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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 21-29 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Inhomogeneous liquids in the presence of an external potential are considered. Exact force balance equations are written explicitly for (a) the classical case with pairwise interactions and (b) the ground-state quantal case of fermions with a general interaction, which embraces the Coulomb repulsion for electrons. Illustrative examples are given in both cases (a) and (b). Finally, a link between (a) and (b) is forged by considering the case of ensembles of finite systems.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 21-29, 1997
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 70 (1998), S. 779-788 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ground-state density amplitude {ρ(r)}1/2 for atoms and molecules satisfies a Schrödinger equation in which the customary one-body potential energy V(r) of density functional theory is supplemented by the addition of the Pauli potential Vp(r). Since neither the exchange-correlation potential Vxc or Vp are presently known as functionals of the electron density ρ(r), approximations are currently unavoidable. Here, widespread use is made of semiclassical approximations, within a self-consistent field framework both with and without magnetic fields. The importance of low-order gradient quantities ∇2ρ/ρ and (∇ρ/ρ)2 is one focal point, while a generalized low-density approximation is another. New relativistic differential equations are given. Then, the arguments are generalized to embrace the so-called Slater sum P(r, β) : β=(kβT)-1, of statistical mechanics, generated by the one-body potential V(r). This is a generalized partition function, and differential equations are set up for this quantity P(r, β) with and without external fields. Finally, some potentially fruitful directions for treating cylindrically symmetric inhomogeneous electron liquids are outlined, following the very recent work of Amovilli and March. These include modeling the Slater sum along the electric field direction for the Stark effect in a hydrogenlike atom.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 779-788, 1998
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 145-149 
    ISSN: 0020-7608
    Keywords: density functional theory ; reduced density gradients ; self-consistent density equation ; generalized Thomas-Fermi approximation ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We prove the following results, relevant for the density functional theory: the Thomas-Fermi-Dirac theory, generalized to include the contribution due to the high electron density result of Gell-Mann and Brueckner for the correlation energy, is shown to lead to a differential equation for the self-consistent ground-state density n(r) in atoms and molecules in the form F(n, {∇n/n}2, ∇2n/n)=1, where the function F is given explicitly. A straightforward extension yields a similar result for the equation determining the Pauli plus exchange-correlation potential and for the divergence of the many-electron force.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 145-149, 1998
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 721-726 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It has been known since the work of March and White that the simplest nonrelativistic density functional theory, namely, the statistical method of Thomas, Fermi, and Dirac, sums subseries of the so-called 1/Z expansion to yield, for heavy neutral atoms, the ground-state energy E= - a0Z7/3+ a1Z2-a2Z5/3+⋅⋅⋅. The term of O(Z5/3) is the Dirac-Slater exchange energy Eexc, and it is of considerable interest to know at what order the correlation energy Ecorr enters this expansion. Dimensional scaling considerations by Kais et al. suggested Ecorr∝Z4/3 in the limit of large Z. Here, attention is focused on whether this can be distinguished empirically from a term of the form (aZ ln Z+bZ) for neutral atoms. If the latter term is correct, then a relationship between Ecorr and the Shannon information entropy can be forged analytically for large atomic number Z in nonrelativistic theory.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 721-726 (1998)
    Additional Material: 2 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 66 (1998), S. 281-283 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A long-term aim in density functional theory is to obtain the kinetic energy density t(r) in terms of the ground-state electron density ρ(r). Here, t(r) is written explicitly in terms of ρ(r) for an arbitrary number N of closed shells in a bare Coulomb field. In the limit as N→∞, closed results for t(r) follow from the earlier analysis of ρ(r) by Heilmann and Lieb. [Phys. Rev. A 52, 3628 (1995)].   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 281-283, 1998
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 907-917 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Density functional theory for the pair potential in liquid Na near melting is first compared with that extracted by liquid structure inversion. All the main features are in quantitative agreement. Quantum chemical representations of metallic crystalline energies are then treated as a function of local coordination number and near-neighbor distance. K and Cu are especially referred to, in different lattice structures. Finally, the Tersoff potential based on density functional theory is discussed in relation to the cleavage force in ideal crystalline Si, and is related to bond breaking.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 907-917, 1997
    Additional Material: 4 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 263-272 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The local energy equation derived by Dawson and March (1984) following the study of Cohen and Frishberg (1976) involves the low-order density matrices. Using this equation, a formally exact route is laid down by means of which the exchange-correlation potential of density functional theory can be derived in terms of the third- and lower-order density matrices. An integral equation for an approximate exchange potential is obtained, which may be solved iteratively within the Slater-Kohn-Sham scheme. © 1997 John Wiley & Sons, Inc.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 695-707 
    ISSN: 0020-7608
    Keywords: clusters ; amorphous solids ; liquids ; metals ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Attention is first drawn to disordered condensed phases of Si and C. Amorphous Si, with clear-cut tetrahedral coordination, is treated by combining sp3 hybridization with a random network model of structure, X-ray and electron diffraction experiments confirm both electron density and structural models. Recent work using the Car-Parrinello technique is then reviewed, with the aim of comparing and contrasting amorphous C and Si and their liquid phases. After a brief review of the structure and bonding in clusters of Al and P atoms, some results on clusters of Na are presented and related to cohesion in the condensed metallic phase. Then, fission of doubly charged Na clusters is treated at some length and, in particular, is related to quantum chemical procedures. A short summary concerning π-bands in graphitic and boron nitride layers is followed by a discussion of BN alternants, both buckytubes and octahedral symmetry cages being considered, along with C analogs. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 695-707, 1997
    Additional Material: 11 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 551-557 
    ISSN: 0020-7608
    Keywords: generalized local density approximation ; force balance equation ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: X-ray scattering allows, for example, the ground-state electron density of a crystal, say hexagonal close-packed Be, or a molecular solid, to be extracted. Two routes will be discussed by means of which progress should prove possible on fundamental aspects of density functional theory, given such information on the electron density. In the first of these, the proposal is to extract from X-ray scattering data a function of the density which generalizes the concept of a local density approximation. Specifically, in a closed-shell atom, such as Kr or Xe, the monotonic decay of the electron density from the nucleus is exploited to propose a generalization of local density theories such as Thomas-Fermi, plus Dirac-Slater exchange together with Gell-Mann and Brueckner correlation. In the second route considered, an essentially experimental area termed quantum crystallography is brought into contact with the density matrix approach to density functional theory proposed by Holas and March. Here, though functions of the density are not presently extractable from crystal Bragg reflection data, a method is summarized, due to Holas and this writer, whereby the exchange-correlation potential can be extracted for a given crystal such as Be. This is possible by generalizing the approach of quantum crystallography to include a potential-locality constraint.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 551-557, 1998
    Additional Material: 1 Ill.
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