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  • Atomic, Molecular and Optical Physics  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Gradient expansion correction to the Dirac exchange term in statistical models for the Na atom with shell structure (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1973-1978 
    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: In the study of the ground-state binding energy of atoms, relatively more attention has been paid to the gradient expansion of the kinetic energy term of the Thomas-Fermi-Dirac model than to the gradient expansion of the exchange term of this model. Recently Shih and Shih, Murphy, and Wang have focused on this problem and calculated the first gradient expansion correction to the Dirac exchange term by making use of electron densities constructed from Hartree-Fock wave functions. In previous work, aimed to introduce the shell structure of atoms via a variational procedure using the energy density functional formalism, electron densities have been obtained for the Na atom within the Thomas-Fermi-Dirac model with and without the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. In this paper we make use of the respective electron densities and calculate the first gradient expansion corrections to the Dirac exchange term. The results show that, for the Na atom, the magnitude of this correction is about 1% of the magnitude of the total binding energy.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230611
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  • 2
    Electronic Resource
    Electronic Resource
    Lower bounds to the Weizsäcker correction in statistical models for the Na atom with shell structure (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 61-64 
    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: Recently, using the Na atom as an example, Csavinszky has introduced the shell structure into the Thomas-Fermi-Dirac energy-density functional with the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. Also recently, two rigorous lower bounds to the Weizsäcker correction in atoms of spherical symmetry have been derived by Gadre and Pathak. The present work investigates the magnitudes of the lower bounds in statistical models of the Na atom with shell structure.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560240105
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  • 3
    Electronic Resource
    Electronic Resource
    Variational principle for obtaining approximate analytical solutions of the temperature-perturbed Thomas-Fermi equation for compressed atoms (1980)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 17 (1980), S. 737-745 
    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 temperature correction to the Thomas-Fermi (TF) model of a neutral compressed atom has been given by Marshak and Bethe. The aim of the present work is to point out that, by formulating a variational principle, one may obtain approximate analytical solutions of the temperature-perturbed TF equation. As a test of the proposed theory, the total energy of a Ne atom, confined to a spherical container, has been calculated as a function of the container radius at T = 0°K. Comparison of the data obtained with energy values calculated by Ludeña, using a self-consistent-field Hartree-Fock approach, shows reasonable agreement. It is, therefore, concluded that the variational approach suggested in this paper is a sound one.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560170414
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