Multipole Refinement Research Articles

Synchrotron X-ray analysis of the electron density in CoF2 and ZnF2

Accurate structure factors for small crystals of the rutile-type structures CoF(2), cobalt difluoride, and ZnF(2), zinc difluoride, have been measured with focused lambda = 0.8400 (2) A synchrotron X-radiation at room temperature. Phenomenological structural trends across the full series of rutile-type transition metal difluorides are analysed, showing the importance of the metal atom in the degree of distortion of the metal-F(6) octahedra in these structures. Multipole models reveal strong asphericities in the electron density surrounding the transition metals, which are consistent with expectations from crystal field theory and the structural trends in these compounds. Transition metal 3d-orbital populations were computed from the multipole refinement parameters, showing significant repopulation of orbitals compared with the free atom, particularly for CoF(2).

Hydrogen Bonds in NH4F and NH4HF2 Crystals. Comparison of Electron Density Distribution Obtained by X-ray Diffraction and by Quantum Chemistry

The quality of the Hartree−Fock and the density functional methods for the description of hydrogen bonds is judged by comparing quantitatively the outcome of calculations on the hydrogen bonds in ammonium (bi)fluorides with the results of accurate electron density studies by X-ray diffraction. X-ray data and analysis for NH4F were taken from the literature; those for NH4HF2 were collected in a single-crystal diffraction experiment. A total of 8522 reflections was measured, yielding the structure factors of 2333 independent reflections. Rint (F2) = 0.03. A multipole refinement converged to Rw (F2) = 0.034. Quantum chemical calculations were carried out with the CRYSTAL package, using the Hartree−Fock and the density functional methods and a 6-311G** basis set. Both the local density and the generalized gradient(GGA) version of the latter were applied. To make a comparison with experiment valid, the theoretical densities were converted to structure factors that then were subjected to the same multipole refi...

Multipolar refinement of aldose reductase at subatomic resolution

Multipolar refinement of aldose reductase at subatomic resolution

Evaluation of net atomic charges and atomic and molecular electrostatic moments through topological analysis of the experimental charge density

The atoms in molecules (AIM) theory may be used to derive atomic charges, atomic volumes and molecular dipole moments from the charge density. The theory is applied to theoretical periodic Hartree-Fock (PHF), density-functional (DFT) and experimental X-ray densities of p-nitroaniline using the program TOPOND and a newly developed program, TOPXD, for topological analysis of densities described by the Coppens-Hansen multipole formalism. Results show that, like dipole moments derived directly from the multipole refinement, AIM-derived atomic and molecular moments are dependent on the multipole model used. As expected, large differences are found between charges derived from the monopole parameters and those from AIM analysis of the experimental model density. Differences between the k'-restricted multipole model (KRMM) and the unrestricted multipole model (UMM) results are preserved in the AIM analysis. The enhancement of the molecular dipole moment of p-nitroaniline in the solid state is confirmed by both experiment and theory but the experimental dipole moment is in much better agreement with theoretical periodic Hartree-Fock and, especially, periodic DFT (PDFT) data when KRMM is used in the refinement. The AIM analysis allows a rigorous definition of the charges of the atoms in molecules and provides a realistic basis for comparison between molecules and between experiment and theory.

Extracting charge density distributions from diffraction data: a model study on urea

The quality of the extraction of electron density distributions by means of a multipole refinement method is investigated. Structure factors of the urea crystal have been obtained from an electron density distribution (EDD) resulting from a density function calculation with the CRYSTAL95 package. To account for the thermal motion of the atoms, the stockholder-partioned densities of the atoms have been convoluted with thermal smearing functions, which were obtained from a neutron diffraction experiment. A POP multipole refinement yielded a good fit, R = 0.6%. This disagreement factor is based on magnitudes only. Comparison with the original structure factors gave a disagreement of 0.8% owing to differences in magnitude and phase. The fitted EDD still showed all the characteristics of the interaction density. After random errors corresponding to the experimental situation were added to the structure factors, the refinement was repeated. The fit was R = 1.1%. This time the resulting interaction density was heavily deformed. Repetition with another set of random errors from the same distribution yielded a widely different interaction density distribution. The conclusion is that interaction densities cannot be obtained from X-ray diffraction data on non-centrosymmetric crystals.

Experimental charge density and electrostatic potential of glycyl-L-threonine dihydrate.

The experimental electron density distribution in glycyl-L-threonine dihydrate has been investigated using single-crystal X-ray diffraction data at 110 K to a resolution of (sin theta/lambda) = 1.2 A(-1). Multipolar pseudo-atom refinement was carried out against 5417 observed data and the molecular electron density was analyzed using topological methods. The experimental electrostatic potential around the molecule is discussed in terms of molecular interactions. Crystal data: C6H12N2O4. 2H2O, Mr = 212.2, orthorhombic, P2(1)2(1)2(1), Z = 4, F(000) = 456 e, T = 110 K, a = 9.572 (3), b = 10.039 (3), c = 10.548 (2) A, V = 1013.6 (4) A3, Dx = 1.3 g cm(-3), mu = 1.2 cm(-1) for lambdaMo = 0.7107 A.

Accurate structure-factor measurements using high-energy synchrotron radiation: a test on cuprite, Cu2O

Using high-energy synchrotron radiation, structure factors were measured on the triple-axis diffractometer at the HASYLAB beamline BW5. A data set for cuprite, Cu2O, was recorded, and the excellent data quality [internal consistencyRint(F2) = 0.0055] allowed full multipole refinements using the programVALRAY. Extinction was still significant, but small. Using data measured at 75, 100, 125 and 150 keV photon energies, it was possible to determine and separate extinction prior to the refinements. After evaluation and comparison of extinction-affected and extinction-free data, significant differences in the electron densities were found.

Charge density in NiCl2.4H2O at 295 and 30 K.

The charge distribution has been determined by multipole refinements against single-crystal X-ray diffraction data. In the refinements a comparison was made between the densities based on H-atom parameters from X-ray and neutron data, respectively. X-ray study: lambda(Mo Kalpha) = 0.71073 Å, F(000) = 408; at 30 K: R(F) = 0.015 for 6686 reflections; at 295 K: R(F) = 0.022 for 4630 reflections. The nickel ion is octahedrally surrounded by four water molecules and two chloride ions, forming a locally neutral Ni(H(2)O)(4)Cl(2) complex. Two of the water molecules are coordinated to nickel approximately in one of the tetrahedral ('lone-pair') directions; the other two are trigonally coordinated. At 30 K one H atom in one of the trigonally coordinated water molecules is disordered, with equal occupation of two different positions. Owing to the polarizing influence of the nickel ion there are two peaks in the lone-pair plane of the water molecules when these are tetrahedrally coordinated; for those trigonally coordinated there is just one peak. The individual ('partial') charge densities, calculated from the deformation functions of only nickel or the separate water molecules, have also been calculated to study the effects of superposition of the individual densities. In the individual density of nickel an excess is observed in the diagonal directions and a deficiency in the ligand directions. However, owing to the influence of the whole crystalline environment, the maxima around nickel are not found in the planes defined by nickel and the six ligands.

The use of CCD area detectors in charge-density research. Application to a mineral compound: the alpha-spodumene LiAl(SiO3)2.

X-ray diffraction data sets collected on both Nonius and Siemens (Bruker) goniometers equipped with charge-coupled device (CCD) area detectors have been tested for the electron-density determination of the aluminosilicate mineral compound alpha-spodumene LiAl(SiO(3))(2), aluminium lithium silicon oxide. Data collection strategies, reflection intensity peak integration methods and experimental error estimates are different for the two instruments. Therefore, the consistency and quality of the two types of CCD measurements have been carefully compared to each other and to high-resolution data collected on a conventional CAD-4 point-detector diffractometer. Multipole density model refinements were carried out against the CCD data and the statistical factors analysed in terms of experimental weighting schemes based on the standard uncertainties of the diffraction intensities derived by the Nonius and Siemens software programs. Consistent experimental electron-density features in the Si-O-Si and Si-O-Al bridges were found from both CCD data sets. The net atomic charges obtained from the kappa refinements against each CCD data set are also in good agreement and quite comparable with the results of the conventional CAD-4 experiment.

Electron density in ammonium dihydrogen phosphate: non-uniqueness of the multipolar model in simple inorganic structures.

X-ray and neutron diffraction data of a single crystal of ammonium dihydrogen phosphate have been used for the determination of the electron density using multipolar expansion of the density around each nucleus. As the ammonium group was found to be nearly neutral from unconstrained multipole refinement, constrained refinements have been performed with the charge of the ammonium group ranging from zero to one. On the other hand, the expansion of the radial functions of the phosphorus atom was varied. All refinements led to almost the same agreement factors and residual densities. The consequences of such uncertainties on the topology of the electron density are discussed, namely the topology of the P-O bond critical point.

X-ray charge density study ofp-amino-p′-nitrobiphenyl at 20 K using a CCD area detector and synchrotron radiation: a very large dipole moment enhancement in the solid state

Accurate 20 K intensity data were collected on a crystal of p-amino-p′-nitrobiphenyl [a = 24.348(1), b = 5.802 (1), c = 7.158 (1) A, α = β = γ = 90°, space group Pca21] at the SUNY X3A1 beamline at the National Synchrotron Light Source, using a CCD area detector and a DISPLEX cryostat. The sharp vertical profile of the synchrotron beam, combined with a slight instability of the cryostat, necessitates a φ-dependent correction, made possible by a large redundancy in the data set, the average multiplicity of the measurements being 8.02. In the multipole refinement, net atomic charges were constrained to those from a κ-refinement, corresponding to a more local definition of the pseudoatoms in the crystal. Both localized and unrestricted refinements show a very large (more than threefold) enhancement of the dipole moment in the solid state compared with that of the isolated molecule.

On the evaluation of molecular dipole moments from multipole refinement of X-ray diffraction data

Lack of physical constraints in the purely mathematical multipole refinement model can lead to basis set overlap errors in the evaluation of static molecular properties from X-ray diffraction data. For the molecular dipole moment, the error is large for several of the crystals tested in this study: dl-histidine, dl-proline, p-nitroaniline and p-amino- p′-nitrobiphenyl. Two restricted models are tested. In the first, atomic charges are constrained at κ-refinement values, while in the second κ′-values based on multipole refinements of theoretical ab-initio structure factors are used to reduce the flexibility of the model. Both models provide a more localized description of the pseudo atoms compared with an unrestricted refinement, but the κ′-restricted model gives a more consistent representation of the molecular dipole moments and superior agreement with the theoretical deformation density for dl-histidine.

Influence of intermolecular interactions on multipole-refined electron densities

This work examines the effect of intermolecular interactions on molecular properties derived from simulated X-ray diffraction data. Model X-ray data are computed from a superposition of ab initio molecular electron densities in the crystal, as well as from periodic crystal Hartree-Fock electron densities, for the hydrogen-bonded systems ice VIII, formamide and urea, as well as the weakly bound acetylene. The effects of intermolecular interactions on the electron density are illustrated at both infinite and finite data resolution, and it is concluded that multipole models are capable of quantitative retrieval of the interaction density, despite the known shortcomings of the radial functions in the model. Multipole refinement reveals considerable enhancement of the molecular dipole moment for hydrogen-bonded crystals, and negligible change in molecular second moments. Electric field gradients at H nuclei are significantly reduced in magnitude upon hydrogen bonding, and this change is also faithfully represented by the rigid pseudoatom model.

Accurate Charge-Density Studies as an Extension of Bayesian Crystal Structure Determination

Many hopes and much controversy have surrounded the application of the maximum-entropy (ME) method to accurate charge-density studies. This paper shows that viewing such studies as an extension of Bayesian crystal structure determination provides practical means of fulfilling many of the hopes invested in the ME method, while essentially eliminating its controversial aspects, the latter being explained in terms of a number of computational artefacts. The positional probability distribution of scatterers having maximum entropy relative to a given `prior prejudice' is computed so as to reproduce a set of phased structure-factor amplitudes; core electrons can optionally be treated as a fixed `fragment' and described using atomic core densities derived from ab initio wave functions. Fragment and prior-prejudice density distributions are computed by fast Fourier transforms and are thermally smeared by aliasing. These various algorithms have been implemented within the BUSTER computer program. Model studies on noise-free synthetic data sets for α-glycine, silicon and beryllium show that all-electron calculations give rise to artefacts when a uniform prior prejudice is used, while valence-only calculations using valence monopole priors are essentially free from artefacts. The maximum-entropy approach is thus optimally implemented by incorporating the prior knowledge of the existence of sharp atomic cores in the form of a fragment not subjected to entropy maximization. These results contribute to settling the debate about the putative existence of non-nuclear density maxima at special positions for crystalline silicon and beryllium, and prepare the ground for developing maximum-likelihood multipolar refinement.

Structure, Charge and Spin Density in Na2Ni(CN)4.3H2O at 295 and 30 K

The earlier reported structure of the title compound, disodium tetracyanonickelate(II) trihydrate, Na2Ni(CN)4.3H2O, has been found to be incorrect and has now been redetermined. The charge distribution has been determined by multipole refinements against single-crystal X-ray diffraction data. In the refinement based on 30 K data a comparison was made between the results obtained using hydrogen positions and displacement parameters from X-ray diffraction with those using the values determined by neutron diffraction. The spin density was investigated by polarized neutron diffraction at 1.6 K. Crystal data: at T = 30 K: a = 7.278 (4), b = 8.856 (5), c = 15.131 (8) Å, α = 89.32 (5), β = 87.39 (4), γ = 83.61 (4)°; at 295 K: a = 7.392 (4), b = 8.895 (4), c = 15.115 (8) Å, α = 89.12 (2), β = 87.46 (2), γ = 84.54 (2)°. The structure contains practically square planar Ni(CN)_4^{2-} ions, which are stacked on top of each other in almost linear chains along the a direction. The separation between the Ni(CN)_4^{2-} planes is rather large, with Ni—Ni distances around 3.7 Å. The six crystallographically independent water molecules are each coordinated to two sodium ions, approximately in the tetrahedral (lone-pair) directions, and the polarizing influence of these sodium ions also appears to be reflected in the deformation density in the lone-pair plane. The charge density based on the deformation functions of all atoms in the structure is compared with the individual densities calculated from the deformation functions of only nickel or the separate water molecules. In this way the effects of simple superposition of the individual densities have been studied. In the planar Ni(CN)_4^{2-} ion the individual deformation density of nickel is in qualitative agreement with that expected from crystal-field theory. As the repulsion from the electrons is much weaker perpendicular to the Ni(CN)_4^{2-} plane than within this plane, the deformation density is considerably larger in the perpendicular direction. However, the largest maxima in the individual deformation density around nickel are not found precisely in the planes defined by nickel and the four cyanide ligands or in the perpendicular direction just mentioned, which illustrates that it is necessary to consider the crystal field due to the whole crystalline environment.

A Test of the Suitability of CCD Area Detectors for Accurate Electron-Density Studies

The performance of the Siemens SMART CCD (charge-coupled device) area detector has been tested to assess its suitability for accurate electron-density (ED) determination. 92043 diffraction intensities (14701 unique reflections, 65 h experiment) have been collected on a reference crystal of methyl 2-[(4-butyl-2-methyl-6-oxo-5-{4-[2-(1H-tetrazol-5-yl)phenyl]benzyl }-1,2-dihydropyrimidin-1-yl)methyl]-3-thiophenecarboxylate (C30H30N6O3S) at T = 120 K and compared with those (51485, 14699 unique, 600 h) obtained from a previous collection at T = 18 K on the same crystal using a diffractometer equipped with a conventional detector. Results from spherical and multipolar refinements (agreement factors, standard uncertainties of refined variables and geometries after correction for thermal motion) have also been compared. The λ/2 contamination, which affects area detectors but not well tuned conventional detectors, has been carefully investigated and proved to be a negligible source of errors (which can anyway be easily corrected). The encouraging results of this test prove that area detectors are also well suited for charge-density studies, offering a cheap and fast data-collection mode, without loss of accuracy, which can be exploited for ED studies on large systems.

Experimental Charge Density and Electrostatic Potential of Triglycine

The experimental electron density distribution in triglycine has been determined using single-crystal X-ray diffraction data at 123 K to a resolution of (sin θ/λ)max = 1.1 Å−1. Several multipolar pseudo-atom density refinements were performed against the 7238 observed data in order to estimate the net charges on the atoms. The electrostatic potential around the two molecules is calculated from the parameters derived from these refinements. A charge transfer between the two triglycine molecules of the asymmetric unit is discussed. Crystal data: C6H11N3O4, Mr = 189.2, triclinic, P1¯, Z = 4 (two molecules in the asymmetric unit), T = 123 K, a = 11.585 (1), b = 14.603 (2), c = 4.800 (4) Å, α = 89.28 (3), β = 95.55 (2), γ = 104.484 (8)°, V = 782.5 (7) Å3, Dx = 1.61 g cm−3, μ = 1.5 cm−1 for λMo = 0.7107 Å.

Charge Density Studies Using CCD Detectors: Oxalic Acid at 100 K Revisited

The charge density of oxalic acid dihydrate has been redetermined from 100 K X-ray diffraction data using a SMART CCD diffractometer. The quality of the data has been carefully analyzed and shown to be at least as good as that obtained using a point detector. The positional and thermal parameters obtained from least-squares refinement and the main features of difference density maps are comparable with those obtained by a number of laboratories as part of the IUCr electron density project. In particular, the comparison study has been completed by two multipole refinements carried out in parallel using both the current data set and that of a previous study [Stevens & Coppens (1980). Acta Cryst. B36, 1864–1876].

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.

The effects of metal binding on a nucleobase: the experimental charge density and electrostatic potential in 1H(+)-adeniniumtrichlorozinc(II) at 123 K and its relationship to that in adenine hydrochloride hemihydrate.

The charge-density distribution in 1H(+)-adeniniumtrichlorozinc(II) has been determined from X-ray diffraction data collected to sin theta/lambda = 1.32 A(-1) at 123 K. The electrostatic potential, isolated from the crystal lattice, and the deformation density in the nucleobase have been calculated following multipole refinements based on the rigid pseudoatom model of Stewart. These and the molecular dimensions have been compared with results from the charge-density study of adenine hydrochloride hemihydrate by Cunane & Taylor [Acta Cryst. (1993). B49, 524-530] to determine the effects of metal binding on the nucleobase. The main conclusions are that while the bond lengths and angles in the pyrimidine ring are similar, those in the imidazole ring are significantly perturbed on complexation; lone-pair electron density at N7 is observed in both structures and lies significantly off the plane of the nucleobases; the positive electrostatic potential of the complexed base extends much further from the molecule than in the uncomplexed one and the regions of negative potential at N3 and N7 are depleted in the complexed base. The observed enhancement of positive electrostatic potential in the nucleobase on binding to zinc is presented in support of a model for the mechanism of reversible unwinding of DNA in the presence of zinc ions.