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  • 1
    Electronic Resource
    Electronic Resource
    A topological definition of a Wigner–Seitz cell and the atomic scattering factor (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 714-725 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An atom is defined as a region of space bound by a surface of local zero flux in the gradient vector field of the electron density. The same boundary condition defines a proper open system, one whose observables and their equations of motion are defined by quantum mechanics. Applied to a crystal, this boundary condition coincides with the original definition of the atomic cell in metallic sodium given by Wigner & Seitz. It is proposed that it be used to generalize the concept of a Wigner–Seitz cell, defining it as the smallest connected region of space bounded by a `zero-flux surface' and exhibiting the translational invariance of the crystal. This definition, as well as removing the arbitrary nature of the original method of construction of the cell in the general case, maximizes the relation of the cell and the derived atomic form factors to the physical form exhibited by the charge distribution of its constituent atoms. The topology of the electron density, as summarized in terms of its critical points, also defines the atomic connectivity and structure within a cell. Attention is drawn to the correspondence of the symmetries of the structural elements determined by the critical points with the site symmetries tabulated in International Tables for Crystallography. The atomic scattering factor is defined for an atom in a crystal and determined in ab initio calculations for diamond and silicon. The transferable nature of atomic charge distributions is demonstrated. It enables one to estimate a structure factor and its phase in a crystal using the density of an atom or functional group obtained in a molecular calculation. Atoms in a crystal, along with defects and vacancies, are identifiable with bounded regions of real space. Their properties are additive and are defined by quantum mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767394003740
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  • 2
    Electronic Resource
    Electronic Resource
    Variational principle and path integrals for atoms in molecules (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 43 (1992), S. 677-699 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two things were done in this paper: (i) A generalization of Schwinger's variational principle to a subsystem was developed within the framework of quantum field theory and applied to the theory of atoms in molecules. This work generalizes the previous derivation given in the Schrödinger formulation. (ii) It is demonstrated that Feynman's path integral, when expressed in terms of the coherent-state representation, can be constructed for a subsystem of a many-electron system if a divergence term, which serves as a variational constraint in the definition of an atom in a molecule, is added to the Lagrangian. This formulation is equivalent to the atomic statement of the variational principle if the divergence term is suitably constructed. It is shown that the path integral can be expressed as a product of the individual atomic contributions to the steps along the paths with the action being determined by a corresponding sum of the atomic contributions to the action integral. © 1992 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560430507
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  • 3
    Electronic Resource
    Electronic Resource
    A regional embedding method (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 44 (1992), S. 997-1013 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new variational embedding method is derived. This method couples Nesbet's use of the R-matrix in the determination of the electronic structure of a crystal with the energy variational technique. The procedure is based on the observation that in many cases the properties for a spatial region of a system change by relatively small amounts when the region is transferred to another system. The transfer of the region from one system to another is accomplished by the embedding potential that is obtained by the inversion of the R-matrix and its energy derivative. It is shown that the interaction between two connected regions can be written as a surface term that is obtained by the continuity conditions on the wave function and its derivative on the surface. The existence of an identity resolution on the surface is demonstrated and this result is used to derive the R-matrix and its inverse. An application of this method to H2+ is given, which shows that the method is accurate and reliable if one chooses the appropriate basis set to construct the R-matrix and to perform the variation. © 1992 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560440605
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    Paper (German National Licenses)
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