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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 10 (1976), S. 545-550 
    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
    Additional Material: 4 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 56 (1995), S. 489-498 
    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: The Boltzmann-Shannon (BS) information entropy Sρ = ∫ ρ(r)log ρ(r)dr measures the spread or extent of the one-electron density ρ(r), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically computed, not even for simple quantum mechanical systems such as, e.g., the harmonic oscillator (HO) and the hydrogen atom (HA) in arbitrary excited states. Here, we first review (i) the present knowledge and open problems in the analytical determination of the BS entropies for the HO and HA systems in both position and momentum spaces and (ii) the known rigorous lower and upper bounds to the position and momentum BS entropies of many-electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the BS entropies and various density functionals. Particular cases of these results are rigorous relationships of the BS entropies and some relevant density functionals (e.g., the Thomas-Fermi kinetic energy, the Dirac-Slater exchange energy, the average electron density) for finite many-electron systems. © 1995 John Wiley & Sons, Inc.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 627-632 
    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: The Weizsäcker functional TW is a necessary element to explain basic physical and chemical phenomena of atomic and molecular systems in the general density functional theory initiated by Hohenberg and Kohn. Here, rigorous inequalities which involve the functional TW and two arbitrary power-type density functionals ωα ≔ ∫ ρα(r)dr are found by the successive applications of Sobolev and Hölder inequalities. Particular cases of these inequalities give lower bounds to the Weizsacker functional of an N-electron system in terms of a fundamental and/or experimentally measurable quantity such as, e.g., the Thomas-Fermi kinetic energy T0, the Dirac-Slater exchange energy K0 and the average electronic density 〈ρ〉 in doing so, some known relationships appear. A numerical Hartree-Fock study of the accuracy of some resulting lower bounds is carried out. Finally, rigorous relationships between the Weizsäcker functional and the Boltzmann-Shannon information entropy of the system under consideration are given. © 1995 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 57 (1996), S. 559-566 
    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: We present ab initio calculations carried out in the framework of the G2 theory on the singlet and triplet potential energy surfaces corresponding to the gas-phase between CH+2 and PO. The global minimum of both potential energy surfaces is a cyclic singlet-state cation. Oxygen attachment of PO to CH+2 in a triplet configuration is accompanied by a P(SINGLEBOND)O bond fission, with the result that the corresponding global minimum is an ion-dipole complex between P+(3P) and formaldehyde. This is also consistent with the fact that our results predict the formation of formaldehyde to be highly exothermic, either as a neutral or as radical cation. Both charge-transfer processes yielding CH2(3B1) or CH2(1A1) are also exothermic. The formation of other carbon and oxygen containing species are endothermic. © 1996 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 58 (1996), S. 11-21 
    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: The present knowledge of the monotonicity properties of the spherically averaged electron density ρ(r) and its derivatives, which comes mostly from Roothan-Hartree-Fock calculations, is reviewed and extended to all Hartree-Fock ground-state atoms from hydrogen (Z = 1) to uranium (Z = 92). In looking for electron functions with universal (i.e., valid in the whole periodic table) monotonicity properties, it is found that there exist positive values of α so that the function go(r; α) = ρ(r)/rα is convex, and g1(r;α) = -ρ′(r)/rα is not only monotonically decreasing from the origin but also convex. This is, however, not the case for the function g2(r; α) = ρ′(r)/rα. Additionally, the conditions which specify values for β such that the function gn(r; β) = (-1) ′ρ(n)(r)/rβ is logarithmically convex are obtained and numerically calculated for n = 0,1 in all neutral atoms below uranium. The last property is used to obtain inequalities of general validity involving three radial expectation values which generalize all the similar ones known to date, as well as other relationships among these quantities and the values of the electron density and its derivatives at the nucleus. © 1996 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 263-272 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Ab initio calculations on the structure of pyrazole have been carried out at different levels of accuracy. At the Hartree-Fock (HF) level, the performance of several basis sets, namely 3-21G, 6-31G, 6-31G**, and 6-311G** was investigated. The influence of electron correlation effects also was studied by carrying out geometry optimizations at the MP2, MP4, and QCISD levels. The performance of a density functional method also was evaluated. We have also investigated the possible influence of the frozen core approximation on the final optimized geometry. Three different statistical analyses were considered in determining which geometry is closest to the experimental microwave geometry - namely Paul Curtin's diagrams, cluster analysis, and multidimensional scaling. From these analyses, we conclude that there is no asymptotic approach to the experimental geometry by increasing the quality of the theoretical model, although, as expected, the more reliable structures are those obtained at the MP2, MP4, and QCISD levels, as well as those obtained by the B3LYP density functional method. We have also found that the values of the rotational constants are a tight criterion to define the quality of a molecular geometry. © 1995 by John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 10 (1989), S. 468-478 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Polarization and correlation effects on the nitrogen inversion barrier of some three-membered rings have been investigated. The characteristics of the barrier have been analyzed in terms of perturbation theory arguments. This analysis shows that the HOMO is the orbital that changes more dramatically along the inversion barrier. As a consequence, there is a good linear correlation between the destabilization undergone by the HOMO along the pyramidalization process and the barrier height. To obtain quantitatively meaningful barriers it is necessary to use polarized basis sets. Although polarization effects at the inverting center are dominant, a proper polarization of the remaining atoms of the ring seems also necessary. In general, with the only exception of 1H-diazirine, correlation effects on the barrier height are small if a polarized basis set is used.
    Additional Material: 5 Ill.
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