Deformation Density Maps Research Articles

Topological analysis of electron density in depleted homopolar chemical bonds

Except for the case of van der Waals interactions, homopolar bonds are covalent and therefore a concentration of the electron density is expected at the bond midpoint. Many experimental and theoretical studies have reported standard deformation density maps and molecular density minus spherical atoms densities, which show a depletion of electron density between formally covalently bonded atoms. For example, electron deficits are found in the theoretical map of the FF bond in F2, in the experimental map of the NN bond in carbonohydrazide, and in the experimental and theoretical maps of the OO bond in 1,2,7,8-tetraaza-4,5,10,11-tetraoxatricyclo[6.4.1.1]tetradecane. Other partitioning schemes, such as subtraction of valence state atoms rather than spherical atoms from the total density, have been proposed to interpret these unexpected features. In the present work we examine these electronically depleted covalent bonds on the basis of the topological analysis of the electron localization function (ELF) of theoretically calculated electron densities. The attractors of ELF determine basins that are either core or valence basins. The valence basins are characterized by the number of core basins with which they share a common boundary, and this number is called the synaptic order. Disynaptic valence basins have been found for the FF bond in F2, for the NN bond in carbonohydrazide and for the OO bond in 1,2,7,8-tetraaza-4,5,10,11- tetraoxatricyclo[6.4.1.1]tetradecane. In the case of F2, polarization functions increase the V(F, F′) basin population, whereas accounting for the Coulomb correlation lowers this basin population. The results calculated for F2 are compared with those obtained for other diatomic molecules, such as N2 and O2, and the ELF picture of the bond compared with the molecular orbital analysis. In the case of carbonohydrazyde, the V(N, N′) basin population is the lowest among all the populations of the disynaptic valence basins present in the molecule, in good agreement with the experimental observations. Analogous results are obtained for the V(O, O′) basin population in 1,2,7,8-tetraaza-4,5,10,11- tetraoxatricyclo[6.4.1.1]tetradecane. Population fluctuation analysis indicates a strong delocalization of the electron density toward lone pairs and adjacent bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1517–1526, 1999

A charge density study of the effect of irradiation on theα-form ofp-nitrophenol

Careful investigation of the structure and charge density of theα polymorph ofp-nitrophenol has been carried out following prolonged irradiation by visible light. Though the change in colour from yellow to red is remarkable, the molecular geometry and the intermolecular hydrogen contacts exhibit only minor changes. However, a charge density analysis in comparison with the pristineα andβ polymorphs has brought out significant differences in the charge distribution in the intra- and intermolecular bonding regions. The deformation density map of theα form reveals many differences in the bonding regions of the molecule before and after irradiation. Charge migration from the nitro and the hydroxyl groups to the phenyl ring of the molecule occurs on irradiation, resembling more the charge distribution in the light stableβ form. The molecular dipole moment in the irradiated crystal is significantly lower compared to that before irradiation. Relief maps of the negative Laplacian in the hydrogen bond region also show less polarization of the oxygen lone pairs after irradiation.

Structural and Electron Density Studies on a Chromium(IV)‐Oxo Complex [CrIV(O)(TMP)

AbstractThe electron density distribution of a chromium(IV)‐oxo complex, [CrIV(O)(TMP)] (TMP = 5,10,15,20‐tetrakis‐p‐methoxyphenyl porphyrin), is investigated by molecular orbital calculation. The molecular and crystal structure of the compound is studied by x‐ray diffraction. It belongs to the space group 1 2, Z = 2, a = 14.979(4) Å, b = 9.752(3), c = 15.605(3) Å, β = 100.97(2)°, V = 2238(1) Å3, Mo Kα radiation λ = 0.7107 Å, R = 4.9%, Rw = 3.5% for 3575 observed reflections. Cr is five‐coordinated in a square pyramidal fashion with the Cr atom located 0.42 Å toward the oxo‐ligand. Deformation density maps are derived from the single point molecular orbital calculation on the basis of HF and DFT(density functional theory) calculations. The accumulation of deformation density along the C‐H, C‐C, C‐N and C‐O bonds in the porphyrin ligand is well represented. The asphericity in electron density around the Cr ion is clearly demonstrated. Natural bond orbital analysis (NBO) reveals that the Cr‐Ooxo is actually a triple‐bond character (σ2π4) and the four N of pyrrole serves as a σ‐donor to Cr. The Cr‐Npyrrole bond is essentially a dative bond d‐Orbital populations of Cr derived from both calculations are in good agreement with each other. Planar dπ‐orbital is the most populated, which is in accord with the prediction from crystal field theory. Detail bond characterization of the Cr‐L, multiple bond is discussed.

Charge and momentum densities of cubic tetracyanoethylene and its insertion compounds.

Charge and momentum electron densities provide complementary views of cohesive forces in solids. This is particularly true for molecular crystals. The examples of cubic tetracyanoethylene (1,1,2,2-ethenetetracarbonitrile) and its alkali-metal insertion compounds are analyzed from a theoretical point of view. Besides the usual deformation density maps and anisotropy of Compton profiles, it is shown that interaction charge density and interaction Compton profiles can be defined and reveal the subtleties of the intermolecular interactions. It is shown that owing to the large cavities in the crystal, alkali-metal atoms can be inserted, leading to a strong charge transfer to the molecules and to a metallic character; the mechanism of insertion is revealed well by the combination of charge and momentum density studies. The combination of the two techniques of X-ray diffraction and Compton scattering should be of great help in the study of rather weak interactions present in molecular solids.

Experimental Electron Density in a Transition Metal Dimer: Metal−Metal and Metal−Ligand Bonds

The accurate experimental electron density distribution of Co2(CO)6(AsPh3)2 has been determined through X-ray diffraction at T = 123 K. Metal−metal and metal−ligand bonds have been investigated by means of deformation densities and the quantum theory of atoms in molecules. The “expected” lack of charge accumulation in the deformation density map is “contradicted” by the presence of a bond critical point and a bond path line linking the two Cobalt atoms, in agreement with theoretical predictions on similar compounds. A careful analysis of the properties of ρ(r) at the bond critical points and of the Laplacian distribution along the bond paths has allowed the full characterization of all bonds in the title compound and, in particular, to discard the apparently straightforward classification of Co−Co as a closed-shell interaction. The radial shape of the atomic Laplacian makes (covalent or polar) shared interactions similar to donor−acceptor ones when at least one “heavy atom” is concerned. Thus, even if it ...

Charge Density Study of the Polymorphs of p-Nitrophenol

A careful investigation of the structures and charge densities of the β and α polymorphs of p-nitrophenol has been carried out. Although the two forms crystallize in different monoclinic cells, the crystal densities are similar. There are, however, several differences in the intramolecular structural features of the two forms, including the C−C−O bond angles and the N−O distances. The α form exhibits a large number of intermolecular hydrogen contacts. More importantly, a detailed charge density analysis of the two forms has brought out significant differences in the charge distribution in both the intra- and the intermolecular hydrogen bonding regions. Deformation density maps reveal many differences in the bonding regions of the molecule in the two forms. Charge migration from the benzene ring region of the molecule to the nitro and the hydroxyl groups occurs as the structure changes from the β to the α form. Relief maps of the negative Laplacians in the plane of the intermolecular hydrogen bonds show polarization of the oxygen lone-pair electrons toward hydrogen. The molecular dipole moments in the solid state, derived from the pseudoatomic charges in the β and α structures, are considerably larger (∼20 D) than the value in the free molecule.

Electron Density Distribution in LiB3O5 at 293 K

The electron density distribution in lithium triborate LiB3O5 has been studied at room temperature by X-ray diffraction using Ag K \alpha radiation up to 1.02 Å−1 [1439 unique reflections with I > 3\sigma(I)]. Conventional refinements with a free-atom model yield R(F) = 0.0223, wR(F) = 0.0299, S = 1.632. Atom charge refinements show that the lithium should be considered a monovalent ion. Multipolar refinements were undertaken up to fourth order, imposing local non-crystallographic symmetry constraints in order to avoid phase problems leading to meaningless multipole populations due to the non-centrosymmetry of the structure (space group: Pn a21). The residual indices decreased to: R(F) = 0.0147, wR(F) = 0.0193, S = 1.106. The net charges are in good agreement with what can be expected in borate chemistry. Deformation density maps are analysed in terms of \sigma and \pi bonding. The experimental electron distribution in the p z orbitals of triangular B atoms and surrounding O atoms has been analysed by introducing idealized hybridized states. In parallel, the electron density has been determined from ab initio Hartree–Fock calculations on fragments of the structure. Agreement with the X-ray determination is very good and confirms the nature of bonding in the crystal. The amount of transfer of \pi electrons from the oxygen to the triangular B atoms is estimated to be 0.22 electrons by theory.

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.

Quantum‐Chemical Investigations of Stabilizing Interactions in μ‐Diborylcarbene Dicobalt Complexes with a Planar Tetracoordinate Carbon Atom

Quantum-chemical methods have been employed to study the nature of stabilization in dinuclear cobalt complexes of the general formula [{(C5 H5 )Co}2 (μ-CR(1) 2 BCBR(2) R(3) )] (6) as well as the "antivan't Hoff-Le Bel" configuration of the planar tetracoordinate carbon (ptC) atom of the bridging diborylcarbene ligand 9. Extended Hückel and ab initio Hartree-Fock calculations have been carried out for the model compounds 6b (R(1) = R(2) = R(3) = H) and 6c (R(1) = R(2) = H; R(3) = C6 H5 ). Ab initio electron deformation density maps and natural population analysis calculations show that complexes 6 are stabilized through push-pull effects by which the ptC experiences π electron density delocalization and σ electron density accumulation. The calculated electronic configuration of the ptC in the free ligand 9b is σ(2.978) π(1.501) , and in 6b σ(3.944) π(1.356) . Electron density donation from one cobalt atom to an aryl group on the bridging ligand further contributes to the stabilization of the complexes 6.

Charge density studies in NH4[Ti(C2O4)2].2H2O crystals at two wavelengths

The crystal structure of ammonium bis-μ-oxalatotitanate(III) dihydrate, NH4[Ti(C2O4)2].2H2O, is reinvestigated by careful single-crystal X-ray diffraction using Mo Kα (room temperature and 130 K) and Ag Kα radiation (room temperature). It crystallizes in noncentrosymmetric hexagonal space group P6422, with cell parameters a = 8.947 (2), c = 10.898 (1) Å, Z = 3, F(000) = 423, Mr = 278.1, Dx = 1.833, R = 0.035, wR = 0.030 for 2296 observed reflections with I ≥ 2σ(I), on Ag Kα data. Accurate data measurement was applied using two wavelengths (0.7107 Å for Mo Kα and 0.5609 Å for Ag Kα in order to study the charge density distribution and also to investigate the wavelength effect in such investigations. A total of 22650 and 20298 reflections were measured using Mo Kα radiation at room temperature and 130 K, respectively, and 18361 reflections using Ag Kα radiation. The Ti atom is coordinated by four oxalate dianions with coordination number 8 in an approximate symmetry of D 4 geometry. Each oxalato ligand is bridged between two Ti atoms and forms an infinite polymeric spiral column along the c axis. The deformation density maps, Δρ, obtained from all three data sets are consistent and agree well. Although the formal charge of Ti in this complex is 3+, with only one electron on the 3d orbitals expected, the net atomic charge on Ti from this study is, ~2+. Charge asphericity around the Ti atom caused by the splitting of 3d orbitals is clearly observed in the deformation density. The d-orbital populations are evaluated from multipole refinement. The expected d 1 electron is mainly located in the dZ2 orbital.

Theoretical study of the deformation densities of d electrons in K2[PdCl6] and K2[PtCl6] crystals

Aspherical distributions of the d electrons in dipotassium palladium hexachloride, K2[PdCl6], and dipotassium platinum hexachloride, K2[PtCl6], crystals were analyzed by theoretical calculations. Hartree–Fock and configuration interaction calculations were performed for [PdCl6]2− and [PtCl6]2− with and without taking into account the Madelung potentials, using a model potential method. The major relativistic effects were incorporated in the model potentials for Pd and Pt. The deformation-density maps calculated were similar to those given by the X-ray diffraction method. The theoretical result suggested that the positive peaks on the threefold axes and the negative peaks on the metal—Cl bond axis correspond to the excess d electrons (4d of Pd and 5d of Pt) in the t 2g (dxy, dxz, dyz ) orbitals and the electron deficiency in the eg (dz 2,dx 2− y 2) orbitals, respectively. The positive and negative peak heights were calculated to be +1.8 and −0.8 e Å−3 for [PdCl6]2− and +1.2 and −0.6 e Å−3 for [PtCl6]2−. The effective charges and effective radii of Pd and Pt, and the number of electrons in the t 2g , eg and t 1u orbitals, were calculated by direct integration. The effects of the Madelung potential and electron correlation on the charge distributions of [PdCl6]2− and [PtCl6]2− were also analyzed.

Estimation of ionicity coefficients in Li2BeF4 crystals by X-ray diffraction

Ionicity coefficients of the atoms in lithium tetrafluoroberyllate (Li 2 BeF 4 ) crystals have been estimated from accurate X-ray diffraction experiments at 81 K, using two different approaches. One is based on a series of least-squares calculations, in which the deviance Q=Σw(I o -I c ) 2 for model-sensitive low-order reflections is evaluated for different procrystal models; the other is based on partitioning of the deformation density. Ionicity coefficients p (p=1 for neutral; p=0 for ionic) based on Q values are about 0.8, 0.7 and 0.6 for Be, F and Li atoms, respectively. The corresponding net charges based on deformation-density maps (Hirshfeld partitioning scheme) are about +0.16, -0.09 and+0.11 e

Anomeric Effect and Charge Density of Dioxane and Dichlorodioxane

Abstract The low-temperature molecular structure and electron density (ED) distribution of dioxane and trans-2,5-dichloro-l,4-dioxane were determined near 100 K from X-ray data. Deformation electron density maps were calculated by Fourier and multipole expansion techniques. The multipole model charge distribution of dioxane determined from experimental data was taken as a reference state, relative to which the ED of the substituted ring was analyzed. These fragment deformation density maps show quadrupolar deformations on atoms O, CI, and anomeric C only. The highly correlated orientation of the lobes at these atomic sites seems to indicate that the observed charge rearrange-ment is caused by three-center interactions.

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.

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

Low-angle atomic scattering factors and charge density of aluminum

All the published experimental and theoretical atomic scattering (form) factors for aluminum have been carefully reviewed and only the low angle 111, 200 and 220 crystal form factors appear to be significantly different from the best free atom values. The best powder X-ray diffraction and high accuracy 111 and 200 electron diffraction form factors for Al are in good agreement with each other and with the best theoretical calculations. The equivalent scattering factors measured by X-ray Pendellösung methods seem somewhat high and are not a good representation of the charge density of aluminum. A (110) deformation charge density map based on the best experimental form factors indicates that bonding in aluminum is achieved by the spherical depletion of electrons from atomic sites and redistribution so that there is a build-up between nearest-neighbor (n.n.), second n.n. atoms, etc; this, of course, is the traditional plcture of a metallic bond. A comparison of the aluminum (110) deformation density map with the equivalent map for copper shows that the bonding schemes for the two elements follow an almost identical pattern. This indicates that even though copper and aluminum have large differences in atomic number and valency, their bonding schemes are primarily determined by the face-centered-cubic crystal structure.

Correction of X-ray Intensities for Multiple Diffraction: Effects on Atomic Parameters and Charge Density

The standard theory for secondary extinction based on intensity transfer equations has been extended to three-beam diffraction for a finite crystal in the Laue case. The expression for the primary diffracted intensity was used to first order to calculate correction factors for the two-beam integrated power assuming a type I mosaic crystal. The corrections were employed to study the effects of multiple diffraction on structure parameters and deformation density for three different crystals with unit-cell volumes in the range 385-1410 A3. In these data sets, 5-8% of all reflections with (sinO/A) :S 0 -7 A-I had relative shifts in integrated power tl'P/'P> 10%. The weak intensities are affected the most, and thus, among the weakest third of the data, 15-21% had relative corrections >10%. The crystallographic Rand goodness-of-fit factors were significantly improved after correction of the data for multiple diffraction. Atomic positional and displacement parameters, obtained from the refinements on corrected and uncorrected data respectively, have been compared, as have also pairs of deformation density maps. Rather unexpectedly, all shifts were very small, within 20" for atomic parameters and within 2�50" for the deformation densities. This implies that the effects of multiple diffraction are nearly random relative to the structure model and even relative to the deformation density.

Theoretical study of the electron density in iron(II) porphyrin bis(water)

Ab initio SCF and Ci calculations are reported for four different electronic configurations of the high-spin six-coordinate iron (II) porphyrin bis)water) molecule considered as a model for iron (II) tetraphenylporphyrin bis(tetrahydrofuran). The 5 B 2g and 5 E g states are the lowest ones in energy and turn out to be nearly degenerate at both levels of theory. The ground-state configuration of iron (II) tetraphenylporphyrin bis(tetrahydrofuran) is assigned as 5 E g on the basis of a comparison between the theoretical electron deformation density maps and the experimental ones

ChemInform Abstract: Electronic Structure of Cobalt Phthalocyanine: A Charge Density Study.

A charge density study of cobalt(II) phthalocyanine based upon 12,163 unique reflections within a (sin /theta/)//lambda/ range 0-10.8 nm/sup /minus/1/, collected by X-ray diffraction at 115 K, was performed. The data was modeled by a conventional multipole analysis as well as by a valence orbital population analysis. When the latter approach was used and data was employed to a (sin /theta/)//lambda/ limit of 8.2 nm/sup /minus/1/, a value of 0.031 was obtained for R/sub w/(I) and 0.015 for R(F). The deformation density maps show bond-centered peaks and lone-pair peaks of ca. 500 e nm/sup /minus/3/ within the phthalocyanine ligand molecule, such as are typical of most good light-atom charge density studies. The rearrangement of the electron density around the cobalt atom is substantial, both in angular function and in radial extent, and suggests a depletion and contraction of the 3d orbitals, combined with a population of more diffuse cobalt-based functions. The valence orbital population analysis quantifies the suggestion, giving a total 3d population of 4.9 (1)e with a radius reduced 35% from the free ion value and a diffuse population (modeled as 4p) of 2.6 (1)e. Those populations are strongly anisotropic: 3d/sub x/sup 2/-y/sup 2///sup 0.0/3d/sub xz,yz//sup 2.4/3d/sub z/sup 2///supmore » 0.8/3d/sub xy//sup 1.8/4p/sub z//sup 1.1/4p/sub xy//sup 1.4/. There seems to be little charge flow from the ligand to the metal atom (0.5 (1)e), but the bonding is obviously quite covalent in character. This is manifest in the distribution of charge between the 3d /pi/ and /sigma/ systems and the diffuse outer regions of the cobalt atom.« less