X-ray orthonormal orbital model of crystallography.
Item
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Title
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X-ray orthonormal orbital model of crystallography.
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Identifier
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AAI9315469
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identifier
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9315469
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Creator
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Huang, Lulu Shulian.
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Contributor
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Adviser: Lou Massa
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Date
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1993
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Language
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English
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Publisher
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City University of New York.
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Subject
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Chemistry, Analytical | Chemistry, Physical
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Abstract
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We discuss how the results of quantum mechanics can be brought to bear on the problem of crystallography. Quantum conditions are used to describe a crystal so that quantum mechanically valid properties may be extracted from X-Ray diffraction experiments. Such quantum properties are not now routinely available to a crystallographer, even though the information is inherent to crystallographic data.;Our goal is to obtain both quantum electronic and atomic structure results. We use three types of observational equations and their derivatives, and derive a least squares procedure to treat electronic and atomic structure parameters. We designed a computer program to execute a least squares procedure. For testing our formalism and program, some simulated results using a Hydrogen atom, Hydrogen molecule, nitrogen molecule, and methane molecule are shown. Also a molecule of maleic anhydride is tested based on real X-Ray diffraction experimental data. In the latter case we obtain a better {dollar}\chi\sp2{dollar} value than had previously been obtained with the same experimental data.;For simplicity we implement our method to obtain only the electronic structure of valence electrons. Therefore the scattering factor of core electrons is assumed known. In fact the core scattering factors for most atoms has been supplied in numerical form by the International Tables of Crystallography. Using a least squares procedure we convert the numeric core scattering factors to an analytical form for the first row atoms B, C, N, O, and F. In analytical form the core scattering factors are much more convenient to use in our overall program and will be of use to others.;Our least squares procedure converges to solution more efficiently if a good initial guess is used for the elements of the molecular density matrix P corresponding to either (a) a sum of spherical atoms or (b) an extended Huckel molecular wavefunction.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
