Multipole Refinement Research Articles

Experimental and theoretical charge distribution in (Z)-N-methyl-C-phenylnitrone.

The total experimental charge density in (Z)-N-methyl-C-phenylnitrone (1) has been determined using high-resolution X-ray diffraction data in combination with neutron diffraction data measured at 100 K in terms of the rigid pseudoatom model. Multipole refinement converged at R = 0.03 for 7163 reflections with I > 2 sigma(I). Topological analysis of the total experimental charge density rho(r) and its Laplacian, -[symbol: see text]2 rho(r) and a comparison with high level theoretical gas-phase calculations reveals an unexpected electron distribution in the N-O group, both atoms having negative atomic charges, contrary to that commonly assumed in nitrone species. This observation is confirmed on examination of both the theoretical charges and the molecular electrostatic potential. Compound 1 contains a large number of hydrogen bonds and these are analysed using the atoms in molecules approach leading to quantitative values for bond strength, ranging from medium to very weak.

The electron density in flavones I. Baicalein

The experimental charge density distribution of 5,6,7-trihydroxyflavone (1), has been determined from high-resolution X-ray diffraction data collected at 100 K. Additionally, high level single-point gas-phase calculations as well as periodic calculations have been carried out for (1). To our surprise, the topological analysis of the experimental electron density revealed a cage critical point in the geometric center of the tri-hydroxy substituted aromatic ring. This feature was independently confirmed by analysis of another study of 1. However, both high-level gas-phase and periodic ab initio calculations failed to reproduce this feature. The degree of bias on the electron density by using the Hansen–Coppens multipole model was tested by a multipole refinement of generated theoretical structure factors. This clearly showed that the cage critical point is not an artefact resulting from the use of the multipole model. Compound 1 contains a large number of weak, intermolecular hydrogen bonds and these are analysed using the Atoms in Molecules (AIM) approach, which leads to quantitative measures for hydrogen bond strength. The experimentally derived lattice energy of −467 kJ mol−1 shows a rather strongly held crystal lattice.

Can a multipole analysis faithfully reproduce topological descriptors of a total charge density?

Total charge densities rho(r) of solid NH(3) have been derived using an ab initio crystalline molecular-orbital approach and also from multipole refinement of the structure factors obtained from the same charge density. Comparison of the topological features of these charge densities, as defined by the quantum theory of atoms in molecules, has been used to probe the ability of the multipole analysis to reproduce exactly known total charge-density distributions. For the most part, multipole refinement satisfactorily returns the features of the original density, although the fit to theoretical data is not as good as that to the experimental data. The one topological parameter that is poorly reproduced is the Laplacian nabla (2)rho(r(b)) at NH bond critical points.

Multipole refinements and maximisation of entropy. Competing or complementary methods

Multipole refinements and maximisation of entropy. Competing or complementary methods

Study of the electron density in MgO, (Mg 0.963 Fe 0.037 )O and Cu 2 O by the maximum entropy method and multipole refinements: comparison between methods

The electron densities determined by the maximum entropy method and by the multipole refinement approach are compared with each other, in terms of some topological properties according to the Bader formalism (Laplacian and eigenvalues of the Hessian matrix of the electron density at the critical points). The cases of MgO, (Mg,Fe)O and Cu2O are examined. The best agreement is observed for the critical points along the Mg–O, (Mg,Fe)–O and Cu–O directions, whereas larger discrepancies occur at the other critical points. Plots of the electron densities generated by the maximum entropy method and the multipole formalism along the most representative crystallographic directions contribute to elucidating the comparison between approaches.

Electron distribution and molecular motion in crystalline benzene: an accurate experimental study combining CCD X-ray data on C6H6 with multitemperature neutron-diffraction results on C6D6.

The electronic properties of the benzene molecule, for example its quadrupole moment and the electric field gradients (EFG's) at the H nuclei, are of fundamental importance in theoretical and experimental chemistry. With this in mind, single-crystal X-ray diffraction data on C(6)H(6) were collected with a charge-coupled device detector at T approximately 110 K. As accurate modelling of the thermal motion in the crystal was regarded as vital, especially for the hydrogen atoms, anisotropic-displacement parameters (ADP's) for the C and H atoms in C(6)H(6) were derived in a straightforward fashion from analysis of the temperature dependence of ADP's for the C and D atoms in C(6)D(6) at 15 K and 123 K obtained by neutron diffraction. Agreement between C-atom ADP's derived from thermal-motion analysis of neutron data and those obtained from multipole refinement by using the X-ray data is extraordinarily good; this gives confidence in the modelling of vibrational motion for the H atoms. The molecular quadrupole moment derived from the total charge density of the molecule in the crystal is (-29.7+/-2.4)x10(-40) C m(2), in excellent agreement with measurements made in the gas phase and in solution. The average deuterium nuclear quadrupole coupling constant (DQCC) derived from EFG tensors at H atoms is 182+/-17 kHz, also in excellent agreement with independent measurements. The strategy employed in this work may be of more general applicability for future accurate electron density studies.

The charge-density distribution, its multipole refinement and the antiferromagnetic structure of dioptase, Cu 6 [Si 6 O 18 ]·6H 2 O

The chemical bonding in the ring silicate mineral dioptase is investigated on the basis of accurate single-crystal X-ray diffraction data. A multipole model is used in the refinements. Static deformation electron density is mapped for the silicon tetrahedron, Cu-octahedron and water molecule in different sections. The silicon tetrahedron exhibits peaks resulting from σ-bonds between Si–sp3 hybrid orbitals and O–p orbitals. The excess density is located on bonds between the Si atom and bridge (in ring) O(1)-, O(1′)-oxygens and across the interior of the Si–O–Si angle. In the Jahn-Teller distorted Cu octahedron, in addition to peaks which result from single Cu–O σ-bonds, there are peaks which are due to 3d electrons. The analysis of crystal-field influence on the Cu charge distribution is made using the tetragonal D 4 d approximation for the low-symmetry (C1) Cu octahedron. The calculation of the occupancies of the 3d atomic orbitals shows that the Cu non-bonding orbitals are most populated (˜20%) and the bonding orbitals least populated (14%), as is typical for the Jahn-Teller octahedron. The effective atomic charge on the Cu atom in dioptase determined from the multipoles is +1.23e: closer to the Cu+1 than to the Cu+2 state. The charge on the Si atom has a value +1.17e, which is in the range typical for Si atoms already determined by this method. The accumulation of density on bridge oxygens and across the interior of the Si–O–Si angle may be explained by additional strain in the bond with the decrease of the Si–O–Si angle in dioptase to 132°. The same effect was found earlier in coesite. A single-crystal neutron diffraction study shows that dioptase becomes antiferromagnetic below a Neel temperature of 15.9(1) K, in contrast to the previously reported specific heat anomaly at 21 K. The magnetic propagation vector is (0, 0, 3/2) on the hexagonal triple cell or (1/2, 1/2, 1/2) in rhombohedral indices. The relation between the antiferromagnetic and the charge-density models for dioptase is discussed. The less occupied Cu d x2−y2 orbitals are responsible for the magnetic properties. These lie in the Cu–O squares, which are approximately perpendicular to c hex, but which are alternately inclined to it by a small angle. The magnetic moments of 0.59(1)μ B on the Cu ions in the same level are ordered ferromagnetically, but between ions in alternate levels the coupling is antiferromagnet. Within experimental error the magnetic moments are perpendicular to the square planes, which make an angle ±13(3)° to the triad axis.

Charge-Density Study of Methane Di(triimido)sulfonic Acid H2C{S(NtBu)2(NHtBu)}2—the NR Analogue of H2C{S(O)2(OH)}2 This work was supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. The discussions in the Würzburger Graduiertenkolleg “Elektronendichte” were very stimulating. We thank one of the referees for valuable comments.

Short bonds explained at long last: The charge-density distribution in the SN bonds of H2C{S(NtBu)2(NHtBu)}2, the NR analogue of methane disulfonic acid H2C{S(O)2(OH)}2, was studied by high-resolution X-ray diffraction and subsequent multipole structure refinement (see picture). This experiment reveals that all three nitrogen atoms at each sulfur atom are sp3 hybridized. The formal SN double bonds are shortened by electrostatic reinforcement and not by pπ–dπ interaction.

Wavefunctions derived from experiment. III. Topological analysis of crystal fragments.

A constrained wavefunction model has been used to extract a Hartree-Fock wavefunction for C2H2O4.4H2O from both low-angle (sin theta /lambda < 0.71 A-1, 571 reflections) and full (sin theta / lambda < 1.00 A-1, 968 reflections) experimental X-ray diffraction data for crystalline alpha-oxalic acid dihydrate (alpha-C2H2O4.2H2O) using polarized double-zeta and triple-zeta Gaussian basis sets. Properties obtained from the zero-flux partitioning of the total charge-density distribution derived from these wavefunctions, as well as from multipole refinement of the experimental data, are calculated and compared. This work represents the first calculation of integrated atomic properties derived from the fitting of Gaussian density functions to experimental X-ray diffraction data. In particular, atomic kinetic energies derived from experimental data are presented for the first time. The results obtained from the constrained (experimental) charge density show qualitatively similar properties to those obtained from conventional ab initio gas-phase calculations, though the quantitative differences are often substantial. The accuracy of integrated properties calculated using this procedure was established from the analysis of a wavefunction derived from simulated random-error diffraction data; that is, data obtained by adding normally distributed errors to the experimental structure factors. Analysis of this random-error wavefunction indicated that most topological properties are accurate to within approximately 5%, although the error is much larger for those properties that have a steep gradient in the region being evaluated [e.g. the value of V(2)rho(rb) at bond critical points] or are very small (e.g. the atomic dipole moment). Calculations of the constrained wavefunction using both the larger basis set and the complete set of experimental data yield results that agree quantitatively with the smaller calculations.

Gradient vector field and properties of the experimental electrostatic potential: Application to ibuprofen drug molecule

The present study focuses on the electric field features and related physical properties which can be derived from the topology of the experimental electrostatic potential. These properties were retrieved from the electron density multipole refinement of high-resolution x-ray data collected on a racemic crystal of ibuprofen drug. The electric field lines are depicted around the molecule revealing gradient vector zero flux atomic basins and critical points (CP’s) having a different significance than that brought out by the topology of the electron density. This method emphasizes a partioning of the molecular system mainly governed by the nuclear–electron interaction. The concept of Slater’s nuclear screening is here explored from the inspection of the gradient field zero flux surface separating the atoms in the molecule. Moreover, empirical parameters like covalent or atomic bond radii are accurately estimated from CP–atom distances in the molecular heteroatomic bonds. The local minima of the electrostatic potential are searched around the ibuprofen molecule in order to locate the binding sites for further molecular interactions with biological targets or with excipients in pharmaceutical preparations. Ibuprofen dipole moment is also estimated by a method based upon the fit to the experimental electrostatic potential values generated around the molecule.

Electron density distribution in paramagnetic and antiferromagnetic CoO: A γ-ray diffraction study

Highly accurate single-crystal structure factors, complete up to $\mathrm{sin}\ensuremath{\theta}/\ensuremath{\lambda}=1.6{\AA{}}^{\ensuremath{-}1},$ have been measured from CoO at 305 K and in the antiferromagnetic state at 10 K using 316.5 keV \ensuremath{\gamma} radiation. Moderate uniaxial pressure was applied in the low-temperature phase to force a single-T-domain sample. A detailed description of the electron-density distribution is presented. The occupancies of the $3d$ shell are computed from multipole refinement parameters, showing significant differences between the two magnetic phases. The spin and orbital contributions to the total magnetic moment of Co are derived from the experimentally determined number of unpaired electrons. Results are compared with ab initio calculations as well as with magnetic form factor measurements. A careful analysis of electronic properties in the internuclear regions reveals the Co-O interaction to be purely ionic. Its physical significance on the antiferromagnetism is discussed.

Fundamental Properties and Nature of CH··O Interactions in Crystals on the Basis of Experimental and Theoretical Charge Densities. The Case of 3,4-Bis(dimethylamino)-3-cyclobutene-1,2-dione (DMACB) Crystal

The CH··O contacts in the 3,4-bis(dimethylamino)-3-cyclobutene-1,2-dione (DMACB) crystal have been characterized through a topological analysis of its experimental and theoretical densities, derived from a multipole refinement of X-ray diffraction data and from periodic Hartree−Fock calculations, respectively. The existence or the lack of an H··O bond critical pointthat is a point through the two nuclei where the gradient of the electron density vanishesallows us to distinguish between bonded and nonbonded CH··O contacts, regardless of the value of their H··O separation. The 23 unique bonded contacts in DMACB are characterized by a large and nearly constant (∼140°) C−H−O angle, denoting the importance of the electrostatic energy contribution to such interactions. Instead, the nonbonded ones (four unique for H··O separations up to 3.0 Å) are more bent and may even be folded down to 90°, since their dominant van der Waals contribution to the interaction energy is independent of the C−H−O angle. The CH··O angular distribution observed for H··O separations greater than 2.7 Å is only apparently isotropic, since such isotropy clearly disappears when the bonded and nonbonded contacts are identified and their angular distributions separately analyzed. The Koch and Popelier criteria (J. Phys. Chem. 1995, 99, 9747) to establish H-bonds are, for the first time, applied in their entirety to a large set of CH··O contacts in a crystalline phase. The criteria are always satisfied by all of the bonded intermolecular CH··O contacts, with a single exception concerning one long bond and one of the six criteria only. The expressions proposed by Espinosa et al. (Chem. Phys. Lett. 1998, 285, 170), relating the potential energy densities at the critical point to the H-bond strengths, fail when applied to the weak CH··O interactions present in the DMACB crystal. The reasons for such a failure are outlined and new relationships are proposed. The importance of the promolecular charge distributions in defining topological properties of interest to the CH··O bonds is investigated. The criticism raised by Spackman (Chem. Phys. Lett. 1999, 301, 425) as to the lack of additional information provided by the experimental results to the description of such weak interactions is discussed. It is shown that the promolecular model yields significantly different electron density values at the critical point and in some instances even different topologies, compared to the corresponding multipole or theoretical densities. On the other hand, when the electron density topologies are the same, the values obtained from either electron density for the potential or kinetic energy density at the critical point, are very much alike.

Electron Density Distributions of Pyrimidine Bridged Cu, Fe, and Co Complexes Showing Magnetic Properties

Experimental electron density distributions of [Cu(NO 3 ) 2 (H 2 O) 2 (pm) 2 ] ( 1 ) and [MCl 2 (pm) 2 ] ( 2 :M=Co, 3 :M=Fe) (pm=pyrimidine) showing antiferromagnetic interactions were determined by the X-ray diffraction method using the multipole expansion refinement. In the crystal structures, the pyrimidine ligand bridges metal atoms to form one-dimensional chains in 1 , and three-dimensional networks in 2 and 3 . The electron populations in the d-orbitals calculated from the multipole population parameters revealed that the unpaired electrons are located in d x 2 −y 2 orbital for each complex. These results show that the strong interactions between the bridging ligand and the unpaired electrons cause the antiferromagnetic interactions mediated by the bridging ligands.

Agostic deformations based on electron delocalization in the alkyllithium-complex [(2-(Me3Si)2CLiC5H4N)2.

Topological analysis of experimental and theoretical charge densities in the title complex [(2-(Me3Si)2CLiC5H4N)2] 1 reveals the nature of the agostic deformation postulated for this complex: delocalization of the Li-C bonding electrons over the entire agostic alkyl group controls the formation of an acute Li-C-Si angle and thus a sufficient electronic saturation of the electron deficient lithium atom via secondary interactions.

Role of the Hydrogen Bonds in Nitroanilines Aggregation: Charge Density Study of 2-Methyl-5-nitroaniline

The electron charge distribution of 2-Methyl-5-nitroaniline has been studied from high-resolution single-crystal X-ray data at 100 K, and ab initio calculations which include X-ray structure factors computed from a superposition of ab initio molecular electron densities. Using the Hansen and Coppens' rigid pseudoatom multipolar model refinements were performed on both the experimental and the theoretical X-ray data sets from which, molecular atomic charges and dipolar moments were obtained. To understand the nature and the magnitude of the intermolecular interactions, the Atoms in Molecules theory was used to investigate the topology of the electron density of the in-crystal, both experimental interacting as well as theoretical noninteracting, and in-vacuum molecules. A meticulous analysis of the topological properties of the experimental charge density and of its Laplacian indicates, contrary to expectations, a two center character of the N−H···O synthons that induce the known polar chain formation in nitroanilines and the presence of a Cmethyl-H···O interaction further strengthening the chains. It also shows the attractive nature of the rather strong C−H···O interactions that help the head-to-tail arrangement of the chains. They build two intermolecular six membered hydrogen bonded rings, embracing a N−H···O interaction, that originate centrosymmetric dimers which impair the macroscopic second harmonic generation of the title compound. The authenticity of a previously proposed closed shell Caryl-H···π interaction between adjacent chains has been confirmed. The latter has not been observed in m-nitroaniline, 2-methyl-4-aniline or other related compounds with chains built from similar N−H···O synthons and assembled head-to-head. Crystallization causes a molecular electric dipolar moment higher than that of the free molecule, the latter being coincident with the experimental value in solution, and with the one calculated from the refinement of the theoretical X-ray data. It also induces changes in the charge density distribution and its topology, and an enhancement of the intramolecular conjugation that can be related to a molecular aggregation mechanism ruled by the N−H···O synthon. These findings strongly point to the existence of cooperative effects.

Electron Deformation Density in Rhombohedral α-Boron

α-boron is the most simple structure of all boron modifications having one B12 icosahedron per (rhombohedral) unit cell. The conventional, free atom crystal structure refinement with R = 6.2% indicates considerable charge redistribution into covalent bonding. In a high order-low order and multipole refinement the R value could be reduced to 1.19%. The ensuing deformation difference density maps reveal bonding between the boron atoms, in the icosahedra and between the icosahedra.

Charge density and topological analysis of l-glutamine

The experimental charge density and related topological properties of the amino acid l-glutamine were derived from a single crystal X-ray diffraction experiment at 130K using conventional MoKα radiation and area detection technique. A multipolar refinement of the 6704 symmetry independent structure factors led to a ‘rigid pseudoatom’ model with crystallographic agreement factors R(F)=1.6%, Rw(F)=1.4%, GoF=1.04. The experimental topology in terms of Bader's ‘atoms in molecules’ (AIM) theory is compared to high-level ab initio calculations and to the average of the experimental topology in the 11 naturally occurring unsubstituted amino acids studied so far.

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 and Topological Analysis of Pentafluorobenzoic Acid

A charge density study of crystalline pentafluorobenzoic acid has been carried out using high-resolution X-ray diffraction data collected at 110 K. Two multipole refinement models based on the rigid-pseudoatom formalism were used for topological analysis, and the results were compared to those of theoretical calculations for the isolated molecule. In an analysis of the topological parameters at the bond critical points, the discussion focuses on the C−F bond, the hydrogen bond, and intramolecular and intermolecular weak F···O and F···F‘ interactions. Moreover, the geometrical distribution of the nonbonded valence shell charge concentrations was studied at oxygen and fluorine atoms on the basis of experimental data.

Recovering experimental and theoretical electron densities in corundum using the multipolar model: IUCr Multipole Refinement Project.

This electron-density study on corundum (alpha-Al2O3) is part of the Multipole Refinement Project supported by the IUCr Commission on Charge, Spin and Momentum Densities. For this purpose, eight different data sets (two experimental and six theoretical) were chosen from which the electron density was derived by multipolar refinement (using the MOLLY program). The two experimental data sets were collected on a conventional CAD4 and at ESRF, ID11 with a CCD detector, respectively. The theoretical data sets consist of static, dynamic, static noisy and dynamic noisy moduli of structure factors calculated at the Hartree-Fock (HF) and density functional theory (DFT) levels. Comparisons of deformation and residual densities show that the multipolar analysis works satisfactorily but also indicate some drawbacks in the refinement. Some solutions and improvements during the refinements are proposed like contraction or expansion of the inner atomic shells or increasing the order of the spherical harmonic expansion.