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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 741-746 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The model based on the assumption of the existence of an interatomic distance-dependent, local, effective crystal field applied to the alkaline metals (Int. J. Quantum Chem. 52, 321-328 (1994)) is modified and applied to the diamondlike structure crystals (C, Si, Ge, Sn). In the referred to model, a part of the electron density was missed - not included in the calculation (the density in the spaces between the shells). Such an approach could be used for the alkaline metals, but for the covalent crystals, this is a bad approximation. To avoid that problem, we assumed that the atom shells can overlap in such a way that the entire electron density is taken into the calculation. In this case, the electron density is “moved” from the outside of the shells mostly into the interatomic bond region. We applied the modified model to the calculation of the binding energy and the bulk modulus for the diamondlike crystals. The results show that well-chosen parameters allows one to reproduce the proper values of the binding energy at the equilibrium position. The bulk moduli calculated for these crystals are in quite good agreement with ones calculated as (regular crystal structure) B = 1/3(C11 + 2 C12), where C11 and C12 are elastic constants. © 1997 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 543-549 
    ISSN: 0020-7608
    Keywords: electron density ; muffin tin ; variational problem ; tranversality condition ; metallic crystal ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The reliability of a variational modeling of electron density in metallic crystal is investigated. The crystal is described within muffin-tin approximation referring to some from the ideas of the divide-and-conquer techniques. The calculations are performed with application of density functional and calculus of variation methods. The problem is formulated as finding a transversal with moving boundaries. Solution of the variational equation formulated for ρ indicates that a first derivative of the electron density must be zero on the border of the muffin tin. An illustrative example of lithium crystal is presented. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 543-549, 1997
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 499-501 
    ISSN: 0020-7608
    Keywords: density-functional theory ; variational principle ; reciprocal problem ; maximum principle ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Formalism of density-functional theory (DFT) is based on the calculus of variation. In the Hohenberg and Kohn theorem, a variational equation minimizing electronic energy with respect to an electron density is constructed. The calculus of variation allows one to formulate a problem which is reciprocal to an original one. Also, we may consider the problem of finding the electron density determining a given energy E=E[ρ] for a maximum number N=N[ρ] of the electrons forming the system. In this work, the reciprocal variational problem is discussed. Mathematical considerations are followed by a presentation of an application of the reciprocal problem (maximum entropy principle). Other possibilities of the applications are sketched.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 499-501, 1997
    Type of Medium: Electronic Resource
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