Experimental Deformation Density Research Articles

Electronic Origin of the Structural Anomalies of Zinc and Cadmium

AbstractThe electron distributions in position and in momentum space of the hcp metals magnesium and zinc are investigated experimentally and compared to results of quantum‐chemical calculations. Furthermore, a survey is given on recent analyses of the bonding properties of zinc and cadmium, using the method of increments. The experimental deformation densities were obtained by refining multipole models to X‐ray diffraction data sets measured at 100 K with either Mo‐Kα (Mg) or Ag‐Kα (Zn) radiation. The final RF values (Valray/Jana2006) are 0.0028/0.0034 (Mg) and 0.0068/0.0068 (Zn). The differences to deformation densities obtained from periodic density functional calculations are discussed. The effect of dynamical electron correlation on the electron density was analyzed, using cluster models. Compton profiles were measured with 88.67 keV synchrotron radiation at beamline ID15B at the ESRF in Grenoble. Varied orientations of the samples allowed for probing the projected momentum distribution along the [100], [423] and [001] directions. Fourier transforms of the computed reciprocal form factor B(r) resulted in the corresponding theoretical Compton profiles. It is suggested that the anomalous hcp structure of zinc is favored by a kinetic balancing of the valence electrons, i.e. correlation mediated 4s‐3d interactions.

Role of sublattices in the formation of electron density in metal nitrites

The self-consistent valence electron densities of NaNO2, AgNO2, and their constituent sublattices are calculated on the basis of the theory of the local-density functional. The quantity characterizing the relation between different sublattices is introduced as the difference density resulting from the subtraction of the densities of the individual sublattices from the total electron density. The role of metal in the formation of electron density is established, and, in particular, it is shown that, in AgNO2, anionic bonds have the covalent component formed at the expense of the electron density of the cation. It is also shown that, qualitatively, the difference density in NaNO2 corresponds to the experimental deformation density.

Experimental and theoretical charge density of DL-alanyl-methionine.

X-ray diffraction data up to d = 0.50 A resolution have been collected at 100 K for a DL-alanyl-methionine single crystal using a CCD area detector. Multipolar crystallographic refinement was carried out and the electron density of the molecule has been analyzed. The deformation electron density around the S atom reveals two lone pairs with an sp(3) hybridization and agrees with the results of density functional theory calculations. The topological properties of the covalent bonds and of the hydrogen bonds have been investigated. Two weak polar intramolecular interactions of the type C(5) (pentagonal cyclic structure) have unfavorable geometrical parameters for hydrogen bonds and are devoid of critical points. The two electron lone pairs of the carbonyl oxygen appear asymmetric in the experimental deformation density. This could be attributed to the different strength of the hydrogen bond and intramolecular polar interaction involving the carbonyl oxygen. In the ab-initio-derived deformation maps, the asymmetry of the electron doublets is reproduced only very partially.

Charge-density distribution of heptasulfur imide (S7NH)

Heptasulfur imide, S7NH, was studied by X-ray diffraction at both 100 and 300 K: space group Pnma, Z= 4, Mr= 239, a= 7.842(2), b= 13.115(2), c= 7.6219(7)Å, at 100 K; R= 0.028 and 0.029 for 2517 and 994 reflections at 100 and 300 K respectively. The crown shape of the compound is similar to that of cyclooctasulfur, with one sulfur atom replaced by an NH group. The experimental deformation density distribution reveals a large positive accumulation between the sulfur and nitrogen atoms; small accumulations were found between the sulfur atoms. A multipole refinement shows much clearer features in the bonding and lone-pair electron regions. The results of theoretical calculations by the extended-Hückel molecular orbital, AM1 and ab initio methods are compared with experimental results. There is evidence of bent S–N bonds with endocyclic maxima in the deformation density distribution. The electrondensity distribution may be affected by the packing of molecules in the solid so that it differs from that of the isolated molecule. The net atomic charges from the multipole refinement indicate that N is negative, H is positive and S are neutral. However, those obtained from the ab initio method show a positive charge on the sulfur atom attached to the NH group.

Electron-density distribution of 4-hydroxy-1,2-benzisothiazol-3(2H)-one 1,1-dioxide sodium salt (UH-AF 50 NA)

Na + .C7H4NO4 S .H20, Mr : 239.2, orthorhombic, Pnam, a = 10.844 (4), h = 12-038 (4), c = 6903 (3) A,, V: 901.1 (9) A, 3, A(Mo Ka) = 071069 A,, Z = 4, Dx -- 1762 Mg m-3, /z : 0.389 mm- i, F(000) = 488, T = 123 K. Two data sets were used in refinements: one low-order data set (sin0/A 0.9 ,~ t): R(F 2) = 0.058, wR(F 2) = 0.064. Experimental electron deformation density maps are calculated by difference Fourier synthesis. They are compared with theoretical 6-31G* deformation density maps of the isothiazoione ring fragment of the title compound. Theoretical and experimental deformation density maps show the influence of the Na -~ cation on the lone-pair density of the carbonyl oxygen atom.

Electron Density Distributions in Molecules

Abstract The electron density that is observed by X-ray diffraction differs from the theoretical static density defined via the Born Oppenheimer approximation because of intermolecular interactions in the crystal and vibrational smearing. Also, the experimental deformation density as mapped by difference Fourier synthesis is often biased by the promolecule model used in the derivation of the nuclear parameters. Better models account for the deformation density in parametric form. With the convolution approximation for vibrational smearing, such models permit the mapping of a static deformation density, provided good high-resolution data are used. Results are usually more accurate in a centrosymmetric space group but the center of inversion itself is assumed without direct experimental evidence. The standard deformation density, relative to spherical ground-state atoms, may be decomposed into components corresponding to hypothetical stages in molecule formation, e.g. atomic orientation and hybridization or formation of submolecular fragments. Derivation of the molecular Coulomb potential requires partitioning the crystal density into molecules. Division into atoms is also arbitrary; model densities built of neutral atoms or of ions are nearly indistinguishable, especially in a small unit cell. H2 is a poor prototype of covalent bonding; in other molecules the exclusion principle works against charge accumulation on the bond axis.

Comparison between Theoretical and Experimental Deformation Density of 1,3,5,7-Tetra-t-Butyl-S-Indacene

1,3,5,7-Tetra-t-butyl-s-indacene is a twelve-membered fused-ring compound; the stabilization of the compound by bulky t-butyl groups is discussed. The distribution of bonding electron density is depicted in terms of deformation density using the experimental X-X method, a multipole expansion model and a calculation according to the extended Hückel molecular orbital method (EHMO). The molecules crystallize according to the space group P21/n with cell parameters a = 9.700(3), b = 11.746(3), c = 10.858(2)Å, β = 107.67(2)°, Z=2 at 100K. The molecule has a center of inversion( ) and belongs to the symmetry point group Ci. The packing of two unique t-butyl groups in the asymmetric unit appears significantly different. However, the map of deformation density in the plane of the ring shows pseudo D2h symmetry. The accumulation of density at the midpoint of the bonds is observed as expected. The theoretical deformation densities agree with the experimental ones. Analyses of the molecular-orbital wavefunctions provide a good illustration of the aromatic π-electron system. A theoretical study of a series of substituents (-H, - CH3, -t-butyl ) on s-indacene illustrates the stabilization effect of the t-butyl group on the 12-π-electron ring system.

ChemInform Abstract: Charge Density Study of Thiourea S,S,Dioxide

Deformation density studies of thiourea dioxide, both by direct inspection of an experimental deformation density map and by construction of it according to a multipole model, lead to a better understanding of the atomic net charge distribution of the molecule. The need of up to octapole terms for building up the density in the bonds is confirmed

Charge density study of thiourea S,S-dioxide

Deformation density studies of thiourea dioxide, both by direct inspection of an experimental deformation density map and by construction of it according to a multipole model, lead to a better understanding of the atomic net charge distribution of the molecule. The need of up to octapole terms for building up the density in the bonds is confirmed

Static deformation densities for cytosine and adenine.

X-ray diffraction intensities for cytosine monohydrate have been measured at 97 K, to 2sin theta/lambda = 2.74 A-1, and used in a deformation refinement. Crystal data for cytosine monohydrate at 97 K: a = 7.728 (1), b = 9.817 (3), c = 7.520 (1), beta = 100.50 degrees, V = 560.94 A3, R = 0.0341 for 6456 unique reflections. The experimental static deformation density of cytosine compares very well with the corresponding theoretical 4-31G deformation density. Differences between theory and experiment occur at hydrogen-bonding sites. They are very similar to the corresponding differences between the theoretical deformation densities of formic acid monomer and cyclic dimer. The experimental static deformation density of 9-methyladenine was obtained in a deformation refinement against the low-temperature X-ray data of Craven & Benci [Acta Cryst. (1981), B37, 1584-1591]. It is similar to the maps presented by these authors. The comparison of the experimental deformation density of 9-methyladenine with the theoretical 4-31G deformation density of adenine shows qualitative agreement, which is improved when the 4-31G results are corrected for the absence of polarization functions in the basis set. Some of the remaining differences reflect the effects of substituting CH3 for H. The weak N...H hydrogen bonds have little influence on the deformation density in this structure.

Basis-set dependence of theoretical deformation density in NO2 −

Electron-density distribution of a nitrite ion was calculated by the ab initio molecular-orbital method using STO-3G, STO-6G, MIDI4 and MIDI4* basis sets. The N-O bonding peak, which was observed in the experimental deformation density of LiNO2.H20, could be reproduced only by using the MIDI4* basis set. This indicates the importance of polarization functions in the study of charge distribution.

Accurate electron densities in molecules

Detailed agreement may reasonably be expected between the experimental deformation density of a light-atom molecule derived from accurately measured high-resolution X-ray intensities via an explicit deformation (multipole) refinement model and ab initio map calculated with an extended basis. Several published studies illustrate the quality of agreement obtained when all these criteria are well satisfied. Two difficulties remain: how to interpret the deformation densities chemically and how to partition the observed density in a crystal so as to derive molecular properties.

Comparison of Theoretical and Experimental Deformation Densities in SO Bonds

Marked similarities are found between the experimental electron‐density maps for sodium thiosulfate, Na2S2O3, and the theoretical maps for amidosulfuric acid, NH2SO3H. Quantum chemical calculations and determinations of the deformation density in the region of the SO bond and the lone pair on oxygen are reported.

Project on comparison of structural parameters and electron density maps of oxalic acid dihydrate

Results obtained from four X-ray and five neutron data sets collected under a project sponsored by the Commission on Charge, Spin and Momentum Densities are analyzed by comparison of thermal parameters, positional parameters and X - N electron density maps. Three sets of theoretical calculations are also included in the comparison. Though several chemically significant features are reproduced in all the experimental density maps, differences in detail occur which caution against overinterpretation of the maps. Large differences between vibrational tensor elements Uij are observed which can often not be corrected by the scaling of all temperature parameters in a set. Positional parameters are reproducible to precisions of 0.001 Å or better. The biggest discrepancies between theoretical and experimental deformation density maps occurs in the lone-pair regions where peaks are higher in the theoretical maps. However, this comparison may be affected by inadequacies in the thermal-motion formalism which must be invoked before experimental and theoretical maps can be compared in a quantitative way.

The electron density of α-oxalic acid dihydrate at 100 K by X-ray diffraction: a contribution to the IUCr Commission on Charge, Spin and Momentum Densities project on the accurate determination of electron densities

The results of the determination of the electron density of u-oxalic acid dihydrate at 100 K by means of X-ray diffraction are reported as part of the project on the accurate determination of electron densities which was initiated by the International Union of Crystallography. An extensive data set, consisting of all reflexions in the whole reciprocal sphere up to sin 0/2 =1.3 ,/~-l, was measured. Most of the structural parameters and experimental deformation densities compare well with the findings of an earlier published study [Stevens & Coppens (1980). Acta Cryst. B36, 1864-1876]; thermal parameters, however, differ significantly. Application of a correction for thermal diffuse scattering increased the vibrational parameters by 12%. The polarization of the water O lone-pair density, found by Stevens & Coppens (1980), is firmly confirmed by this study.

Strukturverfeinerung von Harnstoff mit Neutronenbeugungsdaten bei 60, 123 und 293 K und X–N- und X–X(1s2)-Synthesen bei etwa 100 K

Abstract Neutron diffraction data were collected on urea at 60, 123 and 293 K, and the nuclear parameters were determined [R (F) = 0.034,0.033 and 0.043 respectively]. The parameters at 293 K are compared with the neutron parameters of Pryor and Sanger by means of half normal plots and χ 2 tests, and the low-temperature parameters with the 1s2-core parameters which were determined by Mullen and Hellner with X-ray data. Significant differences of 0.0030 Å, on average, were found between the U 33 components from our low-temperature determination and from the 1s2-core refinement. X – N and X – X(1s2) maps are calculated for about 100 K with two different scale factors and, after an assessment of all parameters, a “best” experimental deformation density is calculated. The effect of large librations of the N atom about the C–O axis (4.2rms degrees) on the density distribution, and the effect of using not fully correct phases are discussed. The errors in the density distribution which are caused by errors in the X-ray data, in the scale factor and in the neutron parameters, are assessed to be 0.07 eÅ−3 at the bond peaks, and 0.45 eÅ−3 at the nuclear positions. The ‘best” experimental deformation density has higher bond peaks (except for the C–O bond) than a (published) theoretical difference density (4-31G basis), but lower peaks in the lone-pair regions of the oxygen atom and no polarization minimum at the oxygen atom.

Electron density and bonding in B 13C 2

A single crystal of well-established composition B 13C 2 was used for a new and thorough structural analysis by X-ray diffraction. Unbiased atomic parameters refined from high-order data ( R = 0.0256) were used for ( X- X) difference Fourier syntheses representing dynamic deformation densities. Further studies of the electron density distribution were carried out by a multipole refinement using all reflections ( R = 0.0278). The resulting atomic multipole coefficients were utilized for the evaluation of static electron deformation densities. The analysis of both experimental deformation density distributions corroborates the main features of the bonding in B 13C 2 deduced from earlier calculations on the isolated B 12 icosahedron by LonguetHiggins and Roberts using the linear combination of atomic orbitals.

Accurate structure determination of trans-2,5-dimethyl-3-hexene-2,5-diol hemihydrate, C8H16O2.0.5H2O, at 86 K. II. Discussion of the electron density distribution

Experimental deformation densities for the title compound are compared with a smeared theoretical deformation density based on ab initio quantumchemical calculations for a model compound (9,5,1/5,2 GTO basis set). Around the C-C bonds in the ethylene plane very good agreement with theory is obtained for the experimental D(HO,r) map. This map is based on high-order parameters of a conventional X-ray refinement, but witli scale and overall thermal motion adjusted to full-angle data. Around the O atoms where D(HO,r) is not reliable, the theoretical map is compared with a multipole map not including monopole deformations and based on a multipole refinement with scattering factors. The multipole map clearly shows the influence of the hydrogen bonds on the deformation density.

Experimental electron density distribution of molecular chlorine

The electron density distribution of solid chlorine is determined from high resolution X-ray diffraction intensity measurements at 90 K. Deformation densities are calculated from the observed X-ray data and parameters obtained from a high order refinement of data with sin ϑ/λ > 0·65 A-1. Refinements including the population of multipole density functions are used to calculate model deformation densities and the asymmetry of the electric field gradient. Inclusion of third and fourth cumulant thermal parameters results in a significant improvement in the fit to the experimental data. The deformation density reveals a torus of non-bonding density at 0·31–0·37 e/A3 encircling the Cl-Cl bond somewhat in the back of each of the Cl atoms. A double peak of 0·22 e/A3 is found in the bonding region of the experimental deformation density similar to the bonding density found in S8. This feature is not properly reproduced in density maps based on the atom-centred multipole functions. The calculated distribution of er...