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ABSTRACT:
This chapter describes the interaction of Xrays, unpolarized and polarized neutrons with the charge and spin densities of
a periodic system. The methods developed for analysis of the electron densities from the diffraction intensities are described
in detail and the concepts used in the interpretation of the results are defined. This chapter is also available as HTML from the International Tables Online site hosted by the IUCr.
12/2003: pages 713734;

Edited by A. J. C. Wilson and E. Prince, 01/1999: chapter Analysis of charge and spin densities,: pages 706727; Kluwer Academic Publishers, Doderecht / Boston / London.

Acta crystallographica. Section A, Foundations of crystallography 01/1998; 54(3):357357. DOI:10.1107/S010876739800124X · 2.07 Impact Factor

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The Sternheimer function gamma(r) describes the shielding/antishielding of the electric field gradient (EFG) at the nuclear position due to polarization induced in the atomic density by the quadrupolar components of the density distribution. The functions for Fe, Fe2+ and Fe3+ have been derived by means of Sternheimer's procedure [Sternheimer (1986). Z. Naturforsch. Teil A, 41, 2436], using a finitedifference method for solving the radial equations for the perturbed wavefunctions and numerical integration for the calculation of gamma(r). The shielding factors R, due to the contributions from the electron density of the atom at the nucleus of which the EFG is being considered (the 'central contributions'), are derived from the gamma functions. Results are given for nearHartreeFock atomic and ionic wavefunctions [Clementi & Roetti (1974). At. Data Nucl. Data Tables, 14, 177478]. Contributions to the shielding from the core and valence electrons are separated. Since the Xray multipole formalism describes a flexible valence shell but uses a frozen core, only gamma(infinity)(core) and R(core) are used in the calculation of Mossbauer splittings from the experimental charge densities. The effect on the shielding of Xraydetermined radial expansion/contraction of the valence shells [Coppens, Guru Row, Leung, Stevens, Becker & Yang (1979). Acta Cryst. A35, 6372] is evaluated. The combination of spectroscopic nuclear quadrupole splittings and Xray charge densities on iron pyrite (FeS2), sodium nitroprusside {[Na2Fe(NO)(CN)(5)].2H(2)O} and [Fe(TPP)(pyridyl)(2)] leads to unweighted and weighted average values for Q(Fe57(m)) of 0.12 (3) and 0.11 (2) x 10(28) m(2), respectively, when the core shielding factors are used.
Acta crystallographica. Section A, Foundations of crystallography 09/1996; 52(5):748756. DOI:10.1107/S010876739600596X · 2.07 Impact Factor

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Ewald's method of accelerated convergence [Ewald (1921). Ann. Phys. (Leipzig), 64, 253287] is generalized to calculate the electrostatic potential of a crystal in which the atoms have overlapping spherical densities, The algorithm is applied to the cubic NaF crystal. The potentials at the Na and F nuclei are calculated for the freeion model and for the results from a kappa refinement of the experimental data of Howard and Jones [Acta Cryst, (1977), A33, 776783]. The kappa refinement indicates an incomplete charge transfer but gives an electrostatic energy close to that of the pointcharge model with full charge transfer and a lattice energy that is in good agreement with the experimental value.
Acta Crystallographica Section A Foundations of Crystallography 01/1995; 51(1):2732. DOI:10.1107/S0108767394004447 · 2.07 Impact Factor

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Formulae for the rotation of real spherical harmonic functions are presented. To facilitate their application, values of the matrices d m ' m (l) (π/2), which occur in the equations, are tabulated for 1≤l≤8 and 0≤m ' , m≤l. The application of the equations to spherical harmonic functions with the normalization commonly used in chargedensity analysis is described.
Acta crystallographica. Section A, Foundations of crystallography 09/1994; 50(5). DOI:10.1107/S0108767394003077 · 2.07 Impact Factor

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Normalization factors N(lj) for the Kubic harmonics K(lj) defined by [GRAPHICS] have been evaluated numerically for l lessthanorequalto 10.
Acta crystallographica. Section A, Foundations of crystallography 05/1994; 50(3):408409. DOI:10.1107/S0108767393013017 · 2.07 Impact Factor

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A method for efficiently evaluating integrals of the type AN, l1, l2, k(Z, R) = ×jl2(SR)Sk dS is discussed and closedform expressions for those integrals useful in the calculation of the electrostatic potential, the electric field and the electric field gradient are given.
Journal of Applied Crystallography 02/1994; 27(1):8991. DOI:10.1107/S0021889893007009 · 3.95 Impact Factor

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A method is presented to calculate the electrostatic potential, the electric field and the electricfield gradient in a crystal from the atomic multipole expansion of the experimental charge density, as described by the HansenCoppens formalism [Hansen & Coppens (1978), Acta Cryst. A34, 909921]. The electrostatic properties are expressed in terms of the positions and the chargedensity parameters of the individual atoms. Contributions due to the procrystal charge density and the deformation charge density are compared. The method is illustrated by the calculation of the electrostatic potential maps of fully deuterated benzene and of iron(II) tetraphenylporphyrin.
Acta Crystallographica Section A Foundations of Crystallography 03/1992; 48 ( Pt 2):18897. DOI:10.1107/S0108767391009820 · 2.07 Impact Factor

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(C10H8S8)2[Cd2I6], M(r) = 1755.60, triclinic, P1BAR, a = 9.067 (2), b = 10.515 (1), c = 12.441 (2) angstrom, alpha = 97.12 (1), beta = 103.43 (1), gamma = 106.13 (1)degrees, V = 1085 (1) angstrom 3, Z = 1, D(x) = 2.69 g cm3, lambda(Mo Kalpha) = 0.71073 angstrom, mu = 59.6 cm1, F(000) = 806, room temperature, R(F) = 0.051, wR = 0.061 for 2761 unique reflections. The structure consists of pairs of BEDTTTF cations [BEDTTTF = bis(ethylenedithio)tetrathiafulvalene] with an interplanar separation of 3.53 angstrom and Cd2I62 anions formed by two CdI42 tetrahedra sharing one common edge. pipi molecular overlap exists within each pair of BEDTTTF molecules, while different pairs are linked via S...S contacts, which are as short as 3.339 (3) angstrom.
Acta Crystallographica Section C Crystal Structure Communications 02/1991; 47(2):279282. DOI:10.1107/S0108270190008071 · 0.54 Impact Factor

Journal of Applied Crystallography 02/1990; 23(1):7173. DOI:10.1107/S0021889889010484 · 3.95 Impact Factor