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1993 (6)
1Author    ElenaL. Belokoneva, VladimirG. Tsirel 'sonRequires cookie*
 Title    Electron Density and Bonding in Ring Silicates: Beryl, Cordierite, Dioptase  
 Abstract    The electron density and bonding in the silicates beryl, cordierite and dioptase has been investi-gated. The replacement of Be, Si and Al atoms in the identical structural fragments leads to a (^-redistribution and changes the cr-bond character from slightly polar to strongly polar. The condensation of [SiOJ-tetrahedra in the rings leads to the accumulation of electron density near bridge oxygens. This phenomenon is expressed especially in dioptase (pure ring silicate). Therefore, the electron density picture may be considered as a supplementary independent criterion for classi-fication of crystal structures. The experimental (5@-maps for H 2 0 molecules in dioptase are in good agreement with theoretical ones. The ^^-distribution of 3 d-electrons and bonding in the Jahn-Teller distorted Cu-octahedron can be interpreted from crystal-field-theory point of view. 
  Reference    Z. Naturforsch. 48a, 41—46 (1993); received January 10 1992 
  Published    1993 
  Keywords    Electron density, Bonding, Ring silicates 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0041.pdf 
 Identifier    ZNA-1993-48a-0041 
 Volume    48 
2Author    E. A. Zhurova, V. E. Zavodnik, S. A. Ivanov, P. P. Syrnikov, V. G. TsirelsonRequires cookie*
 Title    Electron Density and Anharmonic Thermal Atomic Vibrations in Kj_ x Li x Ta0 3 (* = 0, 0.05, 0.15) Perovskites  
 Abstract    The results of accurate X-ray diffraction studies of KTa0 3 , K 0 95 Li 0 05 TaO 3 and K 0 85 Li 0 15 Ta0 3 crystals are presented. Anharmonicity of the thermal motion of the oxygen atoms and deformation electron density maps are discussed. 
  Reference    Z. Naturforsch. 48a, 25—28 (1993); received November 8 1991 
  Published    1993 
  Keywords    Anharmonic thermal vibrations, Electron density, Chemical bond 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0025.pdf 
 Identifier    ZNA-1993-48a-0025 
 Volume    48 
3Author    JohnE. HarrimanRequires cookie*
 Title    Electron Densities, Momentum Densities, and Density Matrices  
 Abstract    Relationships among electron coordinate-space and momentum densities and the one-electron charge density matrix or Wigner function are examined. A knowledge of either or both densities places constraints on possible density matrices. Questions are approached in the context of a finite-basis-set model problem in which density matrices are elements in a Euclidean vector space of Hermitian operators or matrices, and densities are elements of other vector spaces. The maps (called "collapse") of the operator space to the density spaces define a decomposition of the operator space into orthogonal subspaces. The component of a density matrix in a given subspace is deter-mined by one density, both densities, or neither. Linear dependencies among products of basis functions play a fundamental role. Algorithms are discussed for finding the subspaces and construct-ing an orthonormal set of functions spanning the same space as a linearly dependent set. Examples are presented and additional investigations suggested. 
  Reference    Z. Naturforsch. 48a, 203—210 (1993); received October 8 1991 
  Published    1993 
  Keywords    Electron density, Momentum density, Density matrix 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0203.pdf 
 Identifier    ZNA-1993-48a-0203 
 Volume    48 
4Author    Ivar Olovsson, Halina Ptasiewicz-Bak, GarryJ. MclntyreRequires cookie*
 Title    Superposition and Polarization Effects on the Electron Density of Lone Pairs  
 Abstract    There appears to be conflicting experimental evidence on the redistribution of the electron density in the lone-pair and other regions of a molecule due to the interaction with its nearest neighbours. In some experimental as well as theoretical deformation density maps a decrease in the lone-pair density has been reported, whereas in other cases an increase has been found. It appears that two major, counteracting factors are responsible for these differences (apart from experimental errors in the diffraction studies and limited accuracy in the theoretical calculations): an increase in the lone-pair density is expected due to the polarizing influence of the neighbours, whereas simple superposition of the isolated monomer deformation densities will lead to an apparent decrease due to the overlap with the negative contours of the neighbouring atom. Depending on which of these factors is the dominant one, an increase or decrease may thus be observed. These points are illustrated by recent results on nickel sulfate hexahydrate and some other hydrogen-bonded compounds. The electron density based on the fitted deformation functions of all atoms in the structure is compared with the individual densities calculated from deformation functions of the separate monomers. In this way the effects of simple superposition of the individual densities have been studied, and a partitioning of the electrostatic and polarization contributions to the hydrogen bonds and other relatively weak bonds to the oxygen lone-pairs attempted. 
  Reference    Z. Naturforsch. 48a, 3—11 (1993); received January 30 1992 
  Published    1993 
  Keywords    Electron density, Superposition effects, Polarization effects, Lone pairs, Hydrogen bonds 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0003.pdf 
 Identifier    ZNA-1993-48a-0003 
 Volume    48 
5Author    Zhengwei Su, Philip CoppensRequires cookie*
 Title    Electrostatic Properties of Molecules from the X-Ray Charge Density. Application to Deuterated Benzene, 1-Alanine and d,l-Histidine  
 Abstract    It has been shown (Z. Su and P. Coppens, Acta Cryst. A 48, 188 (1992)) that the electrostatic potential, the electric field, and the electric field gradient (EFG) can be expressed in closed forms in terms of the positions and the charge-density parameters of individual atoms, whose aspherical density is described by a pseudoatom model (e.g., N. Hansen and P. Coppens, Acta Cryst. A 34, 909 (1978)). A Fortran program Molprop91 based on this method has been written (Z. Su, State Univ. of New York at Buffalo 1991). The method has been applied to the title compounds. Low-temper-ature X-ray diffraction data of fully deuterated benzene (G. A. and d,/-histidine (N. Li, Ph.D. thesis, State University of New York at Buffalo 1989) were analyzed using the least-squares deformation density refinement program Lsmol90 (a modified version of Molly). Molprop91 was subsequently used to calculate the electrostatic-poten-tial maps in selected sections, and at the nuclear positions. For the latter, the EFGs were also evaluated. The electrostatic potentials were used to fit net atomic charges and estimate the molecular energies. Errors in the derived quantities are given. 
  Reference    Z. Naturforsch. 48a, 85—90 (1993); received April 23 1992 
  Published    1993 
  Keywords    Electron density, Electrostatic potential, Electric field, EFG, Molecular energy 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0085.pdf 
 Identifier    ZNA-1993-48a-0085 
 Volume    48 
6Author    B. Hess, H. L. Lin, J. E. Niu, W.H E SchwarzRequires cookie*
 Title    Electron Density Distributions and Atomic Charges  
 Abstract    Accurate electron densities and X-ray form factors of Li, Be, F and their ions have been calculated. Electron correlation, crystal fields and ionic charge transfer change the form factors by up to a few percent, mainly in the range of sin 0/k < | Ä" 1 . Although electron correlation and crystal fields are small perturbations, their effects on the density and form factor are not additive. Densities or form factors of atomic and ionic systems are very similar; [Li°F°] and [Li + F~] procrystals differ by an effective charge transfer of not more than 0.4 e. Charge transfer and charge overlap in crystals cannot be distinguished uniquely. When the experimental data on Li 2 BeF 4 (approximately reproduced by 3/4 atomic plus 1/4 ionic procrystal) are interpreted from the atomic viewpoint, the atomic partial charges are as low as 0.1 e (Li 2 01 Be + 0,2 F4 *); when interpreted from the ionic viewpoint, the charges are much higher, namely 0.7 e. Intermediate viewpoints are also possible. 
  Reference    Z. Naturforsch. 48a, 180—192 (1993); received January 11 1992 
  Published    1993 
  Keywords    Electron densities, Form factors, X-ray diffraction, Ionic charges, Ionic bonding 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0180.pdf 
 Identifier    ZNA-1993-48a-0180 
 Volume    48