 21  Author
 Jiahu Wang, VedeneH. Smith  Requires cookie*   Title
 Ab initio Study of the Spin Density of Nitroxide Radicals    Abstract
 The spin densities of the nitroxides H 2 NO, (CH 3)HNO and (CH 3) 2 NO have been studied by iterative CI methods. Calculations at different geometries with various basis sets were performed. It is found that the spin distribution is delocalized within the NO group, and substitution of the hydrogen atoms on the nitroxyl group by methyl groups changes the spin distribution significantly. Electron correlation, as well as the basisset quality, plays an important role for the fluctuation of spin populations in the nitroxide radicals. It has been found that the spin density map can be predicted fairly well when correlation was included at certain levels and reasonable quality basis sets were employed. The spin polarization mechanism has been studied through a core excitation method. The superiority of localspindensity (LSD) theory over the unrestricted HartreeFock (UHF) method in spin property studies is discussed.   
Reference
 Z. Naturforsch. 48a, 109—116 (1993); received July 4 1992   
Published
 1993   
Keywords
 Spin density, Nitroxide radicals, Iterative CI, Spin polarization effect, LDA   
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 ZNA199348a0109    Volume
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22  Author
 D. Bordeaux, J. X. Boucherle, B. Delley, B. Gillon, E. Ressouehe, J. Schweizer  Requires cookie*   Title
 Experimental and Theoretical Spin Densities in Two Alkyl Nitroxides    Abstract
 The spin density in the two alkyl nitroxide compounds 4oxoand 4hydroxy2,2,6,6tetramethyl1piperidinyloxy (tempone and tempol) has been determined by polarisedneutron diffraction and compared to theoretical predictions obtained in both the Unrestricted HartreeFock and the Local Spin Density approaches.   
Reference
 Z. Naturforsch. 48a, 117—119 (1993); received February 7 1992.   
Published
 1993   
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 ZNA199348a0117    Volume
 48  
23  Author
 J.X Boucherle, E. Ressouche, J. Schweizer, B. Gillon, P. Rey  Requires cookie*   Title
 Spin Densities in CopperNitronyl Nitroxide Complexes    Abstract
 The spin density in two coppernitronyl nitroxide complexes, viz. bis(hexafluoroacetylacetonato)(2,4,4,5,5pentamethylloxyimidazoline 3oxide)copper(II) and dichlorobis(2phenyl4,4,5,5tetramethylloxyimidazoline 3oxide)copper(II), has been determined by polarisedneutron diffraction. Spin populations and unpaired electron wave functions have been refined.   
Reference
 Z. Naturforsch. 48a, 120—122 (1993); received February 7 1992   
Published
 1993   
Keywords
 Nitronyl nitroxide free radicals, Copper complexes, Polarised neutron diffraction, Spin density   
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 ZNA199348a0120    Volume
 48  
25  Author
 KennethE. Edgecombe, VedeneH. Smith, Florian MüllerPlathe  Requires cookie*   Title
 Nonnuclear Maxima in the Charge Density    Abstract
 Basisset and electroncorrelation 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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 ZNA199348a0127    Volume
 48  
26  Author
 N. Sukumar, B. M. Deb, Harjinder Singh  Requires cookie*   Title
 Electron Charge and Current Densities, the Geometrie Phase and Cellular Automata    Abstract
 Some consequences of the quantum fluid dynamics formulation are discussed for excited states of atoms and molecules and for timedependent processes. It is shown that the conservation of electronic current density j(r) allows us to manufacture a gauge potential for each excited state of an atom, molecule or atom in a molecule. This potential gives rise to a tube of magnetic flux carried around by the manyelectron system. In timedependent situations, the evolution of the electronic density distribution can be followed with simple, sitedependent cellular automaton (CA) rules. The CA consists of a lattice of sites, each with a finite set of possible values, here representing finite localized elements of electronic charge and current density (since the charge density Q no longer suffices to fully characterize a timedependent system, it needs to be supplemented with information about the current density j). Our numerical results are presented elsewhere and further development is in progress.   
Reference
 Z. Naturforsch. 48a, 134—136 (1993); received December 31 1991   
Published
 1993   
Keywords
 Electronic phase, Current density, Anyons, QFD, Cellular automata   
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 ZNA199348a0134    Volume
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27  Author
 ShridharR. Gadre, Christoph Kölmel, Michael Ehrig, Reinhart Ahlrichs  Requires cookie*   Title
 Visualization of Shapes of Molecular Anions    Abstract
 A recently formulated strict definition of the boundary surface of molecular anions has been employed for the visualization of some simple systems. The examples included are CN", N 3 , N0 3 , ClO^, C10 3 , and Br0 3 ions. A discussion on the anisotropy of electrostatic interaction of these anions is also presented.   
Reference
 Z. Naturforsch. 48a, 137—140 (1993); received January 3 1992   
Published
 1993   
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 ZNA199348a0137    Volume
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28  Author
 P. Lazzeretti, M. Malagoli, R. Zanasi  Requires cookie*   Title
 Use of Symmetry in Coupled HartreeFock Calculations of Nonlinear Response Tensors in Molecules    Abstract
 A new computational scheme for electric dipole hyperpolarizabilities has been devised within the coupled HartreeFock method. Only the projection of secondorder perturbed orbitals onto the subspace spanned by unperturbed virtual orbitals is computed. The entire molecular symmetry is exploited to reduce computational effort: a reduced twoelectron integral file containing only symmetrydistinct matrix elements over the atomic basis functions is processed at each iteration. In addition, only symmetryindependent firstand secondorder perturbed density matrices need to be calculated. An efficient computer program implementing the present approach has been developed.   
Reference
 Z. Naturforsch. 48a, 141—144 (1993); received September 23 1991   
Published
 1993   
Keywords
 Second hyperpolarizability, Ab initio calculation, Molecular symmetry   
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 ZNA199348a0141    Volume
 48  
29  Author
 SudhirA. Kulkarni, ShridharR. Gadre  Requires cookie*   Title
 On the Topography of Electron Momentum Densities of Linear Molecules    Abstract
 A topographical study of the electron momentum density (EMD) of some linear molecules is presented with special emphasis on the bonddirectionality principle. A new approach to the bonddirectionality (BD) principle has been proposed. This is based on the analysis of curvatures of critical points at p = 0 and elsewhere on the bonding axis. The linear molecules are classified into three broad categories: those which fully obey or disobey the BD principle as well as those which satisfy it only partly. The Laplacian of the EMD at p = 0 has been associated with the quality of the wavefunction via the electron density in the tail region. Also, the similarity in the critical structure of both the EMD and the spherically averaged EMD at the origin is brought out.   
Reference
 Z. Naturforsch. 48a, 145—150 (1993); received January 3 1992   
Published
 1993   
Keywords
 Electron momentum densities, Eigenvalues, Critical points, Topography, Bond directionality   
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 ZNA199348a0145    Volume
 48  
31  Author
 Michael Springborg  Requires cookie*   Title
 A Comparison between Polyatecylene and Polycarbonitrile    Abstract
 Results of a theoretical, comparative study of the electronic properties of transpolyacetylene and polycarbonitrile are reported. Polyacetylene consists of zigzag chains of CH units, whereas polycarbonitrile has every second CH unit replaced by an N atom. Groundstate properties (structure, electronic bonds and bands, densities of states, momentum distributions, and reciprocal form factors) of the periodic, infinite, isolated chains are studied by means of firstprinciples, densityfunctional calculations. It is demonstrated how the presence of the (nitrogen) heteroatoms in the backbone of polycarbonitrile leads to a partial localization of the electrons. In order to investigate charged chains, model calculations are subsequently performed. These indicate solitons but not polarons to be stable. In total, the analysis demonstrates how the combination of information that can be obtained from various experiments provides a detailed description of the compounds.   
Reference
 Z. Naturforsch. 48a, 159—164 (1993); received November 26 1991   
Published
 1993   
Keywords
 Conjugated polymers, Structure, Electronic structure, Momentum densities, Solitons   
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 ZNA199348a0159    Volume
 48  
32  Author
 A. Bansil  Requires cookie*   Title
 Modern Band Theory of Disordered Alloys: Basic Concepts Including a Discussion of Momentum Densities    Abstract
 An overview of some of the basic concepts in the modern firstprinciples band theory of disordered alloys is given. The question of how the notion of Bloch energy bands and Fermi surfaces generalizes to the case of the disordered system, insofar as the average electronic spectrum is concerned, is stressed. The theory is illustrated with examples chosen from the work on binary alloys; a few examples of the very recent studies of disordered phases of the highT c superconductors are also included. The application of the alloy theory to obtain electron and electronpositron momentum densities involved in the analysis of Compton scattering and positron annihilation (angular correlation) experiments in alloys is discussed, with a selection of relevant theoretical and experimental studies.   
Reference
 Z. Naturforsch. 48a, 165—179 (1993); received January 25 1992   
Published
 1993   
Keywords
 Disordered alloys, KKRCPA, Momentum densities, Compton scattering, Positron annihilation (ACAR)   
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 ZNA199348a0165    Volume
 48  
33  Author
 B. Hess, H. L. Lin, J. E. Niu, W.H E Schwarz  Requires cookie*   Title
 Electron Density Distributions and Atomic Charges    Abstract
 Accurate electron densities and Xray 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, Xray diffraction, Ionic charges, Ionic bonding   
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 ZNA199348a0180    Volume
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35  Author
 Claudia Blaas, Josef Redinger, Raimund Podloucky, Peter Jonas, Peter Schattschneider  Requires cookie*   Title
 Calculation of Compton Profiles Using a Multipole Expansion of the Momentum Density    Abstract
 A practical method for the calculation of Compton profiles for cubic systems with O and O h symmetry is presented that is based on a multipole expansion of the electron momentum density (EMD) in terms of cubic harmonics. The central quantities, the expansion coefficients, are determined by a Gaussiantype integration (special directions) over the angular coordinates. From these coefficients the coefficients of an analogous expansion of the Compton profile can be directly calculated, establishing a transparent relationship between the electron momentum density and the Compton profile. This direct relationship offers the possibility of tracing back Comptonprofile anisotropics to EMD anisotropics more easily, as demonstrated for MgO and FeAl.   
Reference
 Z. Naturforsch. 48a, 198—202 (1993); received December 24 1991   
Published
 1993   
Keywords
 Compton profile, Electron momentum density, Multipole expansion, MgO, FeAl   
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 ZNA199348a0198    Volume
 48  
36  Author
 JohnE. Harriman  Requires cookie*   Title
 Electron Densities, Momentum Densities, and Density Matrices    Abstract
 Relationships among electron coordinatespace and momentum densities and the oneelectron 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 finitebasisset 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 determined 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 constructing 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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 ZNA199348a0203    Volume
 48  
38  Author
 VedeneH. Schmider, Smith, Wolf Weyrich  Requires cookie*   Title
 Hartmut    Abstract
 A recently developed method for the leastsquares reconstruction of oneparticle reduced density matrices from oneparticle expectation values has been applied to isotropic Compton profiles of neon from the literature. The resulting densities in momentum and position space are compared with the ones obtained from abinitio calculations.   
Reference
 Z. Naturforsch. 48a, 221—226 (1993); received June 3 1992   
Published
 1993   
Keywords
 Density matrix, Compton profile, Leastsquares fit, Atomic orbitals, Reconstruction   
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 ZNA199348a0221    Volume
 48  
40  Author
 K. Sturm  Requires cookie*   Title
 Dynamic Structure Factor: An Introduction    Abstract
 The doubly differential crosssection for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, xrays and highenergy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the densitydensity correlation function, is a property of the manybody system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the densitydensity response function defined in linearresponse theory is shown using the fluctuationdissipation theorem. This is important for calculations, since the response function can be calculated approximately from the independentparticle response function in selfconsistent field approximations, such as the randomphase approximation or the localdensity approximation of the density functional theory. Since the densitydensity response function also determines the dielectric function, the dynamic structure can be expressed by the dielectric function.   
Reference
 Z. Naturforsch. 48a, 233—242 (1993); received December 10 1991   
Published
 1993   
Keywords
 Scattering theory, Dynamic structure factor, Inelastic photon scattering, Inelastic electron scattering, Inelastic neutron scattering, Dielectric function   
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 ZNA199348a0233    Volume
 48  
