Electron Density Distribution In Crystals Research Articles

放射光X線単結晶X線回折による価電子密度分布解析

The valence electron density distribution in crystals can be observed with high accuracy by precise electron density analysis using the core differential Fourier synthesis （CDFS） method with high-intensity and high-resolution single crystal X-ray diffraction data obtained at a large synchrotron radiation facility; SPring-8. By observing the spatial distribution of electron density proportional to the square of the wave function, the quantum parameters of the orbital states of can be directly determined. Using this method, not only orbital ordered states and bonding electrons but also degenerate orbital states can be directly observed, which may lead to a new method for structural properties research beyond the conventional structural analysis.

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.

Jahn–Teller Lattice Distortions and Asymmetric Electron Density Distribution in the Structure of TmB12 Dodecaboride in the Temperature Range of 85–293 K

The structure of single-crystal dodecaboride TmB12, which possess metallic properties, has been studied by X-ray diffraction at nine temperatures in the range of 85–293 K. Jahn–Teller distortions of the cubic lattice are revealed. They are found to cause an asymmetric electron density distribution in crystal. Static components of atomic displacements are selected, and characteristic Einstein and Debye temperatures are determined for thulium and boron atoms, respectively. Temperature dependences of interatomic distances are obtained. The problem of localizing conduction electrons by means of X-ray diffraction analysis is stated.

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.

Exploring charge density analysis in crystals at high pressure: data collection, data analysis and advanced modelling.

The possibility to determine electron-density distribution in crystals has been an enormous breakthrough, stimulated by a favourable combination of equipment for X-ray and neutron diffraction at low temperature, by the development of simplified, though accurate, electron-density models refined from the experimental data and by the progress in charge density analysis often in combination with theoretical work. Many years after the first successful charge density determination and analysis, scientists face new challenges, for example: (i) determination of the finer details of the electron-density distribution in the atomic cores, (ii) simultaneous refinement of electron charge and spin density or (iii) measuring crystals under perturbation. In this context, the possibility of obtaining experimental charge density at high pressure has recently been demonstrated [Casati et al. (2016). Nat. Commun. 7, 10901]. This paper reports on the necessities and pitfalls of this new challenge, focusing on the species syn-1,6:8,13-biscarbonyl[14]annulene. The experimental requirements, the expected data quality and data corrections are discussed in detail, including warnings about possible shortcomings. At the same time, new modelling techniques are proposed, which could enable specific information to be extracted, from the limited and less accurate observations, like the degree of localization of double bonds, which is fundamental to the scientific case under examination.

Image definition evaluation functions for X-ray crystallography: a new perspective on the phase problem.

The core theme of X-ray crystallography is reconstructing the electron-density distribution of crystals under the constraints of observed diffraction data. Nevertheless, reconstruction of the electron-density distribution by straightforward Fourier synthesis is usually hindered due to the well known phase problem and the finite resolution of diffraction data. In analogy with optical imaging systems, the reconstructed electron-density map may be regarded as the image of the real electron-density distribution in crystals. Inspired by image definition evaluation functions applied in the auto-focusing process, two evaluation functions are proposed for the reconstructed electron-density images. One of them is based on the atomicity of the electron-density distribution and properties of Fourier synthesis. Tests were performed on synthetic data of known structures, and it was found that this evaluation function can distinguish the correctly reconstructed electron-density image from wrong ones when diffraction data of atomic resolution are available. An algorithm was established based on this evaluation function and applied in reconstructing the electron-density image from the synthetic data of known structures. The other evaluation function, which is based on the positivity of electron density and constrained power spectrum entropy maximization, was designed for cases where only diffraction data of rather limited resolution are available. Tests on the synthetic data indicate that this evaluation function may identify the correct phase set even for a data set with resolution as low as 3.5 Å. Though no algorithm for structure solution has been figured out based on the latter function, the results presented here provide a new perspective on the phase problem.

Experimental study of electron density distribution in crystals of antimony(V) dicarboxylate complexes

The molecular structure and charge density distribution in the crystals of triphenylantimony bis[(2E)-3-phenylprop-2-enoate] [Ph3Sb(O2CCH=CHPh)2] and triphenylantimony bis[(2E)-3-(3-nitrophenyl)prop-2-enoate] benzene solvate [Ph3Sb(O2CCH=CHC6H4NO2-m)2·C6H6] derived from the high-resolution single-crystal X-ray diffraction data at 100 K are reported together with DFT calculations of these molecules. The nature of the chemical bonds and delocalization of electron density in carboxylate ligands was investigated. The intramolecular Sb···O interactions as well as intermolecular π···π, H···π and O···π ones and their energy are discussed.

Investigation of topology of intermolecular interactions in the benzene–acetylene co-crystal by different theoretical methods

Crystal structure of benzene–acetylene co-crystal was analysed based on calculated energies of intermolecular interactions between basic molecules located in asymmetric part of unit cell and their neighbours belonging to their first coordination sphere. It is demonstrated that the basic structural motif of the crystal is represented by infinite chains formed by the hydrogen-bonded benzene and acetylene molecules. Energy of interaction of the basic pair of molecules to neighbours within the chain is 2.2 times higher than the energy of interactions with molecules of any neighbouring chain. This ratio almost does not depend on method of calculation of interaction energy. Also, results of calculations were compared with analysis of topology of electron density distribution in crystal. The possibility to find the basic structural motif of the crystal based on properties of intermolecular bond critical points is demonstrated.

Weak interactions in chain polymers [M(μ-X)2 L 2]∞ (M = Zn, Cd; X = Cl, Br; L = substituted pyridine) – an electron density study

The experimental electron-density distributions in crystals of five chain polymers [M(mu-X)2(py)2] (M = Zn, Cd; X = Cl, Br; py = 3,5-substituted pyridine) have been obtained from high-resolution X-ray diffraction data sets (sin theta/lambda > 1.1 A(-1)) at 100 K. Topological analyses following Bader's 'Atoms in Molecules' approach not only confirmed the existence of (3, -1) critical points for the chemically reasonable and presumably strong covalent and coordinative bonds, but also for four different secondary interactions which are expected to play a role in stabilizing the polymeric structures which are unusual for Zn as the metal center. These weaker contacts comprise intra- and inter-strand C-H...X-M hydrogen bonds on the one hand and C-X...X-C interhalogen contacts on the other hand. According to the experimental electron-density studies, the non-classical hydrogen bonds are associated with higher electron density in the (3, -1) critical points than the halogen bonds and hence are the dominant interactions both with respect to intra- and inter-chain contacts.

The synthesis, structure, and electron density distribution in crystals of 4,5-dihydroxyimidazolidine-2-thiones

1,3-H2-, 1,3-Me2-, and 1,3-Et2-4,5-Dihydroxyimidazolidine-2-thiones were synthesized and their structural peculiarities were studied. A comparative analysis of dihydroxyimidazolidine-2-thione and its carbonyl analog performed in the framework of detailed investigation of the electron density distribution in the corresponding crystals revealed the reason for different number and geometric parameters of the hydrogen bonds formed by the (thio)carbonyl groups in the crystals.

Continua of Interactions between Pairs of Atoms in Molecular Crystals

The electron density distributions in crystals of five previously studied DMAN complexes and five Schiff bases (two new ones) have been analysed in terms of various properties of bond critical points (BCPs) found in the pair-wise interactions in their lattices. We analysed the continua of interactions including covalent/ionic bonds as well as hydrogen bonds and all other types of weak interactions for all pairs of interacting atoms. The charge density at BCPs and local kinetic and potential energy densities vary exponentially with internuclear distance (or other measures of separation). The parameters of the dependences appear to be characteristics of particular pairs of atom types. The Laplacian and the total (sum of kinetic and potential) energy density at BCPs show similar behaviour with the dependence being of the Morse type. The components lambda1, lambda2, lambda3 of the Laplacian at BCPs vary systematically with internuclear distance according to the type of atom pair. For lambda1 and lambda2 the distribution is of the exponential type, whereas lambda3 does not seem to follow any simple functional form, consistent with previous theoretical findings. Analytical nonlinear dependences of Laplacian on charge density have been found. They agree reasonably well with those obtained by least square fit of the Laplacian to charge density data. There are four distinct regions of the [symbol: see text]2rho(BCP)/rho(BCP) space, generated by E(BCP) = 0 and G(BCP)/rho(BCP) = 1 conditions. Two regions clearly correspond to the shared-shell and closed-shell interactions and the other two to some intermediate situation.

Electron density distribution in crystals with potassium perchlorate structure

Within the theory of local electron density functional, the difference densities in crystals of perchlorates, perbromates, and sulfates of metals with potassium perchlorate structure are calculated by the sublattice method. It is shown that the difference-density distribution qualitatively coincides with the experimental deformation-density distribution. Oxygen atoms in nonequivalent crystallographic positions exhibit a different character of electron charge redistribution, which results in their different charge states and different forces of chemical bonding in molecular anions. The mechanisms of charge redistribution in sulfates differ qualitatively from those for perchlorates.

Synchrotron X-ray and molecular dynamics studies of CaYAlO 4: the role of heterovalent solutes in K 2NiF 4-type solid solutions

Three-dimensional diffraction data collected from a small single crystal about 10 μm in size, using synchrotron radiation, were found to be scarcely affected by secondary extinction and provide important information on the structural chemistry of solid solutions as well as the electron density distribution in crystals. A detailed examination of the crystal structure of K 2NiF 4-type CaYAlO 4 coupled with molecular dynamics calculations revealed a wrinkling of the rock-salt-type monolayer caused by the difference in valency between the Ca and Y cations, and by the oxygen vacancies concentrated at the apical O2 sites.

4f-Electron Density Distribution in Crystals of CeB6 at 165 K and its Analysis Based on the Crystal Field Theory

4f-Electron density in single crystals of CeB6, cerium hexaboride, was measured at 165 K by X-ray diffractometry. Significant peaks 2.0 e Å−3 high were found along the \langle100\rangle directions at 0.41 Å from Ce on the deformation density map. Analysis based on the crystal field theory removed the peaks, confirming that they were due to the Ce 4f-electrons on the t 1u -orbital. The deformation density in the B6 octahedron was also markedly improved by the analysis and coincides qualitatively with a theoretical molecular orbital (MO) calculation. It also coincides with the model deformation density map of CaB6 composed of only light atoms. These facts guarantee the accuracy of the intensity measurement for the present study. Since Ce3+ has only one 4f-electron, a highly accurate intensity measurement is necessary to detect its 4f-electron density distribution. A ψ-scan technique was therefore employed to avoid multiple diffraction (MD) and to measure the intensities at ω and χ angles with minimum fluctuation of temperature at the sample position. Relativistic radial functions for orbitals of Ce3+ and the corresponding scattering factors, which take the aspherical electron density distribution of 4f-electrons into account, were used for the analysis. CeB6 is a typical dense Kondo material. The Kondo effect occurs in CeB6 from low temperature to above room temperature. X-ray analysis of the f-electron density based on atomic orbitals (AO) revealed that 1.5 (2) electrons are donated from B6 to Ce and a total of 2.5 (2) electrons localize on the 4f-orbital. κ values are consistent with the 4f-orbitals being highly contracted and thus stabilized. These may be related to the Kondo effect.

Electron density distribution in crystal of polyfluorinated tetraazapentalene based on X-ray diffraction data at 130 K

The electron density distribution in crystal of a new heterocyclic compound, 3,6-(l-H-hexafluoroisopropyl)-2,5-trifiuoromethyl-1,6a,3a,4-tetraazapentalene, has been determined by precision X-ray structural analysis at 130 K. The character and features of the electron distribution in the 10π electron system of the heterocycle have been established using the multipole expansion of the electron density. The charges on the C and N atoms of the heterocycle have been estimated based on X-ray diffraction data.

Distribution of electron densities in crystals studied by channeling radiation spectroscopy

The possibilities for investigating electron density distributions in crystals by measuring the line positions in the radiation spectrum of channeling particles are considered. It is shown that for diamond single crystal channeling radiation spectroscopy provides additional information compared to the X-ray diffraction method. A feature of the potential behavior has been found, which is not described in terms of the known potential models.

Electron density distribution in crystals of sodium nitrite at 120 K

Electron density distribution in crystals of sodium nitrite at 120 K

Electron-density distribution in crystals of K2[MCl6] (M = Re, Os, Pt) and K2[PtCl4] at 120 K

K 2 [ReCl 6 ] (I), a 120 K, cristallise dans Fm3m, avec a=9,7958 A, Z=4; affinement jusqu'a R=0,0219. K 2 [OsCl 6 ] (II), a 120 K, cristallise dans Fm3m, avec a=9,7195 A, Z=4; affinement jusqu'a R=0,0194. K 2 [PtCl 6 ] (IIIa, b) cristallise dans Fm3m, avec (IIIa) a=9,6911 A, Z=4; affinement jusqu'a R=0,0159; (IIIb) a=9,6862 A, Z=4; affinement jusqu'a R=0,0113. K 2 [PtCl 4 ] (IVa, b) cristallise dans P4/mmm, Z=1 avec (IVa) a=6,9961, c=4,1051 A; affinement jusqu'a R=0,0194; (IVb) a=6,9813, c=4,1048 A; affinement jusqu'a R=0,0147. Discussion de la deformation de la sphericite de charge due aux electrons 5d

Electron-density distribution in crystals of 4-chloroaniline, 4-chlorobenzoic acid and 1-chloro-2,4-dinitrobenzene at 110 K

C 6 H 6 ClN cristallise dans Pnma avec affinement jusqu'a 0,026. C 7 H 5 ClO 2 cristallise dans P1 avec affinement jusqu'a 0,027. C 6 H 3 ClN 2 O 4 cristallise dans Pccn avec affinement jusqu'a 0,034

Electron density studies of porphyrins and phthalocyanines. IV. Electron density distribution in crystals of (meso-tetraphenylporphinato) iron(II)

The electron density distribution in crystals of (meso-tetraphenylporphinato)iron(II) has been analyzed using accurate x-ray diffraction data collected at 120 K. The structural results are in agreement with those of the room temperature study. Theoretical calculations predict several different ground states for the complex and in particular support the 3A2g and the 3EgA states. The experimental electron density distribution shows large peaks above and below the iron atom which would not be present for a 3EgA ground state. Comparison with Mössbauer quadrupole splittings and the result of the aspherical atom refinement indicate that the axial peaks may be systematically too high in this acentric crystal structure. Nevertheless, it is concluded that their presence indicates a relatively small contribution of the 3EgA state to the ground state of the complex. This implies that the ground state of FeTPP is different from that of iron(II)phthalocyanine in the crystal. A significant population of electrons is found in the dx2−y2 orbital which is mainly attributed to σ donation of electrons from the porphyrin ligand.