphthalene (1), which exhibits the spatial arrangement of a δ-agostic interaction from geometric considerations, was investigated. Is this just enforced by close 1,8-proximity or is this a favorable interaction? Charge density studies are best suited to investigate the exact origin of the interaction and to quantify the properties. Hence, they are most elucidating. High-resolution X-ray diffraction data of 1 were collected, and a multipole refinement followed by a topological analysis using Bader's quantum theory of atoms in molecules was employed. The resulting bond properties were set in relation to high-level computational parameters. The comparison to Si-H···[M] agostics, hydride bonding, chalcogen bonds, and charge-inverted hydrogen bonds qualified the Si-H···Se noncovalent interaction to be best classified as a chalcogen-hydride bond.

Thermal-induced transformation of glutamic acid to pyroglutamic acid and self-cocrystallization: a charge-density analysis.

Thermal-induced transformation of glutamic acid to pyroglutamic acid is well known. However, confusion remains over the exact temperature at which this happens. Moreover, no diffraction data are available to support the transition. In this article, we make a systematic investigation involving thermal analysis, hot-stage microscopy and single-crystal X-ray diffraction to study a one-pot thermal transition of glutamic acid to pyroglutamic acid and subsequent self-cocrystallization between the product (hydrated pyroglutamic acid) and the unreacted precursor (glutamic acid). The melt upon cooling gave a robust cocrystal, namely, glutamic acid-pyroglutamic acid-water (1/1/1), C5H7NO3·C5H9NO4·H2O, whose structure has been elucidated from single-crystal X-ray diffraction data collected at room temperature. A three-dimensional network of strong hydrogen bonds has been found. A Hirshfeld surface analysis was carried out to make a quantitative estimation of the intermolecular interactions. In order to gain insight into the strength and stability of the cocrystal, the transferability principle was utilized to make a topological analysis and to study the electron-density-derived properties. The transferred model has been found to be superior to the classical independent atom model (IAM). The experimental results have been compared with results from a multipolar refinement carried out using theoretical structure factors generated from density functional theory (DFT) calculations. Very strong classical hydrogen bonds drive the cocrystallization and lend stability to the resulting cocrystal. Important conclusions have been drawn about this transition.

Crystal engineering of a co-crystal of antipyrine and 2-chlorobenzoic acid: relative energetic contributions based on multipolar refinement

The growth and stability of a new 1 : 1 antipyrene–dichlorobenzoic acid cocrystal system has been analyzed in terms of electron density analysis and electrostatic interaction energy contributions.

Charge density studies of single and transient (single to double) boron-oxygen bonds in (NH4)2B4O5(OH)4·2H2O.

A H4B4O92- ion which makes up the (NH4)2B4O5(OH)4·2H2O crystal structure has two types of boron-oxygen bonds, i.e. single B-O bonds and an intermediate between single and double BO bonds. Differences between these two bond types are visible not only because they differ by their lengths but also a topology of electron density distribution differs. This also gives a hint as to how to distinguish between these two bond types. Experimental results based on multipole model refinement gave excellent agreement with theoretical calculations and literature data. Calculations at bond critical points for B-O and BO (electron density, the Laplacian of electron density and the localized-orbital locator function) suggest us how boron-oxygen bonds should be categorised with respect to compounds previously reported in the literature. Additionally, a novel synthesis method for the investigated compound has been developed, which involves crystallization from an aqueous solution of BH3NH3 dissolved in a mixture of tetrahydrofuran and water.

Crystal engineering of co-crystal of nicotinic acid and pyrogallol: an experimental and theoretical electron density analysis

Experimental electron density analysis by means of high-resolution X-ray diffraction data up to sinθ/λmax = 1.11 Å−1 at 100 (1) K has been performed to analyze the detailed structure and the strength of intermolecular interactions responsible for the formation of a new solid form of nicotinic acid (NA), cocrystallized with pyrogallol (PY). There are two NA–PY units in the asymmetric unit. The experimental results are compared with the results obtained from theoretical structure factors modeled using periodic boundary DFT calculations. Both refinements were carried out using the Hansen and Coppens multipolar formalism (in MoPro program). The non-centrosymmetric and polar nature of the crystal system rendered the multipolar refinement challenging which was addressed by involving the transferability principle. This study highlights the significance of the transferability principle in electron density modeling in non-routine situations. The 2:2 cocrystal of NA–PY exhibits a zigzag, brickwall and sheet-like layered structure in three dimensions and is stabilized by strong intra- and inter-molecular hydrogen bonding through N—H...O and O—H...O bonds, some of them due to the zwitterion nature of NA as well as weak interactions between the PY molecules. Ranking these interactions via topological analysis of the electron density shows the leading role of the NA–NA substructure which drives the organization of the cocrystals. These strong interactions between the NA zwitterions may explain why Z′ = 2.

Non-Covalent Interactions in the Biphenyl Crystal: Is the Planar Conformer a Transition State?

A combined experimental and theoretical study of the biphenyl (BP) crystal is presented. The X-ray diffraction data collected at 100 K were subjected to Hirshfeld atom and multipole refinements of the electron density, ρ(r). A theoretical exploration of the potential energy surface (PES) of the crystal was also carried out. This investigation challenges the common assumption that the planar structure of BP in the phase I crystal is an average of two twisted configurations in a double-well potential. The theoretical computations provide compelling evidence that this structure corresponds to a minimum on the PES hence to a stable molecular arrangement. Consistently, the experiment showed no evidence of positional or dynamic disorder. The intramolecular hydrogen-hydrogen bonds detected are not repulsive. The topological analysis of the experimental and theoretical ρ(r) reveals that both the intra- and intermolecular H⋅⋅⋅H and the C-H⋅⋅⋅π contacts stabilize the BP crystal.

X-ray charge density study of the 6-methyluracil derivative in the crystal: Revealing, consequences, and multipole refinement of minor static disorder

The accurate X-ray diffraction experiment was performed on the crystal of 1,6-dimethyl-3-propargyl-2,4-pyrimidinedione at 100 K. The static electron density (ED) was obtained via multipole refinement against these data. The presence of low-intense but nonrandom positive residual density peaks revealed that the structure was complicated by the minor conformational static disorder. Further analysis of the number and positions of critical points (CPs) (3, +3) of Laplacian of ED ∇2ρ(r) and the ratio of eigenvalues of its Hessian matrix unambiguously proved that the multipole-modeled ED of the main disorder component was contaminated by the second one. A method of visualizing the Laplacian minima as CP-ellipsoids with semiaxes inversely proportional to the eigenvalues of Hessian matrix of ∇2ρ(r) was applied to evaluate the correctness of modeled ED. Extra Laplacian CPs (3, +3) were attributed to the incorrect multipole populations, while the elongated shape of the corresponding discoid CP-ellipsoids was mainly considered to be the effect of troublesome kappa-parameters. A number of different multipole models were constructed in order to minimize the undesirable effects of disorder on the multipole ED. The two-component multipole model showed that the heterocyclic moiety of the minor component with an occupancy of 2% underwent the 180° rotation about the N3–C7 bond axis. Furthermore, the partial transfer of multipole parameters from the model refined against theoretical structure factors was utilized on the most problematic atoms, which massively contributed to disorder treatment. This approach allowed us to restore the ED of the main component in the crystal environment, which quality was gauged by the quantum-topological analysis as well as by its conformity to the data obtained from ab initio periodic calculations. Attempts to speculate on reasons for the limited disordering observed were made: theoretical calculations suggest that moderate hydrogen bonds support the disordering in the structure, while multiple weak noncovalent contacts, e.g., pi interactions, may provide the restrictions on the 50:50 disorder.

Experimental Charge Density Analysis and Electrostatic Properties of Crystalline 1,3-Bis(Dimethylamino)Squaraine and Its Dihydrate from Low Temperature (T = 18 and 20 K) XRD Data

Multipolar refinements of structural models fitting extensive sets of X-ray diffraction (XRD) data from single crystals of 1,3-bis(dimethylamino)squaraine [SQ, C8H12N2O2] and its dihydrate [SQDH, C8H12N2O2·2H2O], collected at very low T (18 ± 1 K for SQ, 20 ± 1 K for SQDH), led to an accurate description of their crystal electron density distributions. Atomic volumes and charges have been estimated from the experimental charge densities using the Quantum Theory of Atoms in Molecules (QTAIM) formalism. Our analysis confirms the common representation (in the literature and textbooks) of the squaraine central, four-membered squarylium ring as carrying two positive charges, a representation that has been recently questioned by some theoretical calculations: the integrated total charge on the C4 fragment is estimated as ca. +2.4e in SQ and +2.2e in SQDH. The topology of the experimental electron density for the SQ squaraine molecule is modified in the dihydrated crystal by interactions between the methyl groups and the H2O molecules in the crystal. Maps of the molecular electrostatic potential in the main molecular planes in both crystals clearly reveal the quadrupolar charge distribution of the squaraine molecules. Molecular quadrupole tensors, as calculated with the PAMoC package using both Stewart and QTAIM distributed multipole analysis (DMA), are the same within experimental error.

Magnetization Density Distribution of Sr_{2}IrO_{4}: Deviation from a Local j_{eff}=1/2 Picture.

5d iridium oxides are of huge interest due to the potential for new quantum states driven by strong spin-orbit coupling. The strontium iridate Sr_{2}IrO_{4} is particularly in the spotlight because of the so-called j_{eff}=1/2 state consisting of a quantum superposition of the three local t_{2g} orbitals with, in its simplest version, nearly equal populations, which stabilizes an unconventional Mott insulating state. Here, we report an anisotropic and aspherical magnetization density distribution measured by polarized neutron diffraction in a magnetic field up to 5T at 4K, which strongly deviates from a local j_{eff}=1/2 picture even when distortion-induced deviations from the equal weights of the orbital populations are taken into account. Once reconstructed by the maximum entropy method and multipole expansion model refinement, the magnetization density shows four cross-shaped positive lobes along the crystallographic tetragonal axes with a large spatial extent, showing that the xy orbital contribution is dominant. The analogy to the superconducting copper oxide systems might then be weaker than commonly thought.

Investigation of bond topological and electrostatic properties of plumbagin molecule: An experimental and theoretical charge density study

Plumbagin is a naturally occurring derivative with several medicinal properties including antioxidants, antifungal, antimalarial, leprosy and antitumor properties; their structural and electrostatic properties are yet to be determined. The crystal structure of plumbagin has been solved; it shows that the compound crystallizes in P21/c space group with two molecules in the asymmetric unit. The electron density distribution of both molecules have determined from multipole model refinement. Among all the C–O bonds of both molecules (I & II), the OH group connected C–O bond and the methyl group connected C–C bond exhibits less electron density and the negative Laplacian of electron density as well. Further, the electrostatic potential (ESP) surface of two plumbagin molecules show some difference in their electronegative regions. The carbonyl O-atoms exhibit high electronegative ESP regions which are the key reactive locations of plumbagin when bind with the active site of target protein and in the ESP map, an aromatic π-cloud also observed in one of the molecule. The electron density distribution of O–H⋅⋅⋅O intermolecular interactions between the molecules I and II, reveals that these interactions are found very stronger than the other interactions in the crystal.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study.

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

New Insights into the Catalytic Activity of Cobalt Orthophosphate Co3 (PO4 )2 from Charge Density Analysis.

An extensive characterization of Co3(PO4)2 was performed by topological analysis according to Bader‘s Quantum Theory of Atoms in Molecules from the experimentally and theoretically determined electron density. This study sheds light on the reactivity of cobalt orthophosphate as a solid‐state heterogeneous oxidative‐dehydration and ‐dehydrogenation catalyst. Various faces of the bulk catalyst were identified as possible reactive sites given their topological properties. The charge accumulations and depletions around the two independent five‐ and sixfold‐coordinated cobalt atoms, found in the topological analysis, are correlated to the orientation and population of the d‐orbitals. It is shown that the (011) face has the best structural features for catalysis. Fivefold‐coordinated ions in close proximity to advantageously oriented vacant coordination sites and electron depletions suit the oxygen lone pairs of the reactant, mainly for chemisorption. This is confirmed both from the multipole refinement as well as from density functional theory calculations. Nearby basic phosphate ions are readily available for C−H activation.