Experimental Electron Density Distribution Research Articles

In Search of Covalency Measure of Gd(III)-Ligand Interactions.

Experimental electron density distribution of the [C(NH2)3]3[Gd(EDTA)F2]·H2O crystal was determined. The derived experimental and theoretical (DFT) topological parameters such as ∇2ρc, ρc, bond degree (BD), kinetics, and potential energy were used to study the nature of Gd-O, Gd-F, and Gd-N interactions. The natural charge of the Gd is 1.86; the natural configuration of the cation is [Xe]6s0.134f7.105d0.83, and the covalency of the Gd-L bond is mainly connected with the transfer of charge from the spx ligand orbitals onto the 5d orbitals of the Gd cation. Simultaneously, the donation of charge onto the 6s and 4f orbitals occurs to a lesser extent. Moreover it was found that the donation of the ligand charges onto the Gd(III) is larger for compounds with a lower coordination number. The obtained topological parameters were analyzed in the context of the Gd(III) f-f transition properties, i.e., energy of the excited 2S+1LJ states, Judd-Ofelt intensity parameters, and luminescence lifetimes, of 18 Gd(III) compounds with various O, N, and F donor ligands (DOTA, EDTA, CDTA, DTPA, NTA, EGTA, ODA, F-, H2O, and CO32-). The calculated nephelauxetic β parameter may reflect the penetration degree of electron lone pairs of ligands inside the metal basin. Finally, it was found for the first time that the sum of the Gd(III)-L bond energy (∑EGdL) is correlated with the position of the gravity center of the 8S7/2 → 2S+1LJ transitions and increase of covalency of the Gd(III)-L bonds is associated with decrease of their bond energy. The obtained results may shed light on chemical bonding in systems containing f-elements. Such subtle differences in the covalent contribution to the Ln-L or An-L bond may tune the selectivity of the partitioning processes of lanthanides and actinides.

An approach to surface electron density-sensing property correlation in non-stoichiometric boron carbide

The key to most surface phenomena lies in the surface electron density. Particularly, it is the electron density distribution over the surface that primarily controls the overall interaction of the material with the external environment, say in processes like heterogeneous catalysis. Hence, a precise understanding of surface electron density is essential to understand and design improved surface active materials for catalysis and sensing. Surface structure has been determined primarily using surface sensitive techniques like high-energy surface x-ray diffraction (XRD), the crystal truncation rod scattering method, low-energy electron diffraction, scanning transmission electron microscopy, and grazing incidence small angle x-ray scattering. In this work, using aspherical electron density models of crystal structures in different molecular and extended solids, we show a convenient and complementary way of determining high-resolution experimental surface electron density distribution from conventional bulk x-ray diffraction data. The usefulness of our method has been validated by the surface functionality of boron carbide. While certain surfaces in boron carbide show the presence of substantial electron deficient centers, they are absent in others. Based on that, a new surface property of boron carbide has been inferred and has also been validated by chemiresistive gas sensing experiments.

Experimental electron density distribution of KZnB3O6 constructed by maximum-entropy method

The dynamic charge density of KZnB3O6, which contains edge-sharing BO4 units, has been characterized using laboratory and synchrotron X-ray diffraction techniques. The experimental electron density distribution (EDD) was constructed using the maximum-entropy method (MEM) from single crystal diffraction data obtained at 81 and 298 K. Additionally, MEM-based pattern fitting (MPF) method was employed to refine the synchrotron powder diffraction data obtained at 100 K. Both the room-temperature single crystal diffraction data and the cryogenic synchrotron powder diffraction data reveal an intriguing phenomenon: the edge-shared B2O2 ring exhibits a significant charge density accumulation between the O atoms. Further analysis of high-quality single crystal diffraction data collected at 81 K, with both high resolution and large signal-to-noise ratio, reveals no direct O–O bonding within the B2O2 ring. The experimental EDD of KZnB3O6 obtained aligns with the results obtained from ab-initio calculations. Our work underscores the importance of obtaining high-quality experimental data to accurately determine EDDs.

Quantifying weak interactions in ferroelectric and paraelectric phases of phenazine and chloroanilic acid co-crystal using experimental and theoretical electron densities.

The co-crystal of phenazine and chloroanilic acid is known to display paraelectric properties at room temperature. It shows a paraelectric to ferroelectric phase transition at 253 K and has an incommensurately modulated ferroelectric phase below 137 K. High-resolution synchrotron X-ray data were collected at 160 K to model the experimental electron-density distributions, and derived topological properties from the electron density were used to quantify the weak interactions responsible for the origin of the ferroelectric phase. The structure and non-covalent interactions are analysed using Hirshfeld surfaces and energy frameworks. The topological properties, energies, atomic charges and molecular electrostatic potential surfaces are determined from the experimental data, further supported by theoretical calculations. The results from the ferroelectric phase are compared with the paraelectric phase. Although the structural descriptions indicate neutral phenazine and chloroanilic acid molecules in the ferroelectric phase, the topological properties of the electron density indicate a considerable amount of proton transfer in the O-H...O hydrogen bond. Indeed, the displaced H atom in the O-H...O hydrogen bond suggests a mixed covalent/polar nature of chemical bonding. Subtle changes in the chemical bonding and proton-transfer pathways could be detected from the high-resolution electron-density studies.

The Relevance of Experimental Charge Density Analysis in Unraveling Noncovalent Interactions in Molecular Crystals.

The work carried out by our research group over the last couple of decades in the context of quantitative crystal engineering involves the analysis of intermolecular interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding using experimental charge density methodology is reviewed. The focus is to extract electron density distribution in the intermolecular space and to obtain guidelines to evaluate the strength and directionality of such interactions towards the design of molecular crystals with desired properties. Following the early studies on halogen bonding interactions, several “sigma-hole” interaction types with similar electrostatic origins have been explored in recent times for their strength, origin, and structural consequences. These include interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding. Experimental X-ray charge density analysis has proved to be a powerful tool in unraveling the strength and electronic origin of such interactions, providing insights beyond the theoretical estimates from gas-phase molecular dimer calculations. In this mini-review, we outline some selected contributions from the X-ray charge density studies to the field of non-covalent interactions (NCIs) involving elements of the groups 14–17 of the periodic table. Quantitative insights into the nature of these interactions obtained from the experimental electron density distribution and subsequent topological analysis by the quantum theory of atoms in molecules (QTAIM) have been discussed. A few notable examples of weak interactions have been presented in terms of their experimental charge density features. These examples reveal not only the strength and beauty of X-ray charge density multipole modeling as an advanced structural chemistry tool but also its utility in providing experimental benchmarks for the theoretical studies of weak interactions in crystals.

Local pressure calibration method of inductively coupled plasma generator based on laser Thomson scattering measurement

Based on laser Thomson scattering (TS) measurements and finite element method (FEM) simulations of electron density in inductively coupled plasma (ICP), the simulated local pressure calibration curves of ICP generator are obtained by comparing the experimental and simulated electron density distributions and maxima. The equation coefficients of theoretical model associated with the ICP generator experimental system can be obtained by fitting the simulation curve with the least square method, and the theoretical pressure calibration curves under different absorbed powers can be further obtained. Combined with the vacuum gauge measurements, both the simulated and theoretical pressure calibration curves can give the true local pressure in the plasma. The results of the local pressure calibration at the different absorbed powers show that the density gradient from the vacuum gauge sensor to the center of the coil in ICP generator cavity becomes larger with the increase of electron density, resulting in a larger gap between the measured value and the pressure calibration value. This calibration method helps to grasp the local pressure of ICP as an external control factor and helps to study the physicochemical mechanism of ICP in order to achieve higher performance in ICP etching, material modification, etc.

Rietveld Refinement and X-ray Absorption Study on the Bonding States of Lanthanum-Based Perovskite-Type Oxides La1−xCexCoO3

Metal-oxygen bonding of the Ce-doped LaCoO3 system remains largely unexplored despite extensive studies on its magnetic properties. Here, we investigate the structure and local structure of nanoscale La1−xCexCoO3, with x = 0, 0.2, and 0.4, using the Rietveld refinement and synchrotron X-ray absorption techniques, complemented by topological analysis of experimental electron density and electron energy distribution. The Rietveld refinement results show that LaCoO3 subject to Ce addition is best interpretable by a model of cubic symmetry in contrast to the pristine LaCoO3, conventionally described by either a monoclinic model or a rhombohedral model. Ce4+/Co2+ are more evidently compatible dopants than Ce3+ for insertion into the main lattice. X-ray absorption data evidence the partially filled La 5d-band of the pristine LaCoO3 in accordance with the presence of La–O bonds with the shared-type atomic interaction. With increasing x, the increased Ce spectroscopic valence and enhanced La–O ionic bonding are noticeable. Characterization of the local structures around Co species also provides evidence to support the findings of the Rietveld refinement analysis.

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K.

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å−1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ–3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long–range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least–squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.

Insights into the structure-property relationship of pharmaceutical co-crystals: Charge density and quantum chemical approaches

A subset of co-crystal systems of the antipyretic and analgesic drug, propyphenazone, are used to probe the nature of the drug···co-former interactions. The experimental electron density distribution, based on very high-resolution single crystal diffraction, has been modelled and an analysis undertaken using Bader's Atoms in Molecules approach. Atomic charges, intermolecular interactions and their energies have been subsequently derived and compared between systems. Complementary theoretical calculations are used to derive interaction energies for intermolecular interactions beyond atom···atom contacts. These permit the deconvolution of the intermolecular interactions into their constituent energy components for a comprehensive analysis. This approach provides an insight into the factors affecting the assembly of the solid state, with the case of pharmaceutical co-crystals being highlighted in this work. Furthermore, this approach enables analysis of the effect of the co-former on various influencing factors that determine the physicochemical properties of these multi-component systems.

In Situ Growth of Bi Nanoparticles on NaBiO3, δ-, and β-Bi2O3Surfaces: Electron Irradiation and Theoretical Insights

Herein, we present a combined experimental and theoretical study of the in situ growth of Bi nanoparticles on NaBiO3, δ-, and β-Bi2O3 surfaces mediated by the electron beam of a high-resolution transmission electron microscope. Density functional theory and quantum theory of atoms in molecule calculations were used to gain a deeper insight into the experimental observations and to provide an atomistic basis for understanding the formation mechanism of Bi NPs on NaBiO3, δ-, and β-Bi2O3 under electron beam irradiation. Analysis of the experimental data and electron density distributions suggests that the formation of Bi NPs can be related to the structural and electronic changes occurring within the octahedral [BiO6] clusters, and to a lesser extent, [NaO6] clusters, which serve as the constituent building blocks of NaBiO3. Our findings indicate that as a function of the number of added electrons, the formation of β-Bi2O3 takes place first followed by the subsequent appearance of metallic Bi NPs generated i...

Charge density and electrostatic potential of hepatitis C anti-viral agent andrographolide: an experimental and theoretical study

Andrographolide (AGH) is a hepatitis C anti-viral agent which targets the host cell by covalently binding with the NF-κBreceptor. The experimental electron density distribution study of AGH has been carried out from high-resolution X-ray diffraction data collected at 110.2 (3) K. The unit-cell packing of AGH was stabilized by strong O—H...O and weak C—H...O types of intermolecular interactions. The dissociation energy of the strong hydrogen bond O2—H22...O1 is very high, 32 kJ mol−1. The percentage occupancy of H...H interactions is found to be maximum (68.5%) when it comparing with the other types of interactions occurring in the AGH crystalline phase. The atomic valance index (V topo) of the C16 atom is low compared with other carbon atoms; this shows that C16 could be the possible reactive location of the AGH molecule. All atoms in the OH groups have very low V topo values; this indicates their role in strong hydrogen bonding interactions. The electrostatic potential (ESP) surface of AGH shows the polarization of the C16=C17 bond and ESP contour map shows several maxima at the vicinity of the C16 atom; these results strongly demonstrate that the C16 atom is the reactive location of the AGH molecule. The molecular covalent docking analysis of AGH with the NF-κB receptor has been performed and confirmed this result. The highly electronegative region around γ-butyrolactone can be helpful for initial alignment of the AGH molecule in NF-κB receptor active site. The atomic volumes of the hydrogen atoms which participate in the H...H interaction are found to be low.

Electronic structure of two isostructural `paddle-wheel' complexes: a comparative study

The experimental electron density distribution in two isostructural and isomorphous complexes, tetrakis(μ2-acetato)diaquadicopper(II) [H2OCu(ac)2Cu(ac)2H2O] (I) and tetrakis(μ2-acetato)diaquadichromium(II), [H2OCr(ac)2Cr(ac)2H2O] (II), has been obtained from high-resolution X-ray diffraction data in order to shed light on the bonding properties in the compounds studied. It has been shown that from accurate X-ray data it is possible to discuss the bonding capability of the metal atom (Cu/Cr) and the ligands in these complexes. A comparison of results obtained from averaged and non-averaged X-ray data demonstrates that using the non-averaged data and introducing an anisotropic correction for secondary extinction errors provides a more detailed distribution of the electron density in the area of the metal atoms. In both complexes studied, the bonding of the acetate oxygen atom to the central metal atom is significantly affected by the formation of hydrogen bonds. The electron density and its Laplacian at the bond critical point of metal–oxygen coordination bonds for those oxygen atoms not involved in the intermolecular hydrogen bonds are approximately 10% larger compared with the case when oxygen atoms take part in hydrogen bonds with the neighboring water molecules. It is shown that metal–oxygen bonds in a quasi-equatorial plane are typical coordination bonds and differ significantly from the apical metal–oxygen bond. Metal–metal interaction with a small positive value of the electron density Laplacian at this bond critical point is mainly of electrostatic character. The metal–metal interaction is definitely not a bond according to the classical definition. Based on a search of the Cambridge Structural Database, it can be argued that there are four typical coordination bonds in the [CuO6] chromophore, similar to the four Cu—O coordination bonds in the basal plane of the CuO5 pyramid in one of the complexes under study.

Experimental Electron Density Distribution in Two Cocrystals of Betaines with p-Hydroxybenzoic Acid

Experimental determination of electron density distribution in crystals by means of high-resolution X-ray diffraction allows, among others, for studying the details of intra- and inter-molecular interactions. In case of co-crystals, this method may help in finding the conditions of creating such species. The results of such analysis for two co-crystals containing betaines, namely trigonelline (TRG: nicotinic acid N-methylbetaine, IUPAC name: 1-methylpyridinium-3-carboxylate) and N-methylpiperidine betaine (MPB: 1-methylpiperidinium-1-yl-carboxylate) with p-hydroxybenzoic acid (HBA) are reported. TRG-HBA crystallizes as a hydrate. For both of the co-crystals, high-quality diffraction data were collected up to sinθ/λ = 1.13 Å−1. Hansen-Coppens multipolar model was then applied for modelling the electron density distribution and Atoms-In-Molecules approach was used for detailed analysis of interactions in crystals. A number of intermolecular interactions was identified, ranging from strong O-H···O hydrogen bonds through C-H···O to C-H···π and π···π interactions. Correlations between the geometrical characteristics of the contacts and the features of their critical points were analyzed in detail. Atomic charges show that in zwitterionic species there are regions of opposite charges, rather than charges that are localized on certain atoms. In case of MPB-HBA, a significant charge transfer between the components of co-crystal (0.5 e) was found, as opposed to TRG-HBA, where all of the components are almost neutral.

Probing Cyclic π-Electron Delocalization in an Imidazol-2-ylidene and a Corresponding Imidazolium Salt.

The extent of cyclic π-electron delocalization in the N-heterocyclic ring of an imidazol-2-ylidene (i.e., 1,3,4,5-tetramethylimidazol-2-ylidene) and its corresponding imidazolium salt (i.e., 1,3,4,5-tetramethylimidazolium chloride) has been investigated theoretically by using Bader's quantum theory of atoms in molecules (QTAIM) descriptors, delocalization indices, electron localizability indicators (ELI-Ds), and the source function tool. In addition, the experimental electron density distribution for the imidazolium salt has been obtained and analyzed from 100 K X-ray diffraction data. A significant drop is found in the ellipticity of the electron density along the Ccarbene -N bond path in the imidazol-2-ylidene. This is shown to be a natural consequence of the σ lone pair of the Ccarbene atom, which overwhelms the π-electron density, rather than a sign of a significantly diminished degree of π-electron delocalization in the imidazol-2-ylidene compared to its imidazolium salt. In fact, the source functions, the ELI-Ds, and the delocalization indices all probe a quite similar extent of cyclic π-electron delocalization in the N-heterocyclic rings of the two compounds.

Understanding electronic and magnetic transitions in ball milled diluted magnetic semiconductor Si1-xNix through experimental electron density distribution

The diluted magnetic semiconductor (DMS) Si1-xNix with four different dopant concentrations x = 0, 0.03, 0.06, 0.09 and 0.12 has been processed using ball milling technique. Powder X – ray diffraction data sets were collected for the samples and the structural and charge density analysis were carried out using Rietveld technique and maximum entropy method (MEM) respectively. The local structure was analyzed using pair distribution function (PDF) analysis. Magnetic measurements taken using vibrating sample magnetometer (VSM) reveal the ferromagnetic nature of the prepared DMS samples. Experimental estimation of charge density using maximum entropy method (MEM) complements semiconductor to metal transition and p – n type transition of Si1-xNix system as a function of concentration of Ni impurity in the system. The utility of Si1-xNix as a DMS material is established from these studies.

Charge density studies of an inorganic-organic hybrid p-phenylenediammonium tetrachlorocuprate

High quality single crystals of an inorganic-organic hybrid, p-phenylenediammonium tetrachlorocuprate (pPDA:CuCl 4 ), suitable for high-resolution X-ray data collection, have been crystallized. pPDA:CuCl 4 crystallizes at special positions in the P21/c space group of the monoclinic crystal system with only halves of the moieties in the asymmetric part of the unit cell. This compound forms a hybrid structure consisting of separate inorganic anion and organic cation layers linked by weak N-H∙∙∙Cl hydrogen bonds. The Cu atoms are located at the centers of symmetry and each of them is surrounded by six chlorine atoms thus forming a tetragonal bipyramid. Two pairs of the chlorine atoms form short Cu-Cl bonds (2.27964(4) and 2.29765(4) A), whereas the third pair forms the longest Cu-Cl bond (2.90452(4) A). Experimental and theoretical electron density distributions have been established. There is an excellent agreement between theoretical and experimental properties at bond critical points. The total charge of the organic cation is equal to +1.64 $$ \overset{-}{\boldsymbol{e}} $$ and is neutralized by the charge of the inorganic anion. The orbital population analysis of the copper 3d electrons and analysis of geometry of the tetrachlorocuprate have been performed and they clearly show presence of the Jahn-Teller effect. Comparison of some experimentally derived parameters such as area and linear density distribution with those calculated on the base of relations derived from literature shows that a longer series of experimental charge density investigations of the hybrid structures should be measured. It should allow for obtaining more reliable relations among different parameters for the hybrid structures with a strong predictive power of such relations. Analysis of residuals of measured intensities of reflections and those resulting from the refined model shows a serious underestimation of esds of measured reflections used in the refinement.

Experimental Observation of the Nature of Weak Chemical Bonds in Labile Compounds.

Accurate single-crystal X-ray diffraction data afford a total electron density distribution for crystalline materials by employing an aspherical atomic model with comparable accuracy to that of theoretical calculations. Chemical bonds and intermolecular interactions in the crystalline state are characterized based on the electron density distribution of valence electrons, as well as structural parameters. Herein, the bonding nature of weak chemical bonds in labile compounds, such as hypervalent bonds and delocalized π-bonds, is explored on the basis of electronic structures derived from experimental electron density distribution analyses. In addition, the visualization of a radicalic orbital distribution on an sp2 -hydridized carbon atom is demonstrated.

Bonding in Uranium(V) Hexafluoride Based on the Experimental Electron Density Distribution Measured at 20 K.

The electron density distribution of [PPh4][UF6] was obtained from high-resolution X-ray diffraction data measured at 20 K. The electron density was modeled with an augmented Hansen-Coppens multipolar formalism. Topological analysis reveals that the U-F bond is of incipient covalent nature. Theoretical calculations add further support to the bonding description gleaned from the experimental model. The impact of the uranium anomalous dispersion terms on the refinement is also discussed.

Maximum Entropy Method Applied in the Experimental Visualization of Electron Density Distributions in BiFeO3

The BiFeO3 is a largely studied compound with magnetoeletric coupling at room temperature. This is due its potential technological applications that can be directly used in advanced technologies. BiFeO3 is an oxide with perovskite structure and R3c space group (rhombohedral symmetry). In this work, synchrotron radiation X-ray powder diffraction data was used to obtain a detailed description of BiFeO3 crystal structure. Thereafter, experimental electron density distribution calculations were obtained using by the maximum entropy method (MEM) statistical approach. The ionic/covalent nature of the bonding and the interaction between the ions are clearly revealed by constructing electron density maps. The Fe3+-O2− and Bi3+-O2− bonding were studied in 1 and 2 dimensional electron density distributions. Due the high resolution of the obtained maps, it can be regarded as the most precise electron density distributions seen inside the material.

Mapping the complete bonding network in KBH4 using the combined power of powder diffraction and maximum entropy method

The combined power of the maximum entropy method (MEM) and synchrotron powder X-ray diffraction (SPXRD) is exerted to accurately reconstruct the electron density distribution (EDD) of the hydrogen storage material, KBH4. Its crystal structure features thermally activated disorder among the BH4- moieties, and weak secondary bonding effects occupy a key role in determining the energetic barrier for this dynamical effect. The MEM reconstruction is meticulously optimised and inspected for errors, in what may be envisaged as a general manual for this kind of studies. The successful outcome constitutes an experimental EDD of cutting-edge quality, from which atomic charges and the complete bonding network are mapped by topological descriptors. Remarkably, the chemical insights even extend to the delicate interplay of closed-shell bonding in excellent correspondence with ab initio and two-channel MEM calculations. For the current class of functional materials, access to such subtle electronic features is essential for the fundamental understanding of hydrogen desorption pathways.