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  • Computational Chemistry and Molecular Modeling  (14)
  • gaussian quadrature  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Molecular modelling with spherical Gaussians (1970)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 533-539 
    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 mathematical model of a molecule is proposed. The electronic structure is described using a molecular orbital wave function constructed from a small number of spherical Gaussians with optimized parameters. The models exhibit the desirable properties of numerical stability, objectivity and transferability. Results are given for CH4, C2H6, cyclo-propane, H2O, CH2O and C2H4. They can be given a chemical interpretation in terms of chemical bonds, lone pairs and atomic cusps.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560040508
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Gauge invariant gaussian orbitals and the ab initio calculation of diamagnetic susceptibility for molecules (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 15-25 
    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: It is shown that gauge terms can be introduced into the Gaussian functions used as the basis functions for an ab initio calculation of the energy of a molecule in the presence of a uniform magnetic field so that all the integrals become independent of the origin of the vector potential. The perturbation treatment of the diamagnetic susceptibility is considered in the molecular orbital approximation. The results show that the susceptibility can be calculated using only the unperturbed orbitals and their first-order corrections. All the integrals that arise can be expressed in terms of known functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070104
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Symmetry properties of one- and two-electron molecular integrals (1971)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 657-668 
    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: The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560050606
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Fitting electron densities of molecules (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 25 (1984), S. 881-890 
    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: Compact, convenient expressions for the electron density are derived using a fitting functional. Results are given for H2O, CH4, HF, NH3, and PH3, and show the accuracy obtainable using differing numbers of functions on each center. The definition of an atomic charge using these expressions is discussed and it is shown that the Bader virial-partitioning definition, in which the density is integrated over a volume around each nucleus, leads to convergent results.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560250510
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  • 5
    Electronic Resource
    Electronic Resource
    A minimum principle for molecular systems allowing the use of discontinuous wave functions (1970)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 5-20 
    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 this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh-Ritz method is also preserved.The theory is applied to the H2+ ion, potential energy curves are obtained for various “cut-off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut-off” region so that the upper bound is minimized is also discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560040103
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  • 6
    Electronic Resource
    Electronic Resource
    A minimum principle for atomic systems allowing the use of discontinuous wave functions (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 195-204 
    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 this paper a variational principle proposed by Hall [1] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. It is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh-Ritz method.The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various “cutoff” wave functions. It is usually possible to define an optimum “cut off” distance which minimizes the upper bound.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030205
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Diabatic surfaces which permute into one another (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 31 (1987), S. 383-391 
    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: Some of the problems, discussed recently, with the idea that every molecule has a structure can be removed by adopting the idea that some molecules have several structures with probabilities of transfer between them. This is supported theoretically by using diabatic energy surfaces and wave functions. Since these are not easy to define in general, their definition is given in the special case where the surfaces permute into one another. Two kinds of permutation operations are required. The analysis is given more fully for two intersecting diabatic surfaces. The analogy to the double-valued property of the wave function near a conical intersection is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560310309
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  • 8
    Electronic Resource
    Electronic Resource
    Optimal population analysis (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 31 (1987), S. 685-692 
    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: An easy method of approximating the electron density of a molecule by expressing it as a sum of squares of atomic orbitals is described. The coefficients are determined by minimizing the error in the electric field. The optimal population analysis is an integration of this optimized density over the orbitals belonging to one atom. The Mulliken population analysis can be interpreted as the integral of a Mulliken density that is a similar expression with fixed coefficients. The two densities are compared in détail using calculations on the water molecule and, more briefly, HF, LiH, BH, and C2H4. The error in the densities is identified and examined. The optimal population analysis is strongly recommended as a practical improvement to the Mulliken populations.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560310413
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  • 9
    Electronic Resource
    Electronic Resource
    Spherical hybrids (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 197-214 
    Details
    ISSN: 0020-7608
    Keywords: group theory ; hybrid functions ; gaussian quadrature ; alias functions ; solid harmonics ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general solution is presented to the problem of finding hybrid functions which point from the center toward the vertices of a regular solid. Results are given for the examples of 6, 8, 12, and 24 vertices. By taking linear combinations with suitable alias functions, the hybrids have been given nodes passing through all vertices except their own. This allows them to be used for interpolation and quadrature. The various functions required are defined as solid harmonics and group theoretical methods of generating these are discussed fully. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 197-214, 1997
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 10
    Electronic Resource
    Electronic Resource
    Electrostatic water models (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 42 (1992), S. 1237-1250 
    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: The possiblity of creating a useful model for the electrostatic potential around the water molecule is examined from two different starting points. It is suggested that the simplest and most accurate model will have three point charges on the nuclei together with a diffuse Gaussian charge centered near the nuclear center of the charge. This will represent the lone-pair cloud, include the penetration effects, and improve the representation of the electron density. The alternative use of atomic dipoles is explored but seen to be less effective.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560420510
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