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  • 1980-1984
  • 1965-1969  (1,927)
  • 1969  (1,927)
  • Polymer and Materials Science  (1,791)
  • Atomic, Molecular and Optical Physics  (104)
  • Engineering General  (32)
Source
Material
Years
  • 1980-1984
  • 1965-1969  (1,927)
Year
Keywords
  • 101
    Electronic Resource
    Electronic Resource
    Theoretical study of isoelectronic systems: Diazomethane, ketene and allene (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1013-1025 
    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: All-electron SCF-LCAO-MO computations for diazomethane, ketene and allene are presented. The basis functions are contracted Gaussian orbitals. Theoretical results are discussed and related to available experimental data.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030620
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  • 102
    Electronic Resource
    Electronic Resource
    Zero-field splitting parameters in heterocyclic molecules II. Calculations using SCF, SCF CM and UHF wave functions (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1055-1058 
    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
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030623
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  • 103
    Electronic Resource
    Electronic Resource
    Rational function approximation for atomic and molecular wave functionsSupported in part by a National Science Foundation Grant. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1067-1068 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030627
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  • 104
    Electronic Resource
    Electronic Resource
    Masthead (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969) 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030101
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  • 105
    Electronic Resource
    Electronic Resource
    Exposé d'une méthode de détermination des orbitales virtuelles pour les interactions de configurations.Après que cet article ait été soumis pour publication Schaefer et Harris ont indépendamment soumis un article (Phys. rev. 167, 67 (1968)) où cette méthode est utilisée dans on calcul relatif à l'état fondamental de l'atome de bore. Ce calcul très précis confirme remarquablement l'intérêt de la présente méthode. Application à l'etat fondamental de l'atome de béryllium (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 3-11 
    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 method for the determination of the virtual orbitals for configuration interaction is described. This method is a generalization of the one used by Watson in 1960 for the ground state of the beryllium atom. The important point in the method is to complete the set of functions used successively. As an illustration the method is applied to the ground state of the beryllium atom. The method seems to be efficient.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030103
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  • 106
    Electronic Resource
    Electronic Resource
    Error bounds for the overlap of approximate wave functions (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 57-66 
    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: Variational upper and lower bounds for the overlap between an approximate and the true wave function are proposed, and it is shown that the error bounds introduced recently by Gordon are special cases of the variational formulas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030109
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  • 107
    Electronic Resource
    Electronic Resource
    The first excited triplet states of the nucleotide bases calculated with different semiempirical SCF schemes (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 79-92 
    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 π-electron distributions, spin densities, and energies of the first triplets of the nucleotide bases, uracil, thymine, cytosine, adenine, and guanine, were investigated in various semiempirical approximations. Results are presented for calculations using the semiempirical form of the closed-shell SCF configuration interaction method, of the different orbitals for different spins (unrestricted Hartree-Fock) treatment, with and without spin projection, and of the Roothaan's open-shell procedure.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030112
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  • 108
    Electronic Resource
    Electronic Resource
    Convergent iterative solutions for the lowest state of a system with large perturbations (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 635-650 
    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: Iterative methods for the calculation of the lowest eigenvalue and the corresponding eigenvector are derived from the partitioned Schrödinger equation in matrix form. While they have a formal similarity to the Brillouin-Wigner perturbation expansion, they converge for a much wider class of matrices. The double iteration methods (DIM and DIMA) lead to a series of upper and lower bounds to the desired lowest eigenvalue in accordance with Löwdin's bracketing theorem and can be used in a strategy which insures convergence to the solution for arbitrarily large perturbations. A much more efficient single iteration method (SIMA) produces the proper solution even for numerically very ill-conditioned matrices (large offdiagonal elements and small separation of the diagonal elements from the lowest). An important feature of the iterative methods is their insensitivity toward roundoff errors which makes them especially suited for very large matrices, where direct diagonalisation, for example by the Jacobi method, is impracticable.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030510
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  • 109
    Electronic Resource
    Electronic Resource
    Off-Diagonal hypervirial relations (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 699-710 
    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 generalization of a theorem on off-diagonal hypervirial relations is obtained and is used to demonstrate when to expect exact solutions of eigenvalue problems using the hypervirial method. Links are established between the hypervirial method and other approximation methods. The harmonic oscillator and hydrogen atom problems are given as examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030514
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  • 110
    Electronic Resource
    Electronic Resource
    Announcement (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 750-750 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030519
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  • 111
    Electronic Resource
    Electronic Resource
    Mirror reflection symmetry and the phase relations for partially and almost filled shells of equivalent atomic electrons (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1001-1012 
    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 mirror reflection symmetry which consists in the correlation of the substitution j → -j -1 with the reflection of the coordinate system and of m → -m with the reflection of the space with respect to the xy-plane has been applied to the quasi-spin formalism. The phases of the wave functions of the shell of equivalent atomic electrons treated as partially filled, as they relate to those when the same shell is treated as almost filled, have been established. The mirror reflection symmetry has been generalized for the supplementary quantum numbers used for distinguishing the terms of the same kind. The phases of the coefficients of fractional parentage of almost filled shell enabling us to determine them from those of partially filled shell have been specified. Corresponding phase relations for the matrix elements of operators have also been considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030619
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  • 112
    Electronic Resource
    Electronic Resource
    Improved variational bound for the overlap (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1058-1061 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030624
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  • 113
    Electronic Resource
    Electronic Resource
    Announcement (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 749-749 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030518
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  • 114
    Electronic Resource
    Electronic Resource
    Remark on lower bounds to eigenvalues (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 751-751 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030521
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  • 115
    Electronic Resource
    Electronic Resource
    The projection operator for a space spanned by a linearly dependent set (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 767-780 
    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 explicit form of a projection operator constructed from a linearly dependent set is found. The relationships with canonical orthonormalization and with the cofactor matrix of the set's metric matrix are discussed. Similar expressions are obtained for the inner projection of a positive definite operator using a linearly dependent set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030604
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  • 116
    Electronic Resource
    Electronic Resource
    The relationship of flux quantization to charge quantization and the fine structure constant (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 269-287 
    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
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030303
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  • 117
    Electronic Resource
    Electronic Resource
    The kinetic energy of molecular charge distributions and molecular stability (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 327-347 
    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: This paper examines the relationship between the topographical features of a molecular charge distribution and the kinetic energy of the system. Specifically, the spatial contributions to the kinetic energy are related to the Laplacian of the total charge density and to the gradients of the natural-orbital densities. It is concluded that a necessary requirement for molecular stability is the existence of a net negative curvature for the molecular charge distribution in the internuclear region. It is shown that the charge density accumulated in the internuclear region of a stable molecule is distributed in such a way as to keep the accompanying increase in the kinetic energy to a minimum. A comparison of the contributions to the kinetic energy from the atomic and molecular charge distributions indicates that in the formation of a stable molecule the contribution from the molecular charge density in the binding region is decreased relative to that of the atoms.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030308
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  • 118
    Electronic Resource
    Electronic Resource
    Note on two-center Fourier transforms (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 489-492 
    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 method for the evaluation of the Fourier transform of two-center functions is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030407
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  • 119
    Electronic Resource
    Electronic Resource
    On the projection of many-electronThis work was supported in part by the U.S. National Science Foundation, Grant GP-7010 spin eigenstates (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 513-521 
    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 translation is made of spin projection methods into the language of second quantization. This leads to a new formula for the Sanibel coefficients and expressions convenient to use for automatic calculation of spin projections.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030410
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  • 120
    Electronic Resource
    Electronic Resource
    Theory of intermolecular interactions: The long range terms in the dipole-dipole, monopoles-dipole, and monopoles-bond polarizabilities approximations (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 537-551 
    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 problem of evaluating the long range terms (electrostatic, polarization, dispersion) of the interaction energy between molecules at intermediate distances (i.e. distances of the order of magnitude of the molecular dimensions) is considered. Instead of being approximated by its dipole part, the exact interaction Hamiltonian is treated as proposed by Longuet-Higgins [11], i.e. the matrix elements are interpreted as electrostatic interactions between state and transition charge distributions. These charge distributions are approximated in a systematic way by sets of point charges (localized on the atoms) or sets of dipoles (localized on the bonds). The various contributions to the energy may then be expressed in terms of atomic net charges and bond polarizabilities. More refined approximations of the charge distributions could be used and correspondingly improved formulae could be derived: as an example, a formula for the σ-π dispersion energy is derived, where the σ charge distributions are approximated by bond transition dipoles (leading to σ bond polarizabilities in the final formula) while the π charge distributions are approximated by atomic charges.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030502
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  • 121
    Electronic Resource
    Electronic Resource
    Variational lower bound for the polarizability of the ground state (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1061-1064 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030625
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  • 122
    Electronic Resource
    Electronic Resource
    Wellenmechanische absolutberechnung schwingungsspektroskopischer daten am äthylen (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 881-887 
    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 ethylene molecule has been investigated by means of the General SCF-MO-LC(LCGO) Program System for 12 different nuclear positions, taking all electrons into account. The equilibrium distances and angles as well as all force constants of the totally symmetric vibrations with the corresponding frequencies have also been calculated.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030610
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  • 123
    Electronic Resource
    Electronic Resource
    Electronic structure of graphite (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 983-999 
    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: Semi-empirical calculations of the π-band structure of planar and three-dimensional graphite are described. Special attention is given to the significance of band parameters. The theoretical results are in good agreement with experiment.
    Additional Material: 15 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030618
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  • 124
    Electronic Resource
    Electronic Resource
    Spin-other-orbit and spin-orbit interactions in ƒ2 and ƒ3 electron configurationsSupported in part by a grant (No. 9510-65) from the Defence Research Board of Canada and in part by a grant from the National Research Council of Canada. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1045-1054 
    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: Expressions of the matrix elements of the spin-other-orbit and spin-orbit interactions for the various multiplets of all the states of ƒ2- and ƒ3-electron configurations are reported and used to evaluate the Hartree-Fock values of these interactions in the neutral atoms Ce(4ƒ2), Pr(4ƒ3), Ho(4ƒ11) and Er(4ƒ12). The required values of the spin-spin parameters M(K)s, and the spin-orbit parameter ζ for these atoms were obtained using numerical Hartree-Fock wave functions.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030622
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  • 125
    Electronic Resource
    Electronic Resource
    Foundations of quantum chemistry. Author: T. E. Peacock. Published by: John Wiley & Sons Ltd., London, New York, Sydney, Toronto, 1968. Price: $6.50. No. of pages: 162 (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1069-1070 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030628
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  • 126
    Electronic Resource
    Electronic Resource
    Transition probability and oscillator strength by perturbation theory: 1s3p1,3P-1s3d1,3D transition in helium isoelectronic sequence (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 17-24 
    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
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030105
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  • 127
    Electronic Resource
    Electronic Resource
    A remark on the Born-Oppenheimer approximation (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 25-32 
    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 method of calculating wave functions for an electron-nucleon system by a variational method originally suggested by Born and Oppenheimer [1] is rigorously investigated. As an application we sketch the calculation of a simple nonadiabatic wave function for the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030106
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  • 128
    Electronic Resource
    Electronic Resource
    Selected scientific papers of Egil A. Hylleraas. Edited by: John Midtdal, Harald Wergeland, and Knut Thalberg. Published by: NTH Press, Trondheim, Norway, 1968. Price: $27 for both volumes (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 246-246 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030211
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  • 129
    Electronic Resource
    Electronic Resource
    Theoretical considerations of the electronic spectra of methyl flavinsPart VII of the series, “Electronic Structure and Photochemistry of Flavins”. See Part VI, J. Am. Chem. Soc. 90, 6507 (1968). (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 303-316 
    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: Methyl groups in flavins are best treated by the group-orbital approximation. The pseudo-heteroatom approximation overestimates methyl hyperconjugation with the Pariser-Parr-Pople SCF-MO method. Singlet π → π* transition energies are calculated by various MO methods with differing degrees of sophistication, and the results from the P—P—P method agree reasonably with the experimental values. 2- and 4-thioflavin analogs are also treated satisfactorily. The effects of position and number of the methyl groups on the spectra of flavins are described in detail. Rough estimates of the n → π* energies of flavins suggest that the lowest singlet excited state is (π, π*), consistent with the fluorescence and phosphorescence polarization data.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030306
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  • 130
    Electronic Resource
    Electronic Resource
    Study of the convergence radius of the Rayleigh-Schrödinger perturbation series for the delta-function model of H2+ (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 349-370 
    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 convergence radius of the series expansion for the energy of H2+ in the δ-function model (in terms of the perturbation parameter μ/λ, where μ is the charge of the perturbing nucleus and λ the fixed charge of the other nucleus) is investigated. A lower bound of this convergence radius (possibly equal to it) previously defined by Robinson [5] is studied analytically as a function of the internuclear distance R and computed numerically. The results differ strikingly from those previously obtained by Robinson who used a simplified but poorer lower bound: in contrast with this poorer bound, the one studied in the present paper is larger than for I every R, from which fact it may be concluded that, contrary to Robinson's previous result, the series expansion of the energy, in the δ-function model under consideration, still converges when μ = λ for every R.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030309
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    Zur eindeutigkeit der darstellungen von energiehyperflachen (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 123-130 
    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 first part of this paper gives an introduction of different kinds of atomic associations. Furthermore it will be shown that partial systems of united atoms are not only described by their nuclear-charge number, but additionally by their number of electrons. Both characteristics of a partial system of atomic associations may lead to an apparent multiple-valuedness in the transitions between atomic associations. It is shown that the multiple-valuedness of the atomic associations can be understood and eliminated within the Born-Oppenheimer-approximation, which leads to the concept “energyhypersurface”. An example is given by the system {He, H, H, H}+.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030116
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  • 132
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    Masthead (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969) 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030201
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  • 133
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    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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  • 134
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    The symmetry of molecular polarization tensorsThis paper is an extended account of a lecture given at the Adam Mickiewicz University, Poznań and at the Nicholas Copernicus University, Toruń during a visit to Poland in March and April 1968. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 231-243 
    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: Polarization tensors are discussed in terms of their intrinsic symmetry group which is a direct product of the point group and the subgroup of the permutation group relevant to the experiment. The study of these latter groups is simplified by use of the isomorphism with certain point groups and permutations of suffixes can be visualized by rotations and reflections of the vertices of various objects in space. The approach unites the previous treatments and provides a means of constructing the bases for the irreducible tensor components. The difficulties introduced by Laplace's equation are explained and the information obtainable from induced birefringence experiments (Kerr and Cotton-Mouton effects) discussed for various systems.
    Additional Material: 13 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030209
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  • 135
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    Generalized Brillouin theorem for multiconfigurational SCF theories (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 247-247 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030213
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  • 136
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    Expansion of linear combinations of slater-type orbitals in eigenfunctions of the three-dimensional isotropic harmonic oscillatorThis is the second of a series of papers on the expression of atomic and molecular orbitals in terms of functions related to Gaussians. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 289-295 
    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: Several classes of functions related to the Gaussian have been used with success as basis sets for the representation of atomic and molecular orbitals.We have compared the representation of a hydrogen 1s orbital by a sum of Gaussian lobe functions with its expansion in eigenfunctions of the three-dimensional isotropic harmonic oscillator. The lobe functions are shown to achieve better expectation values of the energy, with fewer terms. The lobe functions have the further computational advantage of not containing high powers of the radius.It is concluded that the lobe functions are a superior basis set for use in calculations of the electronic structure of atoms and molecules.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030304
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  • 137
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    An extended Wolfsberg-Helmholz calculation on europium tetraacetylacetonate (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 373-376 
    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
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030311
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  • 138
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    Remark on lower bounds to eigenvalues (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 371-373 
    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 the familiar Temple, Stevenson-Crawford, and Weinstein lower bound formulas for eigenvalues are consequences of a much stronger general lower bound formula and the weak “Eckart criterion” for the overlap of the approximate and true wave functions.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030310
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  • 139
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    Molecular correlation integrals. Two center one electron integrals containing a function of interparticle distance in one center expansion approximation (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 397-415 
    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: Two-center one-electron integrals needed in certain molecular correlated wave function calculations, using one-center expansion approximation, have been studied. The form of the basic correlated function used in this study is \documentclass{article}\pagestyle{empty}\begin{document}$$ h(r_{12}) = r_{12}^n e^{ - \zeta r_{12} } $$\end{document} The parent integral is expressed in terms of an angular integral, and an auxiliary radial integral depending upon the variables r1, r2, and r12. Several analytical formulas, and a recursive formula are derived for the auxiliary integral, and other related integrals. All these formulas are given in computationally useful forms. Logical flow charts and FORTRAN programs were constructed for computing the basic integrals discussed in the paper. Numerical values of some integrals, thus obtained, are tabulated for comparisons.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030403
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  • 140
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    Dimeres composes de molecules dont l'excitation electronique entraine un deplacement de la configuration nucleaire d'equilibre accompagne d'un changement de constante de forceSoumis pour publication à l'International Journal of Quantum Chemistry. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 377-396 
    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: We have studied the validity of the traditional model of a dimer that has been treated exactly by Merrifield and Fulton and Gouterman, solving the vibronic coupled equations by a numerical method. This model takes into account the modification of the nuclear equilibrium configuration, but it neglects the variation of the force constant when the monomer is electronically excited from the fundamental to a given excited state (the corresponding electronic potentials are both considered as harmonic). We have shown by inspection of the absorption and fluorescence spectra calculated by solving the vibronic equation exactly that the variation force constant cannot be neglected, even if it is weak, particularly in the weak coupling region. The weak, intermediate and strong coupling criteria have been deduced, for the model studied, by examination of the dimeric electronic potential surfaces for different cases of intermolecular interactions.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030402
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  • 141
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    Semiempirical approach to the problem of the radiative lifetime of the excited F-color center (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 485-487 
    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 emphasized that for the theoretical consideration of many problems of defect centers in crystals (especially of problems which need the correct asymptotic behavior of the wave functions) the semiempirical approach can be effective. As an example the spontaneous radiative time decay of the excited F-center in alkali halides is calculated by using the experimental energies of absorption and emission bands.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030406
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  • 142
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    The calculation of matrix elements for valence bond functionsThis work has been supported in part by grants from the National Science Foundation and the AF Office of Scientific Research to Indiana University. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 523-534 
    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: Pauling's formulas for the calculation of matrix elements for valence bond functions are derived using a simple substitutional process. The results generalize and simplify the formulas. In particular, the formulas do not depend upon orthogonality of atomic orbitals nor upon the nature of the choice of bond structures (canonical or not). The results are particularly adaptable to automatic computation.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/qua.560030411
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  • 143
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    Théorie quantique du pouvoir rotatoire magnétique des molécules diamagnétiques. II. Applications (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 593-610 
    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 general formalism of the variational theory of the Faraday effect established in the first part of this paper is now applied to the actual computation of the Verdet constant of the hydrogen molecule, of water and of some saturated hydrocarbons. The numerical results have a correct order of magnitude and even, for hydrogen, are rather close to the experimental value.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030507
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  • 144
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    Expansion of r12 and r12-1 in terms of analytical functionsWork was performed at the Ames Laboratory of the U.S. Atomic Energy Commission. Contribution No. 1932. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 493-501 
    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: Expansions in terms of the spherical coordinates of two particles are given for the interparticle distance and its inverse. The expansions are characterized in that each term is a product of analytical one-variable functions. While it is possible to find acceptable expansions for r12, those obtained for r12-1 exhibit extremely slow convergence, unacceptable for practical use. The same objections must be raised against related expansions of multi-centered molecular integrals.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030408
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  • 145
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    Masthead (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969) 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030501
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  • 146
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    Bounds for eigenfunctions of one-electron molecular systemsThis work has been supported in part by the NATO Research Grants Program under the number SA5-2-05(170)1757PS and in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, Contract numbers AS-7-283 and AS-8-0001. (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 581-586 
    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: This article gives pointwise bounds for the wave functions of one-electron molecular systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030505
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  • 147
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    Wellenmechanische absolutrechnung am HeHHe+ (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 115-121 
    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 wave function of the HeHHe+ molecule has been calculated by means of the GENERAL SCF-MO-LC(LCGO) PROGRAM SYSTEM, taking all four electrons into account. The calculations were carried out for a number of linear equidistant, linear non-equidistant, and bent nuclear arrangements. The minimum energy of -5.7930 a.u. was found for a linear equidistant configuration with a He—H distance of 0.939 Å. The corresponding ionization energy was 37.9 eV. An estimation of the energy of formation of HeHHe+ from HeH+ and He based on SCF-calculations on HeH+ and He gave 7.9 kcal/mole. The frequencies of the normal vibrations were calculated.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030115
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  • 148
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    Announcments (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 145-145 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030119
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  • 149
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    On the least squares procedure for atomic calculations (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 169-184 
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    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 discuss the properties of one version of the least squares (LS) method for the solution of the Schrödinger equation. These properties are exemplified by a number of calculations on the n1S and n3S states of helium, up to principal quantum number three, which are very much more accurate than previous LS calculations on helium. Particular attention is paid to the convergence properties of the LS procedure and we compare it with the simpler Rayleigh-Ritz (RR) procedure in the case when the RR matrix elements are evaluated numerically over the same quadrature mesh as used in the LS procedure. We conclude that although the LS procedure is capable of high accuracy it has no advantages which would justify its sole use in place of the RR procedure. However, it does have some advantages when used in conjunction with RR, in that it gives an estimate of the numerical accuracy of the RR energies.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030203
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  • 150
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    Theory of biorbitals. Study of conjugated systems in their ground and excited electronic states (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 205-218 
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    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 biorbital theory called also “identical geminals theory” is applied to the study of a number of conjugated molecules. All basic integrals are determined by means of the Pariser-Parr-Pople procedure. The biorbital theory reproduces about 40 per cent of the correlation energy of the ground state of the molecule; this number is raised to about 70 per cent for the lowest triplet state. The low lying excited states are well represented from the point of view of transition energy as well as from the point of view of symmetry. The occupation number matrix and the charge-bond order matrix are defined and discussed. The overall chemical description of conjugated molecules produced by the biorbital theory is similar to that produced by other theories of electronic structure of molecules. It is concluded that the biorbital theory provides a description the quality of which is, roughly speaking, about half way between those provided by the SCF-MO and complete CI theories, respectively.
    Additional Material: 10 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030206
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  • 151
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    Applied group theory. Author: G. G. Hall. Published by: Longmans, Green and Co, London, 1967. Price: 25s. (paperback). No. of pages: 135 (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 246-247 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030212
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  • 152
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    LCAO-MO studies on hydrogen bonding: The interaction between carbonyl and hydroxyl groups (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 851-871 
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    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: Potential curves that show the energy dependence of hydrogen bonds between carbonyl and hydroxyl groups on the O—H bond length, on the distance between the molecules, and on the angle between the functional groups have been calculated with the CNDO/2 method. The results are presented for a small model system-formaldehyde/water - and for the dimer of formic acid. Good agreement is obtained with the available experimental data. The influence of the molecular geometry on the calculated results is discussed.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030608
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  • 153
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    Wellenmechanische untersuchungen am 2-buten unter berücksichtigung aller elektronen (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 889-891 
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    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: 2-butene has been investigated for different nuclear positions taking all 32 electrons into account, using the SCF-MO-LC(LCGO) method. The calculations show that the energy of the trans-form is 1.1 kcal/mol lower than that of the cis-form. The potential curve between these two forms is shown graphically. The ionization energy was estimated to be 9.0 eV.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030611
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  • 154
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    Fermi surfaces and electron-impurity interactions in simple metals (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 969-981 
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    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 review is given of the current status of our work on electron transport properties and Fermi surfaces in simple metals. A simple classical model is proposed to extend existing theory to account for the effects of electron-impurity interactions on the behavior of magnetoacoustic absorption and the size and shape of the Fermi surface in the alkali metal potassium. The theoretical prediction is compared with measurements of the magnetoacoustic absorptionand Fermi surface diameters in potassium crystals of different impurity levels. An attempt is made to explain, on the basis of the theory of electron-impurity interactions, the decrease by 9% in the Fermi diameter and the departure by 53% in the phase factors of the impure potassium crystal. The results are compared with observations on a zone refined potassium crystal which satisfies the nearly-free-electron model.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030617
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  • 155
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    Long-range interactions in the ground and two excited states of the HeH+ molecule (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 945-968 
    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 long-range interaction energies for different dissociation products of the HeH+ molecule have been calculated using the Rayleigh-Schrödinger perturbation theory up to the third order in the energy. The calculations were carried out for the ground state (He(ls2) + H+), the first excited state (H(ls) + He+(ls)) and the second excited state Π(H(2pπ) + He+(ls)). The unperturbed states correspond to the dissociation products denoted in parentheses. Assuming the overlap to be zero, expanding the interaction potential in the inverse powers of the internuclear distance R and using the familiarly known perturbation-variational technique, the coefficients of various powers of R-1 in the energy expansion were evaluated. They correspond to different multipole-multipole interactions. The potential energy curves of all three states under consideration were calculated for large values of R. Also calculated were the multipole polarizabilities of the hydrogen atom in the is and 2pπ states and of the helium atom in the ground state.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030616
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  • 156
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    Laplace transform wave functions (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 1027-1043 
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    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 wave function defining a quantum-mechanical system is considered as the Laplace transform of some distribution and the consequent form of the Variational Principle derived; an integral equation defines the eigenfunctions of a certain subclass. The model of the hydrogen-like atom is used to test the theory; the eigenfunctions and associated energy levels of the ground and excited states are obtained for arbitrary values of the orbital quantum number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030621
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  • 157
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    Vibronic absorption spectrum of the ethylene dimer (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 569-580 
    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: Vibronic coupling theory is used to construct the vibronic absorption spectrum of the ethylene dimer. It is shown that in this case an extended four-parameter form of the vibronic Hamiltonian should be considered. In addition to the commonly used three vibronic parameters, the difference between the ground and excited state force constants of the monomer is taken into account.Numerical calculations were performed for the dimer geometry resembling that of norbornadiene. Some comments on the interpretation of the absorption spectrum of norbornadiene are made.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030504
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  • 158
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    Free-electron model for electronic spectra of benzene (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 611-619 
    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: Using a three dimensional free-electron model for the π-electron system the energies of the various singly and doubly excited configurations of benzene have been calculated. It has been found that the energies of the various singly excited configurations are in good agreement with the values obtained by Craig; whereas the energies of the doubly excited configurations are higher than those obtained by Craig. Therefore the configurational mixing for the doubly excited configurations is not necessary in this kind of model.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030508
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  • 159
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    The hydrogen atom in a cubic field of electric dipoles (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 663-681 
    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 full rotational symmetry of the hydrogen atom is lowered to that of the double group of Oh. This is done by a cubic field of electric dipoles. Symmetry-adapted spin orbitals have been calculated and with them the energies of the lowest states as functions of the distance from the dipoles to the atom, the dipole moment, and the size of the atoms forming the dipoles. The Hamiltonian used is obtained by starting with the Dirac equations and then making some simplifications and approximations.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030512
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  • 160
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    Many-Electron problems. II. Energy expansions and internal fields (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 723-730 
    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: Energy relations are derived for neutral atoms and isoelectronic sequences. It is shown that the field of the electrons at the position of the nucleus follows a very simple law and the diamagnetic shielding constant may be given in simple analytic form as a function of the atomic number.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030516
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  • 161
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    Valence configuration interaction calculations for atomic scattering (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 751-751 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030520
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  • 162
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    On uncoupled approximation with approximate form of the Hartree-Fock operator (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 763-766 
    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 the uncoupled approximation of Dalgarno with the approximate form of the Hartree-Fock operator gives no bound for the second order energy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030603
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  • 163
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    The distribution of electronic charge in the ground state of cubic boron nitride (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 753-762 
    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 distribution of electronic charge in cubic boron nitride is investigated using the bond orbital wave functions recently calculated by Coulson and Doggett. Plots of the one-electron density function, in the (110) plane, are found to be insensitive to the choice of atomic basis functions, in contradistinction to the previously calculated effective atomic charges. A number of structure amplitudes are also calculated for each of the bond orbital wave functions.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030602
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  • 164
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    Energy levels of paramagnetic ions: Algebra. II (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 795-822 
    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 correspondence rules between the algebra of coupling coefficients of the special unitary group SU(2) and the associated algebra of a subgroup G of SU(2) are presented. The matrix elements of the irreducible representations of G are written in a convenient quantization scheme and different relations between these matrix elements and the Clebsch-Gordan coefficients of G are derived. Such a formalism is appropriate for numerous spectroscopic problems. As an example, it is applied to crystal field theory and electron paramagnetic resonance. General formulas from which a large number of results are rederived and generalized in a straightforward fashion are given. Numerical values of coupling coefficients for the tetragonal and cubic groups are listed in the Appendix.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030606
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  • 165
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    Theory of two shells of atomic electrons using non-orthogonal radial orbitals (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 913-930 
    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 theory for handling non-orthogonal radial orbitals of two shells of atomic electrons based on the mathematical apparatus of irreducible tensor operators is presented. The general expressions for one- and two-electron operator matrix elements are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030614
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  • 166
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    Nature of the chemisorption bond on semiconductor surfaces (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 249-267 
    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: Results obtained by various quantum-mechanical approaches in studying localized states on crystal surfaces are summarized and discussed. The one- and many-electron aspects of the problem are compared and shown to lead to similar results. Emphasis is laid upon localized chemisorption states on intrinsic semiconductors. The problem of the calculation of chemisorption heat on solid surfaces is also mentioned.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030302
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  • 167
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    Wellenmechanische behandlung der protonisierung des äthylens unter berücksichtigung aller elektronen (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 873-879 
    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 system C2H5+ has been investigated as ethyl cation and as protonated ethylene using the SCF-MO-LC(LCGO) method. Equilibrium distances and angles have been estimated by different potential curves. No difference in total energy was found between the π- and the σ-complex.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030609
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  • 168
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    The asymptotic Casimir-Polder potential from second-order perturbation theory and its generalization for anisotropic polarizabilities (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 903-911 
    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 how the leading term for very large R of the Casimir-Polder potential, that is the term varying as R-7, arises in second-order perturbation theory applied to the interaction Hamiltonian - \documentclass{article}\pagestyle{empty}\begin{document}$ - \sum\limits_\sigma {\frac{1}{2}\alpha (\sigma){\rm E}^{ \bot ^2 } (\sigma)} $\end{document}. The generalization to anisotropic molecules is calculated and the angular dependence of the long range intermolecular potential in this case is given explicitly in terms of the principal polarizabilities and their corresponding directions of the two molecules.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030613
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  • 169
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    Masthead (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010101
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  • 170
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    Basis of finite element methods for solid continua (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 3-28 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010103
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  • 171
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    Editorial (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 1-2 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010102
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  • 172
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    Transmission of vibration in beam systems (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 47-66 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three methods for finding natural frequencies and modes of complex structures composed of beam elements are described and compared. The analysis is extended to include hysteretic damping for the determination of response and transmissibility without a modal analysis. Experimental comparison is given for the response of a simple engineering structure.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010105
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  • 173
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    A refined triangular plate bending finite element (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 101-122 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The derivation of the stiffness matrix for a refined, fully compatible triangular plate bending finite element is presented. The Kirchhoff plate bending theory is assumed. Six parameters or degrees of freedom are introduced at each of the three corner nodes resulting in an 18 degree of freedom element. This refined element is found to give better results for displacements and particularly for internal moments than any plate bending element, regardless of shape, previously reported in the literature.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010108
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  • 174
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    Numerical treatment of mixed boundary value problems in two-dimensional elastostatics (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 67-73 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite difference treatment of two-dimensional problems in elastostatics is usually based on the differential equations for the displacement vector or the Airy stress function, depending on whether boundary conditions are on displacement or stress. In either case, determination of stresses requires numerical differentiation and therefore use of a rather fine grid. Moreover, neither method is suited to the treatment of mixed boundary conditions. The alternative method developed in this paper uses the first derivatives of the displacement components at the grid points as basic variables and hence does not require numerical differentiation in the evaluation of stresses. Appropriate finite difference equations are established, and their use is discussed in connection with a specific example with known explicit solution.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010106
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  • 175
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    A conforming quartic triangular element for plate bending (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 29-45 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory, function generator routine and testing procedures are given for a six-node 18 degree of freedom triangular element. At corner nodes the variables are the displacement and the two slopes. At midside nodes the variables are the displacement, the slope normal to the side, and the rate of change of this along the side - i.e., the rate of torsion. Of two options, one divides the triangle into three and takes different quartic displacements in the three regions, and the other uses displacement functions with singularities at the vertices. According to a test which compares the energies of the two formulations by eigenvalues, the second is the better if the integration is accurate. The same test, together with others based on finite differences and on nodal values, etc. checks the correctness of the routine decisively.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010104
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  • 176
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    Analysis of large deflection of plates by the finite element method (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 123-133 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The large deflection problem of a rectangular plate is analysed by using the finite element method and employing the iteration technique. In the present study, the stiffness matrix of a rectangular plate element for bending proposed by Greene is employed, and results of numerical examples duly justifies applicability of the present method.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010109
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  • 177
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    Elasto-plastic solutions of engineering problems ‘initial stress’, finite element approach (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 75-100 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents first a general formulation of the elasto-plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new ‘initial stress’ computational process is proposed which is shown (1) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain development and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010107
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  • 178
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    Masthead (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010201
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  • 179
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    The damped transient behaviour of finite beams and plates (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 151-162 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010203
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  • 180
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    A polygonal finite element for plate bending problems using the assumed stress approach (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 135-149 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The assumed stress distribution approach is used to derive the stiffness matrix of a plate-bending element of general polygonal shape having any number of nodes. The effect of assuming various numbers of unknown coefficients in the stress distributions is examined and the convergence properties of the resulting elements compared with others derived form assumed displacements.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010202
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  • 181
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    Numerical solution and utilization of Green's functions (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 169-175 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for obtaining the Green's functions for Laplace's, Poisson's, and the transient heat diffusion equations is presented. The Green's functions thus obtained are then employed to rapidly obtain numerical solutions of the above equations by matrix multiplication, with subsequent considerable savings in machine time.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010205
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  • 182
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    A method of solution for non-linear simultaneous algebraic equations (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 177-180 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the large numbers of non-linear algebraic equations occurring in analyses of non-linear structural systems using finite differences or finite elements is time consuming even for the fastest computers. This paper presents a method of solution based on a Taylor's expansion technique which is an aid in the solution of such systems of equations.Examples presented show that in the finite element analysis of moderately non-linear structural systems the technique provides sufficiently accurate solutions. For more non-linear systems the technique provides excellent starting values for the Newton-Raphson method.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010206
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  • 183
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    Improved deformation functions for the finite element anlysis of beam systems (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 163-167 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Deformation functions which, in addition to satisfying the continuity conditions at nodes. Also satisfy. Approximately, the governing differential equation within the element allow system eigenvalues to be found more accurately, with a given number of elements, than is possible with previously published deformation functions. This is illustrated for the case of beams.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010204
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  • 184
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    Economical computer techniques for numerically integrated finite elements (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 201-203 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010208
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  • 185
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    A general theory of finite elements. I. Topological considerations (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 205-221 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general theory of finite elements. The concept of finite elements is cast in a general topological framework valid for spaces of finite dimension. It is shown that the idea of finite element models can be developed in higher-dimensional spaces, independent of specific co-ordinate systems, for any type of continuous abstract function defined on the space. Generalizations of the familiar Lagrange and Hermite interpolation functions are presented as well as a general statement of the notion of generalized variables and conjugate fields. It is also shown that admissible finite elements can be developed for non-Euclidean spaces of finite dimension. Topological properties of finite element models are examined in Part I of the paper. Part II is devoted to certain applications.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010209
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  • 186
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    Announcement (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 224-224 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010302
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  • 187
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    Masthead (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010301
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  • 188
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    A matrix for the solution of mixed rotating and non-rotating vibration systems (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 225-245 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented based on matrix algebra for the dynamic analysis of a mixed rotating and non-rotating vibration system. Such systems occur in practice when turbo-alternator sets are mounted on flexible steel foundations.The mathematical model considered consists of a rotating non-uniform, bi-symmetric shaft connected via three or more flexible-film bearings to a flexible structure throughout which mass is distributed. The shaft, which is assumed to rotate at constant speed, is heavy, flexible and carries several rigid axi-symmetric discs. Viscous damping is assumed to act in all parts of the system and gravitational effects are ignored.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010303
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  • 189
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    End displacements of semi-infinite cylinders due to annular loadings (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 181-200 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Surface displacements at the end of a semi-infinite, circular cylinder due to an axisymmetric ring of forces on the end are examined. The solution which has been found may then be used to find surface displacements for general axisymmetric loadings by convolution. The solution, in tabular form, is given as corrections to the counter-part half-space solution.The method of solution involves a three step superposition process. First, the displacement due to a ring of forces on a half-space is found by using the Boussinesq solution. Then, the excess tractions on the half-space, over that of the cylinder, are removed. This is done in two parts. The problem of an infinite cylinder with linearly varying pressure and shear over a short length of the lateral surface is solved by using Fourier integrals. This is used for the removal of the pressure and shear on the lateral surface of the cylinder by convolution. Next, the stresses at the mid-section of the infinite cylinder are removed. This is done by finding a set of boundary conditions for the end which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate the tractions which must be removed.With the solution thus obtained, two sample problems are shown: 1. an elastic cylinder in contact with a half-space; 2. a rigid punch in contact with an elastic cylinder.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010207
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  • 190
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    A general theory of finite elements. II. Applications (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 247-259 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of the this paper, topological properties of finite element models of functions defined on spaces of finite dimension were examined. In this part, a number of applications of the general theory are presented. These include the generation of finite element models in the time domain and certain problems in wave propagation, kinetic theory of gases, non-linear partial differential equations, non-linear continuum mechanics, and fluid dynamics.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010304
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  • 191
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    A version of the Aitken accelerator for computer iteration (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 275-277 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010306
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  • 192
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    A rectangular plate bending element the use of which is equivalent to the use of the finite difference method (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 261-274 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A presentation is made of a rectangular plate bending element, the use of which corresponds to the finite difference method. The element stiffness matrix is arrived at by approximation of the strain energy of the element by suitably selected finite difference expressions which contain not only values in respect of the deflection, but also values of its first derivatives. On the basis of the connection found between the two methods, some changes are suggested in the finite difference method, which involve a more realistic way of considering the detailed distribution of the loading. The effect of these modifications is illustrated in two applications.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010305
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  • 193
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    A theory of the solution of steady state network problems with special reference to mine ventilation networks (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 279-299 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When calculating complex interconnected systems (electrical, power, water supply, gas systems, etc.) by digital computer, a number of common problems arise, connected both with the mathematically correct formulation of the problem under investigation, and with the algorithms of the solution, the programming of which makes it possible to reduce the computing time, the store capacity and the volume of input data required. The present article is devoted to the solution of these problems. The procedure is illustrated by formulating and manipulating the equations relating to complex interconnected mine ventilation networks.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010307
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  • 194
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    Masthead (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010401
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  • 195
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    Derivation of stiffness matrices for problems in plane elasticity by Galerkin's method (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 301-310 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Solution of plane elastic problems by piecewise linear approximation is outlined. This method is based upon Galerkin error distribution technique, which leads to simultaneous algebraic equations identical to those associated with the Finite Element Method. In addition, this method permits definition of the discretization error, which can be computed once the displacement components are known. Properties of the interpolation functions are discussed, and a sequence of internally compatible plane elastic elements is defined.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010308
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  • 196
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    Minimum weight design of structures with application to elastic grillages (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 311-331 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress-ratio, linear programming-cutting plane and usable-feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non-convex stress constraints and numerous relative optima. Instances are given of non-fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design problems.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010402
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  • 197
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    Mass condensation : A semi-automatic method for reducing the size of vibration problems (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 333-349 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re-entry to the structural analysis program for the purpose of computing dynamic stresses.A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped masses’.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010403
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  • 198
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    Application of non-linear programming to optimum grillage design with non-convex sets of variables (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 351-378 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of non-linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non-convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum.It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in-plane loads may be performed efficiently by means of non-linear programming.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010404
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  • 199
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    A finite element method of viscoelastic stress analysis with application to rolling contact problems (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 379-394 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo-viscoelastic observations.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010405
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  • 200
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    Letters to editor (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 395-395 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010406
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