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1993 (7)
1Author    Renzo Restori, Dieter SchwarzenbachRequires cookie*
 Title    X-Ray Diffraction Study of the Electron Density and Anharmonicity in K 2 PtCl 6  
 Abstract    X-ray diffraction data in heavy-atom compounds may be sensitive to anharmonic atomic displacements, since the large core electron densities result in appreciable scattering amplitudes at large reciprocal distances. Since bonding electron densities may also exhibit sharp features affecting high-order reflections, they may be difficult to distinguish from anharmonic effects. We have ana-lyzed an accurate room-temperature single-crystal X-ray data set of K 2 PtCl 6 using least-squares anharmonic displacement and charge density formalisms. The Hirshfeld charge density formalism, which has successfully been applied to many light-atom structures, fails to parametrize satisfactorily the data, whereas the electron densities at K and CI are easily accounted for by an anharmonic Gram-Charlier expansion to 4th order. Densities around Pt are parametrized only by a combination of anharmonicity and charge density formalisms. If economical parametrizations of the experimental data are preferred to more complicated ones, anharmonicity may be conjectured to play an impor-tant role while the main bonding feature consists of a preferential occupation of the 5d-orbitals of Pt with t 2g symmetry. 
  Reference    Z. Naturforsch. 48a, 12—20 (1993); received December 19 1991 
  Published    1993 
  Keywords    Charge density, Thermal motion, Anharmonicity, X-ray diffraction, d-orbitals 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0012.pdf 
 Identifier    ZNA-1993-48a-0012 
 Volume    48 
2Author    R. Destro, F. MeratiRequires cookie*
 Title    Preliminary Results of a 20 K X-Ray Study of Citrinin  
 Abstract    A total of about 37 000 diffracted intensities has been measured at 20 K for a spherical single crystal of citrinin. Using a multipole formalism to interpret the X-ray data, maps of the charge density and of its Laplacian, as well as for the electrostatic potential have been derived. A value of 7(2) D has been obtained for the magnitude of the molecular dipole moment. A study of the electric field gradient (EFG) at the nuclei has yielded the atomic quadrupole coupling constants (QCC) and asymmetry parameters (r\). A topological analysis of the charge density has been performed to characterize the intramolecular covalent and hydrogen bonds. tures, in the sequence: 293, 20, 240, and again 293 K. From the combined X-ray results of the two investiga-tions, the thermodynamic parameters for the proton transfer occurring in the crystals of citrinin have been derived [2]. Furthermore, it has been shown that it can be safely assumed that the 20 K X-ray structure of citrinin describes the pure p-quinonemethide form. In h16b 4a 018 Fig. 1. Atomic numbering scheme for citrinin. 
  Reference    Z. Naturforsch. 48a, 99—104 (1993); received October 18 1991 
  Published    1993 
  Keywords    Electrostatic properties, Charge density, Topological analysis, Very low temperature, Citrinin 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0099.pdf 
 Identifier    ZNA-1993-48a-0099 
 Volume    48 
3Author    Teiji Kobayasi, Hisashi NaraRequires cookie*
 Title    Core-Orthogonalization Effect in Pseudopotential Theory of the Charge Density Distribution of Valence Electrons in Semiconductors with Comments on the Effects in Momentum Space  
 Abstract    A pseudopotential calculation has been performed for the charge density distribution in Si and Ge, with the core-orthogonalization terms fully included. The state of a positron subject to the Coulomb field of the resultant electron distribution in Si is also calculated. A possible improvement of the calculated distributions of electrons and positrons in momentum space is discussed. 
  Reference    Z. Naturforsch. 48a, 193—197 (1993); received January 3 1992 
  Published    1993 
  Keywords    Charge density, Momentum density, Pseudopotential theory, Core orthogonalization, Semiconductors 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0193.pdf 
 Identifier    ZNA-1993-48a-0193 
 Volume    48 
4Author    DouglasM. CollinsRequires cookie*
 Title    Entropy Maximizations on Electron Density  
 Abstract    Incomplete and imperfect data characterize the problem of constructing electron density represen-tations from experimental information. One fundamental concern is identification of the proper protocol for including new information at any stage of a density reconstruction. An axiomatic approach developed in other fields specifies entropy maximization as the desired protocol. In particular, if new data are used to modify a prior charge density distribution without adding extraneous prejudice, the new distribution must both agree with all the data, new and old, and be a function of maximum relative entropy. The functional form of relative entropy is a = — g In (g/z), where g and x respectively refer to new and prior distributions normalized to a common scale. Entropy maximization has been used to deal with certain aspects of the phase problem of X-ray diffraction. Varying degrees of success have marked the work which may be roughly assigned to categories as direct methods, data reduction and analysis, and image enhancement. Much of the work has been expressed in probabilistic language, although image enhancement has been somewhat more physical or geometric in description. Whatever the language, entropy maximization is a specific and deterministic functional manipulation. A recent advance has been the description of an al-gorithm which, quite deterministically, adjusts a prior positive charge density distribution to agree exactly with a specified subset of structure-factor moduli by a constrained entropy maximization. Entropy on an iV-representable one-particle density matrix is well defined. The entropy is the expected form, and it is a simple function of the one-matrix eigenvalues which all must be non-neg-ative. Relationships between the entropy functional and certain properties of a one-matrix are discussed, as well as a conjecture concerning the physical interpretation of entropy. Throughout this work reference is made to informational entropy, not the entropy of thermodynamics. 
  Reference    Z. Naturforsch. 48a, 68—74 (1993); received May 26 1992 
  Published    1993 
  Keywords    Charge density, Correlation energy, Density matrix, Entropy maximization, Hohenberg-Kohn theorem 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0068.pdf 
 Identifier    ZNA-1993-48a-0068 
 Volume    48 
5Author    NielsK. HansenRequires cookie*
 Title    Electrostatic Properties of Ions in Crystals from X-Ray Diffraction Data  
 Abstract    A procedure for calculating the electrostatic potential and the electrostatic energy of an ion in a crystal is presented. It is based on a mixed direct and reciprocal space approach, and it takes into account the detailed charge density distribution in the crystal which can be obtained from accurate X-ray diffraction measurements. 
  Reference    Z. Naturforsch. 48a, 81—84 (1993); received December 24 1991 
  Published    1993 
  Keywords    Electrostatic potential, X-ray diffraction, Charge density, Ionic crystals, Ionic con-duction 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0081.pdf 
 Identifier    ZNA-1993-48a-0081 
 Volume    48 
6Author    KennethE. Edgecombe, VedeneH. Smith, Florian Müller-PlatheRequires cookie*
 Title    Nonnuclear Maxima in the Charge Density  
 Abstract    Basis-set and electron-correlation effects on the appearance and disappearance of nonnuclear maxima in the electron density are examined in Li 2 , Na 2 , Na 4 and Na 5 . It is shown that nonnuclear attractors can be removed in all cases except Li 2 . The appearance of a pseudoatom in a lithium molecule correlates remarkably well with the size of the region, in an atomic calculation, of V 2 Q (r) for the valence shell of the atom. This and the fact that the pseudoatom is also present in the promolecule indicate that the pseudoatoms are remnants of, or in fact are portions of, atoms that are not perturbed enough in the molecule to remove an essentially atomic characteristic. 
  Reference    Z. Naturforsch. 48a, 127—133 (1993); received May 27 1992 
  Published    1993 
  Keywords    Li 2, Na 2, Topological analysis, Pseudoatoms, Charge density, Electron correlation 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0127.pdf 
 Identifier    ZNA-1993-48a-0127 
 Volume    48 
7Author    Jean-Louis CalaisRequires cookie*
 Title    Momentum Distribution and Charge Density in Solid-State Theory  
 Abstract    We present a discussion of a number of conceptual and methodological aspects associated with the theoretical characterization and computation of charge densities and momentum distributions in solids. The main ambition has been to stress properties that both exact and approximate quantities must possess. We have also attempted to point out conceptual and computational trends which would seem to be of importance for the future of the subject. 
  Reference    Z. Naturforsch. 48a, 151—158 (1993); received May 14 1992 
  Published    1993 
  Keywords    Solid-state theory, Charge density, Momentum density, Density matrices, Hartree-Fock approximation, Density functional theory 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0151.pdf 
 Identifier    ZNA-1993-48a-0151 
 Volume    48