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  • 1995-1999
  • 1975-1979  (591)
  • 1978  (591)
  • Engineering General  (257)
  • Biochemistry and Biotechnology  (178)
  • Atomic, Molecular and Optical Physics  (156)
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  • 1995-1999
  • 1975-1979  (591)
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  • 101
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 747-755 
    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: Ab initio calculations are presented for the [F-; e+] and [CN-; e+] complexes. Positron affinities of 4.99 and 3.79 eV are obtained for F- and CN-, respectively. The excitation energies to the low-lying excited states of the positron complexes are also calculated.
    Additional Material: 1 Ill.
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  • 102
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 757-766 
    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: From the general formalism of elastic x-ray scattering and a few meaningful assumptions we have shown that for an atom, ∫ρ2dτ is an experimentally measurable quantity related to the intensity scattered by an element. We have labeled this quantity (p), the “average electron density.” If ψ obeys the virial theorem, within the Thomas-Fermi approximation we show (within a multiplicative constant) that 〈ρ〉 is a lower bound to (∑ ionization potentials )3/2. Thus, the scattered intensity of x rays is related quantitatively to the energy of the scattering atoms. Inequalities have been developed to express these relationships and have been confirmed for the more exact Hartree-Fock wave functions.
    Additional Material: 3 Tab.
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  • 103
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 767-777 
    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: Ab initio molecular-orbital theory with the STO-3G and 4-31 G basis sets has been used to study the 1,3-sigmatropic hydrogen rearrangements: propene→propene, formic acid→formic acid, and vinyl alcohol→acetaldehyde, and the1,5-shifts:1,3-pentadiene→ 1,3-pentadiene and β-hydroxyacrolein→ β-hydroxyacrolein. Transition states have been determined using gradient procedures. Improved descriptions of the energies of the reactions have been obtained using 3 × 3 configuration interaction. In accord with expectations based on orbital-symmetry considerations, the calculated barriers are considerably greater for 1,3- than for 1,5-shifts. The forbidden pathway for the degenerate 1,3-shift in propene is predicted to require less activation energy than the allowed pathway, a result that can be rationalized in terms of interactions with subjacent and superjacent orbitals.
    Additional Material: 1 Ill.
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  • 104
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 801-813 
    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 multiple perturbation method for the study of molecular reactivity following multiple site interactions has been extended to trimolecular systems. The theory is reformulated by the many-body diagrammatic method. While adding no new physical content to the previous theory, the present formulation allows for a systematic way of evaluating higher-order energies. The additivity of perturbation contributions to the modification of molecular reactivity is tested on dihydrated adenine. The results compare favorably with supermolecule calculations.
    Additional Material: 3 Ill.
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  • 105
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 839-850 
    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: Monte Carlo calculations for clusters consisting of 200 water molecules surrounding glycine in the neutral and zwitterionic forms were carried out at 300 K; all the relevant interaction potentials have been obtained by means of quantum-mechanical calculations. Water-water and amino acid-water energies were calculated, and the zwitterion was found to be strongly favored with respect to the neutral molecule, as expected. A detailed analysis of the energetic results yielded some information on the special extension of the solute-induced perturbation. The structural results were found to be in reasonable agreement with predictions that can be obtained by analyzing isoenergy contour maps, calculated for the two-body amino acid-water potential.
    Additional Material: 7 Ill.
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  • 106
    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: Ab initio MODPOT/VRDDO calculations have been carried out on carcinogenic benzo(a)pyrene and its metabolites. The MODPOT/VRDDO method incorporates two very desirable options into our fast ab initio Gaussian programs: MODPOT - ab initio effective core model potentials - and a charge-conserving integral prescreening approximation which we named VRDDO (variable retention of diatomic differential overlap). For orbital energies and population analyses the MODPOT/VRDDO results agree to essentially three decimal places with completely ab initio calculations using the same valence atomic basis set. For this series of very closely related congeners a new MERGE technique was implemented that allows reuse of integrals of a common skeletal fragment. Since our program computes integrals efficiently by blocks, reusing information common to the block, it was more difficult to implement a MERGE technique than for integral programs which calculate the integrals one-byone. The MODPOT/VRDDO calculations were performed for benzo(a)pyrene (BP), BP oxides, BP dihydrodiols, and BP dihydrodiol epoxides. The metabolites investigated were BP-7,8-oxide, BP-4,5-oxide, BP-7,8-dihydrodiol [cis(e, a), cis(a, e), trans(e, e), and trans(a, a)], and BP-7,8-dihydrodiol-9,10-epoxide [β,β,β (the most stable), β,β,α; α,α,β, and α,α,α all derived from cis-BP-7,8-dihydrodiol and β,α,β; α,β,β and α,β,β derived from trans-BP-7,8-dihydrodiol]. Several different conformations were calculated for each of the BP dihydrodiols and BP dihydrodiol epoxides. Calculations were carried out for the opening of the C9 - O - C10 epoxide ring both toward C9 and C10 for the, most stable β,β,β isomer of BP-7,8-dihydrodiol-9,10-epoxide. Opening the epoxide ring between C10 and O leads to a more stable intermediate than opening the epoxide ring between C9 and C10. However, there is no buildup of positive charge in C10 as has been postulated by some cancer researchers, but rather the C10 becomes slightly more negative. Nor is there a buildup of negative charge on the O atom. rather it becomes slightly less negative. As the epoxide ring is opened further than 90° for the O - C9 - C10 or O - C10 - C9 angles, there appears to be a possible mixing of configurations that is being investigated further.
    Additional Material: 3 Ill.
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  • 107
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 779-791 
    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 reports an ab initio molecular-orbital (MO) study of binding of SH2 and SH- with ZnII. The mechanism of binding of ZnII with these ligands is investigated using a detailed analysis of the energy decomposition and of the electronic distribution. The dependence of the results on the choice of the basis set for sulfur (in particular the effect of incorporation of diffuses p and d orbitals) on the geometry of ligand binding, the binding energy, and the proton affinity of SH- are investigated. Comparison made with the corresponding results concerning the binding of OH2, OH-, and NH3 shows that sulfur binding is less favorable although more covalent. Both sulfur ligands show a marked preference for angular conformations for binding with the metal ion. The effect of ZnII binding on the ease of deprotonation of H2S is quite similar to the corresponding effect found earlier for H2O.
    Additional Material: 2 Ill.
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  • 108
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    International Journal of Quantum Chemistry 14 (1978), S. 815-838 
    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 new theoretical approach to study the enthalpy variations occurring during an enzymatic reaction is presented. The structural modifications of the enzyme-substrate complex along the reaction path are distinguished as macro- and microdeformations. Macrodeformations, which concern primarily the approach of the substrate to the enzyme and the release of the reaction products and arise from nonbonded interactions, are treated with an empirical method for computing the energy of a macromolecule. Microdeformations, which are local displacements driven by variations of the electronic structure and its energy and involve only a limited portion of the complex, are treated with the ab initio SCF-LCAO-MO method. The reaction path is idealized as a sequence of major steps: at each step, first the empirical program REFINE is used to calculate the geometry of the system for that step, then the energy of an appropriate subsystem is computed ab initio with the program IBMOL, using the geometry provided by REFINE and applying small concerted atomic displacements. Thus along the entire reaction path one can obtain an energy profile computed with the ab initio method and compatible with the structure of the whole complex. This approach was applied here to the first steps of the reaction of proteolysis catalyzed by papain. The formation of an ion pair ImH+ …S- between the side chains of residues His-159 and Cys-25 was examined in detail. The results show that the instability of the ion pair decreases by ˜ 11.5 kcal/mol when the interactions with residues Asn-175 and Ala- 160 are taken into account; the instability is further decreased by ˜2 kcal/mol after a partial geometry optimization. The energies of the noncovalent enzyme-substrate complex and of the tetrahedral intermediate were computed, considering N-methyl acetamide (NMA) as model substrate and representing papain with the residues Cys-25, His-159, Gln-19, and Ala-160. The interaction energy of the noncovalent complex is -3.8 kcal/mol, compared to the value of +7.4 kcal/mol for the CH3S- -NMA complex. The tetrahedral intermediate is found to be less stable than the noncovalent complex by 27 and 38.5 kcal/mol, respectively, for the papain-NMA and the CH3S- -NMA systems. While these rather large energy differences are possibly due to the incorrect geometry of the tetrahedral intermediate and optimization of the structure is required, it appears that the interactions with the various protein residues represent a very important stabilization factor, which lowers the onthalpy variations during the reaction.
    Additional Material: 9 Ill.
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  • 109
    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 MINDO/2 SCF MO geometry optimization of cytosine (C), thymine (T), uracil (U), the imino tautomer of cytosine (C*), the enol tautomer of thymine (T*), and the enol tautomer of uracil (U*)was made. The optimized geometries for cytosine, thymine, and uracil agree well with crystallographic data. The optimized geometries for the tautomers show the correct trends in bond lengthening and bond angle except for the C4 - O4 length and C4 - O4 - H angle of T* and U*. The energies of tautomerization were found to be 10.3, -9.0, and -14.2 kcal/mol for C⇌C*, T⇌T*, and U⇌U*, respectively, when optimized geometries are used. The overestimation of the C4 - O4 - H angle is speculated to arise because of an inadequacy in the parametrization of the one-center integrals in MINDO/2.
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  • 110
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    International Journal of Quantum Chemistry 13 (1978) 
    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
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  • 111
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    International Journal of Quantum Chemistry 13 (1978), S. 27-39 
    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: Hamiltonian matrix elements between pairs of explicitly correlated Singer polymals are derived. A new method for 1/r12 matrix elements is found which avoids the 6 by 6 matrix inversion required at each quadrature point in the old method. The new formula requires about half the computer time of the old one. The electron repulsion and nuclear attraction matrix elements are shown to be related to incomplete elliptic integrals. Simplified formulas are derived for the special cases of cylindrical symmetry, spherical symmetry, and single-center expansions. An upper bound approximation formula for the purpose of neglecting matrix elements is derived. These bounds may be useful for single-center expansions but are found to be too high for the general case.
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  • 112
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    International Journal of Quantum Chemistry 13 (1978), S. 89-124 
    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 upper and lower ground state energy bounds for many-fermion systems is considered from the viewpoint of reduced density matrices. Model density matrices are used for upper bounds to, first uncoupled, then coupled fermions. Model Hamiltonians are developed for lower bounds in corresponding fashion. Both mathematical and physical models are constructed for setting up universally valid inequalities on density matrices. These are joined by both inequalities and equalities in which the explicit form of the system at hand is used. A few illustrative examples are presented.
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  • 113
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    International Journal of Quantum Chemistry 13 (1978), S. 143-148 
    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 determining idempotent one-densities which integrate to the exact or to a highly correlated particle density is considered. A method for obtaining the minimum energy idempotent one-density integrating to a given correlated particle density within a finite basis is described. The implications of this are twofold. First, Hartree-Fock accuracy can be exceeded in describing the electron density with an idempotent one-density; this is particularly relevant to the problem of constructing orbitals from experimental x-ray scattering data. Second, electron densities from analytic CI or MCSCF wave functions can be made available in a form as compact as the Hartree-Fock density by reporting the orbitals which define the correlated density via an idempotent one-density. A numerical example of the new method is given in which an accurate correlated density for He is “fitted” by an idempotent one-density represented in a finite (near Hartree-Fock) basis. Considering the deficiencies of the basis for this purpose, a technique is suggested for constructing basis sets optimized for prediction of one-electron properties rather than for energy.
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  • 114
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    International Journal of Quantum Chemistry 13 (1978) 
    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
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  • 115
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    International Journal of Quantum Chemistry 13 (1978), S. 169-187 
    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 electronic structure, potential energy curves, and radiative transition probabilities of excimer systems have been examined using quantum mechanical methods. These molecules are characterized by repulsive or weakly bound ground state potential curves and by bound, strongly ionic, or Rydberg, excited states. They constitute a very interesting class of molecules which offer the possibility for high power, high efficiency UV laser operation. Calculations have been carried out using the density functional SCF-Xα method, modified extensively to correct for well known errors arising from approximations to the potential and exchange terms. A limited number of ab initio calculations were also carried out for comparison purposes. For the ArF system we find that the lowest excited ionic state has symmetry 2∑½+, and that the dominant laser transition observed at 1933 Å should be assigned to B 2∑½+ → X 2∑½+. The C 2Π3/2 → X 2∑½+ transition is calculated to be two orders of magnitude smaller in emission intensity than the dominant transition, thus ruling out this assignment for the observed laser line in ArF. Preliminary calculations carried out for Ar2F indicate that the bound upper ionic state has 2B2 symmetry and that the most probable ground state also has 2B2 symmetry. This polyatomic system is predicted to exhibit a broadband emission spectrum with a relatively long radiative lifetime.
    Additional Material: 6 Ill.
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  • 116
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    International Journal of Quantum Chemistry 13 (1978), S. 227-233 
    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: General analytic formulas for derivatives of real Slater orbitals with respect to the Cartesian coordinates x and y have been derived. The application of this result to molecular geometry optimization or to the construction of a force constant matrix is briefly discussed.
    Additional Material: 2 Tab.
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  • 117
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    International Journal of Quantum Chemistry 13 (1978), S. 255-260 
    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 windows in the absorption spectrum of a harmonic oscillator coupled to a bath can be given a two-parameter form identical to the Fano windows in the absorption cross section of an atom with an autoionizing state.
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  • 118
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    International Journal of Quantum Chemistry 13 (1978), S. 297-310 
    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: Multipole expansions of Gaussian-lobe atomic orbitals around their centers are theoretically investigated in order to study the exact angular dependence of such functions. Analytical expressions of the multipole coefficients are derived for standard lobe orbitals. It is shown that the average-square values of multipole components are related to a unique orbital parameter λ. The numerical values of p- and d-components are given for selected λ and the choice of this parameter is discussed on the basis of symmetry and computational arguments. The transferability of optimized atomic exponents from harmonic (or Cartesian) functions to lobe functions is established so that the possibility of applying the Gaussian-lobe orbital approach in chemical studies is greatly extended.
    Additional Material: 1 Ill.
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  • 119
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    International Journal of Quantum Chemistry 13 (1978), S. 17-26 
    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 possible mode for the capture of a cation by the carrier molecule valinomycin has been simulated. The intramolecular nonbonded energy and the binding energy for a centrally located potassium ion at different stages in the capture process have been evaluated using a method proposed earlier. Contrary to intuitive expectations the open conformation of valinomycin is also found to have a strong affinity for K+. There appears to be a rather high potential barrier between the open and closed symmetric conformations.
    Additional Material: 3 Ill.
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  • 120
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    International Journal of Quantum Chemistry 13 (1978), S. 83-88 
    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: Most commonly the nonorthogonality of geminals is weakly expressed so that the exchange and overlap integrals ζ(η), ϕ(η) are negligible for large exchange parameters η. The conditions which allow the terms with large η to be discarded are considered. The integrals ζ(η), ϕ(η) are derived for η = 2, 3, 4.
    Additional Material: 2 Tab.
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  • 121
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    International Journal of Quantum Chemistry 13 (1978), S. 155-158 
    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
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  • 122
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    International Journal of Quantum Chemistry 14 (1978) 
    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
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  • 123
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    International Journal of Quantum Chemistry 14 (1978), S. 163-169 
    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 operators of dynamical observables of the crystal electron (velocity vector components. reciprocal mass tensor components and their functions) commute with the energy operator; hence, the averages of these observables can be adequately approximated by the eigenfunctions for the energy operator. Calculations of the averages were based on the LCAO eigenfunctions classified according to incompletely symmetric irreducible representations of the point group of the cubic crystal, and a similar classification was made for the averages.
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  • 124
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    International Journal of Quantum Chemistry 13 (1978), S. 263-263 
    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
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  • 125
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    International Journal of Quantum Chemistry 14 (1978), S. 127-152 
    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 the studies on impure metals where the perturbation potential due to the impurity has symmetry of the point group of the crystal, subdivision of the electron density of the pure metal into irreducible representations of the point group is of significance. A method is presented for the calculation of wave functions of the perfect cubic crystal which transform according to the incompletely symmetric irreducible representations of the point group. The functions were evaluated in the LCAO approximation using s-type AOS for the face centered cubic lattice. These are in the form of standing waves, and their coefficient functions are linear combinations of the products of the cubic harmonics of a suitable type and the spherical Bessel functions. Properties of the solutions obtained were examined. Numerical calculations were made for four irreducible representations of the point group.
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  • 126
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    International Journal of Quantum Chemistry 13 (1978), S. 1-16 
    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 an STO-3G basis set, energy localized molecular orbitals (LMO) were determined for the ten electron series HF, H2O, NH3, and CH4 as well as for CH3OH and C2H2F2. The method of conjugate gradients is shown to be a viable alternative to other non-eigenvalue methods. The characterization of the LMO in terms of first and second moment measures indicates that the STO-3G basis set LMO may be accurately correlated to larger sp basis set LMO. Also, it is shown that the first and second moment measures display a good linear correlation with the classical concept of electronegativity.
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  • 127
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    International Journal of Quantum Chemistry 13 (1978), S. 41-65 
    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: Various forms of the unrestricted Hartree-Fock (UHF) scheme are studied for a simple three-electron model system, represented by the PPP (Pariser-Parr-Pople) π-electron model of the allyl radical. Both spin and space symmetry are violated in the UHF trial wave function, either individually or simultaneously. A comparison with the projected Hartree-Fock (PHF) schemes studied earlier is made and the effect of the order in which various symmetries are broken in both UHF and PHF schemes is studied. The effectiveness of various schemes follows from a comparison of the correlation energy and the wave function is obtained by various UHF (or projected UHF) and PHF schemes, in the whole range of the coupling constant, with the corresponding quantities given by the exact solution of the model. Finally, the implications of the stability of the restricted HF solutions for the behavior of various single- and multiparameter UHF and PHF schemes are briefly outlined and exemplified on the studied model.
    Additional Material: 11 Ill.
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  • 128
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    International Journal of Quantum Chemistry 13 (1978), S. 149-153 
    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 homogeneity properties of the kinetic and potential energy operators are used to obtain expressions for the second derivatives of the energy expectation value. These are used to demonstrate that in atoms as well as in molecules in the neighborhood of the equilibrium geometry the variational energy cannot have maxima with respect to the non-linear parameters.
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  • 129
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    International Journal of Quantum Chemistry 13 (1978), S. 159-159 
    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
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  • 130
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    International Journal of Quantum Chemistry 13 (1978), S. 189-198 
    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 consider the “Hartree Problem,” here defined as the problem of finding the orthogonal one-electron states which in a single determinant minimize the electronic energy, excluding exchange contributions. These states may provide a useful basis for correlation-energy studies. It is shown how the “Hartree Problem,” although superficially not of pseudoeigenvalue form, can nevertheless be cast in such a form and solved by an iterative diagonalization process.
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  • 131
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    International Journal of Quantum Chemistry 13 (1978), S. 221-226 
    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 primary purpose of the present paper consists in obtaining a correction to Dingle's potential for a (point) impurity ion (embedded) in Si or Ge. This goal is accomplished by making use of a variational principle in taking into account the effect of the spatial variation of the dielectric constant in the respective medium. It is found that the resulting impurity-ion potential can be represented as the product of Dingle's potential and a factor which, with increasing distance from the charged impurity, approaches unity. The secondary purpose of the present paper consists in suggesting a way for the modification of an impurity-ion potential that has been obtained previously with a boundary condition, that, in retrospect, is open to criticism. It is shown that the modified impurity-ion potential can be represented as the product of the author's previous potential and a factor which, with increasing distance from the charged impurity, approaches unity.
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  • 132
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    International Journal of Quantum Chemistry 13 (1978), S. 261-262 
    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
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  • 133
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    International Journal of Quantum Chemistry 13 (1978), S. 265-270 
    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 perturbation contributions to the correlation energy of the H2 molecule are analyzed. This analysis is based on the computer solutions of several two-electron equations in the Gaussian geminal basis set. The pair equations differ by the choice of the two-electron interaction potential which may result from distinct infinite summations of correlation diagrams in Rayleigh-Schrödinger perturbation theory.
    Additional Material: 1 Ill.
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  • 134
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    International Journal of Quantum Chemistry 13 (1978), S. 325-330 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis is presented that shows how the angular symmetry defects of lobe orbitals constructed from a polyhedric edifice can be accurately evaluated, and how these lobe orbitals can be related to harmonic Gaussian functions, the exponents being tranferred by a scale factor procedure.
    Additional Material: 2 Tab.
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  • 135
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    International Journal of Quantum Chemistry 13 (1978), S. 375-390 
    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 symmetry of first-order vectors in Hartree-Fock perturbation theory is developed. This leads to the definition of symmetry-adapted basis vectors to be employed at first order in the perturbation. It is shown that computer time can be saved, to some extent, in the calculation of second-order properties, by exploiting molecular symmetry. Specific examples are given for methane, ammonia, and water.
    Additional Material: 11 Tab.
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  • 136
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    International Journal of Quantum Chemistry 13 (1978), S. 443-454 
    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 the method of alternant molecular orbitals (AMO), it is shown that the energies of AMOS (Ekσ) for an arbitrary heteronuclear alternant system, having a singlet ground state, are connected with the energies of MOS (ek(k)) obtained by means of the conventional Hartree-Fock (HF) method (SCF-LCAO-MO-PPP) via the formula: \documentclass{article}\pagestyle{empty}\begin{document}$$ E_{k\sigma } = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}\left( {e_k + e_{\bar k} + \delta _{1,k\sigma } } \right) \pm \sqrt {\left( {\frac{{e_k - e_{\bar k} }}{2} + \delta _{2,k\sigma } } \right)^2 + \delta _{3,k\sigma }^2 } $$\end{document} In the general case, the determination of the correlation corrections δi,kσ is connected with the solving of a complicated system of integral equations, which is considerably simplified if the Hubbard approximation is accepted for the electron interaction.The energy spectrum of a chain with two atoms in the elementary cell (AB)n is considered as an example. It is shown that if nontrivial solutions exist (δi,kσ ≠ 0), the correlation correction for AMOS of different spin are different (δi,kσ ≠ δi,kβ), from which it follows, that the width of the energy gap ΔE∞ for AMOS with different spin is different: ΔE∞,α ≠ ΔE∞,β.
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  • 137
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    International Journal of Quantum Chemistry 13 (1978), S. 553-562 
    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: When considering the dynamical properties of a molecule in contact with an external medium whose degrees of freedom are at equilibrium, one can adopt either of two approaches to the problem. The equations of motion which govern the coupled molecule-medium system can be solved (or approximately solved), after which the initial values of the medium's coordinates are averaged over (with an equilibrium distribution function as weighting factor) to obtain the desired property of the molecule. In the second approach, which is the subject of the present work, the effects of the medium on the molecule of interest are incorporated into a time-dependent effective potential which contains the equilibrium average molecule-medium interaction as well as terms arising from fluctuations in the medium's coordinates about their equilibrium values. By introducing such an effective potential via the cumulant expansion technique, the problem of studying dynamical properties of the molecule is reduced to the study of a molecule which is in the presence of a time varying external field which no longer depends explicitly upon the coordinates of the medium. In addition to developing the basic method for treating such problems, applications of the method to interesting problems are briefly discussed.
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  • 138
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    International Journal of Quantum Chemistry 13 (1978), S. 619-626 
    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 possibility of level crossings is discussed from a general multidimensional partitioning viewpoint. By extending the traditional motion of a self-adjoint Hamiltonian to a self-adjoint analytic family of operators, it is found that level intersections that appear fall into two mutually exclusive categories: the conventional diagonal one corresponding to Jordan blocks of order m = 1, and the nondiagonal one with m ≥ 2. Consequences with respect to some recent examples, such as Longuet-Higgins “sign-reversing loop” construction and the 1II near degeneracy in SiO, are discussed and examined.
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  • 139
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    International Journal of Quantum Chemistry 13 (1978) 
    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
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  • 140
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    International Journal of Quantum Chemistry 13 (1978), S. 731-736 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some structural features of the diagonal problem of reduced density matrix theory are investigated by considering the cone Br introduced elsewhere. In some special cases, we discover a very tight connection between the group structure of Gr, the invariance group of Br, and the convex structure of Br. We also state a general theorem that relates the convex structure of Br to the group structure of Gr.
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  • 141
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    International Journal of Quantum Chemistry 13 (1978), S. 737-742 
    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 pointed out that the density matrices of the ground state contain valuable information concerning the calculation of particle-hole excited states. As an illustration, results on the nuclei 16O, 20Ne, and 28Si are presented, using small model spaces.
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  • 142
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The RPA, SCRPA, Tamm-Dancoff, and full CI methods are compared by analyzing their transition density matrices, oscillator strengths, and energy moments of oscillator strengths for the 1Sground - 1Podd transitions of the 4-electron B+ ion in the frozen K-shell approximation. It is found that the RPA gives transition density matrices that are aligned nearly as well as possible along those of the full CI, but have vector lengths that are significantly too long. The corresponding transition energies are significantly too small. These errors compensate to give oscillator strengths for the dominant transition that, for all forms of the oscillator strength, are within 1.6% of the corresponding full CI values. The SCRPA gives better transition density matrices than the RPA, but poorer oscillator strengths. The Tamm-Dancoff approximation gives very good values for the mixed length-velocity form of the oscillator strength. The RPA gives a static electric dipole polarizability that is nearly 20% larger than that of the full CI. The SCRPA gives a value 15% smaller than - and the Tamm-Dancoff approximation gives a mixed length-velocity value that is 11% larger than - that of the full CI. Other energy moments of oscillator strengths are also reported. Certain other approximations related to the RPA and the SCRPA are reported as well.
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  • 143
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    International Journal of Quantum Chemistry 14 (1978), S. 1-11 
    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 MCSCF wave functions of Das for Li2, and Das and Wahl for F2, have been analyzed in terms of Berlin's binding and antibinding regions. The effect of electronic correlation on the charge distributions in these regions is studied. The process of bond formation in going from separated atoms to the correlated molecule is also discussed with reference to Berlin's regions.
    Additional Material: 2 Ill.
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  • 144
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    International Journal of Quantum Chemistry 14 (1978), S. 55-63 
    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 Eckart frame is a frame of orthonormal vectors ei, i = 1, 2, 3, which follow a vibrating molecule while it rotates. The frame is orientated by the so-called Eckart condition, which Eckart found by requiring the Coriolis interaction to be minimal. In the present paper we shall see that Eckart's frame also can be characterized by a simple least squares property. Eckart showed how to construct the ei's by a certain orthonormalization of three vectors Fi, i = 1, 2, 3. We observe that this orthonormalization is in fact Löwdin's symmetric. Then we consider the least squares property in the light of the Carlson-Keller theorem - which is given a slightly different form. It is shown that the complete solution to Eckart's condition can be generated from the one of interest by C2 rotations around axes in an orthonormal set which originates from the Fi's by Löwdin's canonical Orthonormalization.
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  • 145
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    International Journal of Quantum Chemistry 14 (1978), S. 121-126 
    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 proved that two molecular symmetry-lobe orbitals, belonging to different irreducible representations, can have a non-negligible overlap. Using a previously reported multipolar analysis of Gaussian-lobe orbitals (GLOs), it is demonstrated that such defects occur when individual symmetry orbitals (SOs) are both contaminated in a given Y1m subspace, even if such contaminations are very small. A numerical application illustrates this result in the case of the NH3 molecule, and it is shown that axial-GLOs allow for the exact cancellation of the symmetry defects.
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  • 146
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    International Journal of Quantum Chemistry 14 (1978), S. 253-269 
    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 demonstrated for a spin-free, nonrelativistic, complete molecular Hamiltonian that there is an optimal solution to the separation of electronic and nuclear motions. The adiabatic approximation is obtained as a special limiting case. A fruitful interpretation of intermolecular correlation results from the assumption that such correlation involves the degeneracy of a molecular-energy state of one molecule with that of another chemical species, e.g., cubane and cyclooctatetraene. As a consequence, rigorous relationships are established for the influence of nodal patterns of the electronic functions on intermolecular correlation. Also derived are stringent symmetry rules which both electronic and nuclear functions involved in the correlation must obey. Throughout the treatment is a many-electron one.
    Additional Material: 3 Ill.
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  • 147
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    International Journal of Quantum Chemistry 14 (1978), S. 313-318 
    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 new method is presented for the variational calculation of a set of vectors under the condition that the metric of the vectors remains unchanged through the process of variation. Application of this method to typical measures (energy, overlap, distance, etc.) in quantum chemistry gives rise to new variational equations, for which the solution yields the Löwdin symmetric orthonormalization, the Kashiwagi-Sasaki generalization, the symmetric deorthogonalization, and the Adams localization, etc.
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  • 148
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    International Journal of Quantum Chemistry 14 (1978), S. 337-340 
    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.
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  • 149
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    International Journal of Quantum Chemistry 14 (1978), S. 343-352 
    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 complex scaling method, also known as the complex coordinate or dilatation transformation method, is discussed in relation to the Stark effect and to the calculation of the position and width of resonant states of atoms or molecules. The significance of resonant scattering in atomic physics is briefly reviewed.
    Additional Material: 2 Ill.
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  • 150
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    International Journal of Quantum Chemistry 14 (1978), S. 419-441 
    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
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  • 151
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 152
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    International Journal of Quantum Chemistry 14 (1978), S. 613-621 
    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: Even after completing a multiconfiguration self-consistent-field (MCSCF) calculation, one must often include additional configuration interaction (CI) to obtain quantitative or semiquantitative results. There is some question of whether the prior MCSCF calculation is worthwhile, if additional CI is needed later. We have developed a new MCSCF computational method, which, because of our assumptions about the nature of the configurations, yields one Fock-like operator for all the “filled” orbitals (high occupation numbers) and a second Fock-like operator for all the “virtual” orbitals (low occupation numbers). Since there are only two matrices to build, our method is considerably faster than other MCSCF approaches. Because of these similarities to standard molecular-orbital (MO) calculations, we have termed our approach generalized-molecular-orbital (GMO) theory. However, the “virtual” orbitals, unlike those of standard MO theory, are optimized to correlate the “filled” ones and can he used in a subsequent CI calculation. Results are presented for the correlation energy of H2O, the spectroscopic constants of N2, the singlet-triplet energy separations in CH2, and the nature of the chromium-chromium quadruple bond. Although these results are at a very low level of CI, the GMO approach appears to correct for the gross deficiencies of the single-determinant SCF procedure.
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  • 153
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    International Journal of Quantum Chemistry 14 (1978), S. 695-702 
    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 is a summary of a detailed treatment, given elsewhere, in which (gauge invariant), equations of change (at points in configuration space) of arbitrary dynamical properties of an N-particle quantum-mechanical system in the presence (or absence) of an arbitrary (time- and space-varying) classical electromagnetic field are derived for an arbitrary Hamiltonian by making use of both the Maxwell and the Schrödinger time-dependent equations. The properties at a point in configuration space are defined so as to be closely related to observables and the forces are related to their classical counterparts. The rates of change of linear momentum and angular momentum are closely related to the classical Lorentz force and the Lorentz torque, respectively. The rate of change of energy is the work done on the system by E(t), the time-dependent part of the external electromagnetic field. The reason for E(t) and its definition of the energy for a system in a time-varying electromagnetic field is explained. The Breit-Pauli Hamiltonian is required to treat “state-to-state” molecular problems and the detailed equations of change using this Hamiltonian are used as examples.
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  • 154
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    International Journal of Quantum Chemistry 14 (1978), S. 717-726 
    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: Ab initio self-consistent-field (SCF) and configuration interaction (CI) calculations on the ground and excited states of carbonyl fluoride (F2CO) were carried out at its experimental ground-state equilibrium geometry. Vertical transition energies deduced from the CI results provide assignments for the electronic systems I-IV, experimentally observed by Workman and Duncan. The singlet excited state, 1A1 (π→π*), is found to be a mixed valence-Rydberg state and to he 1 to 1.2 eV above the suggested experimental value, irrespective of the choice of the basis used for the CI calculations.
    Additional Material: 5 Tab.
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  • 155
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    International Journal of Quantum Chemistry 14 (1978), S. 727-736 
    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 aspects of the numerical application of the complex-coordinate method for calculating helium autoionizing resonances are discussed. A direct-search algorithm is used to locate resonance eigensolutions that satisfy the virial theorem, and the influence of the basis set on the accuracy of the calculated positions and widths is investigated. The complex-coordinate method is related to the stabilization method of Holøien and Midtdal.
    Additional Material: 7 Ill.
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  • 156
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    International Journal of Quantum Chemistry 14 (1978), S. 741-746 
    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 of extended-basis SCF calculations indicate that BeF2- may exist as a metastable species. Comparison of results obtained from SCF calculations on neutral BeF2 with those of BeF2- shows that the orbital occupied by the electron of BeF2- is well approximated by the lowest unoccupied molecular orbital of neutral BeF2.
    Additional Material: 1 Ill.
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  • 157
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 59-65 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note presents the closed form equations for the stiffness terms in the elastic-plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl-Reuss flow rule and von-Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
    Additional Material: 2 Ill.
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  • 158
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 85-92 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
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  • 159
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 93-99 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note describes improvements to the Suhara-Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
    Additional Material: 6 Ill.
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  • 160
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 183-185 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
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  • 161
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    International Journal for Numerical Methods in Engineering 12 (1978) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1-10 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 47-57 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady-state visco-plastic flows.
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  • 164
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 101-114 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element formulation for large elasto-plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress-strain curves for several proportional loadings, effect of change of loading path on stress-strain curve, subsequent yield loci for uniaxial and equi-biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
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  • 165
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 382-383 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 166
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 405-414 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 167
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 453-469 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
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  • 168
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1375-1382 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
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  • 169
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1367-1373 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A recent paper by Donald Gignac describes some difficulties with a certain matrix eigenvalue problem. This paper shows that the difficulties result from the naturue of the matrix itself. Quantities called condition numbers, which measure the sensitivity of the eigenvalues, are computed, and numerical results given.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1383-1397 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The boundary-integral equation medthod is particularly well suited for solution of stress concentration and elastic fracture mechanics problems. The method was not previously applicable to anisotropic three dimensional problems because no efficient technique existed for calculation of the required point load solution for an infinite body. A technique has been developed to evaluate numerically the anisotropic point load soultions, and used to generate data bases for various materials. An intrpolation technique is used to evaluate the point load solutions efficiently within a higher order boundary-intgral equation code. The effectiveness of the technique is verified by solution of problems involving both uniaxial stress states and stress concentrations.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1473-1477 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 172
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  • 173
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1659-1666 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 174
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1635-1650 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A diagonal lumped mas formulation with non-zero inertia terms is presented for Ahmad's general shell element. The effect of co-ordinate transformation of the mas matrix is demonstrated. Due to arbitray co-ordinate transformation on nodal variables, the diagonal lumped mas matrix becomes a banded matrix of half bandwidth three. It is shown that with some approximations this matrix can be made diagnoal without effecting the results appreciably. Numerical examples are presented to illustrate the accuracy of the formulation. Similar lumped mass matrix formulation is also given for axisymmetric shell elements.
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  • 175
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1651-1657 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite-difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly-rectangular domain for a wide variety of partical problems. The introduction of sheared co-ordinates in this computational domain then provides for solution of the problem in a nearly-orthogonal (in fact, nearly-conformal) co-ordinate system, with its boundaries corresponding to co-ordinate lines. The method is based upon the Schwarz-Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1667-1676 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a thin plate element formulated along parallel lines to the general three-dimensional Semiloof shell element. This plate version possesses only one half of the total number of degrees-of-freedom of the shell element and has the advantqage that the formulation of the strains and other terms is very much simplified. The element is first assessed in static situations and then its performance in the solution of eigenvalue problems is considered.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1697-1704 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper analyses the oscillatory nature of central difference approximations to the heat transport equation when convection is the important mechanism of heat transport. The effects of three different boundary conditions, various heat source profiles, the Peclet Number and the parity of the number of meshes on the amplitudes of these oscillations are described. A boundary condition is presented which suppresses the oscillations to insignificant amplitudes in the one-dimensional situation.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1764-1771 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Upwinded parabolic and cubic elements are derived on a uniform grid of size h for the finite element Galerkin method applied to the solution of the model conduction-convection problem εu″  -  Ku′ = 0, ε, K 〉 0, subject to the boundary conditions u(0) = 1, u (1) = 0. Extension of the results to more complicated problems is indicated. Finally numerical results are given comparing some of the methods derived for a range of L(=Kh/2ε), the grid Peclet number.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1819-1839 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper describes a hybrid stress finite element formulation for geometrically non-linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger-Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi-field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non-linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton-Raphson iteratioin. Numerical examples presented in the paper include complete snap-through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non-linear shell problems of high complexity.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1883-1889 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1890-1896 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Symmetric three point quadrature schemes are at present available for triangles for exact integration of polynomials of degree 2. There are other possible symmetries, which provide higher accuracies. Exact integration of polynomials of a higher degree is possible. General formulations are made and a set of three integration points for improved accuracy is given.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1898-1900 
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  • 183
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1897-1898 
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  • 184
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    International Journal for Numerical Methods in Engineering 13 (1978), S. 203-228 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A brief review of the structural optimization literature and a description of the present status of optimization methods are presented. The scope of the review is limited and does not profess to cover the entire literature.Results of the optimization of two structures (by the optimality criteria approach) are presented. There are some conclusions and recommendations for future developments in structural optimization.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 11-33 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The discretization of the media at all spatial co-ordinates but one is presented here. This partial discretization leads to continuous finite elements as opposed to fully discrete ones and the problem resolves, for the cases presented here, into a set of linear differential equations rather than algebraic equations. The general problem of first derivative functionals in elastostatics is considered and it is shown, in general, how the continuous finite elements required for the solution may be obtained. Plane states, axisymmetric and three-dimensional continuous elements are obtained to illustrate application to particular cases.Different methods of solution for the set of differential equations are discussed and it is shown that several existing and widely used finite element related techniques are particular cases of this local partial discretization. Three numerical examples are solved to demonstrate the good comparison obtained between the numerical and the exact solutions. The semi-infinite examples included also illustrate the treatment of these types of problems without the use of fictitious boundaries.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 67-76 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: For a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 115-127 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents the finite element method of the analysis of tidal flow. Assuming that tidal flow is periodic, the Galerkin approach is employed as the numerical integration procedure in time using a trigonometric function as the interpolation function. The present method has shown to be suitable for computation especially from the point of computing time and numerical stability.
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  • 188
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 169-181 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The visco-plastic model is used in the context of large displacement (geometrically non-linear) analysis. As the process now involves in numerical computation an updating of relevant stiffness matrices, formulation which is stable and computtionally more efficient. The applications shown demonstrate the applicability of the process to large displacement elasto-plastic shell analysis as well as to problems of creep buckling.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 185-186 
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 194-194 
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 229-235 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The approximation of normal derivatives along a curved boundary becomes a major difficulty in obtaining finite difference solutions for irregular regions. A number of authors (for-example, Allen,1 Fox,2 Greenspan3 and Parker and Ma4) have suggested various solutions to this problem. However, most of these suggested methods are fairly cumbersome to use since they require the use of different formulas for various combinations of mesh and boundary geometries. This note shows a different way to approximate a quite general boundary condition along curved boundaries. The method uses a uniformly spaced mesh, is simple, general, relatively easy to program and appears to give accurate results.
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  • 192
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 267-278 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In many systems it is known a priori, that some states are ony weakly coupled with others. If such systems are solved on parallel processor it is possible to partition the states in such a way that one set of states is assigned to one processor and the other set of weakly coupled states to another. Computations can then be done in parallel. Because of the weak coupling it may not be necessary for information from the two sets to be communicated to each other for many integration steps. This can result in significant cost savings. In this paper, a partitined Runge - Kutta scheme is formulated for use on weakly coupleld systems of ordinary differential equations. An error expression is derived which provides a means for predicting the number of step sizes over which the partitioned formulas can be used in terms of a prespecified error tolerance. Numerical examples are presented both to verify the error expressions and to compare solutions using partitioned and unpartitioned schemes.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 319-329 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The diferential equations governing two-phase flow through a porous medium are derived and the space discretization is carried out by the Galerkin finite element method. An examination of the eigenvalues of the resulting system follows in order to decide on a suitable stability criterion to be satisfied by the time-stepping algorithm. A class of time-stepping schemes is introduced and their behaviour when applied to a specific problem is analyzed. The aim is to achieve an adequate modelling of the water-oil interface and to preserve reasonable values of the capillary pressure. A technique to clustering the mesh around the interface is used to improved the modelling, and a boundary condition based on the relative mobilities of the two fiuids is imposed to enable the program to calculate the water-oil ratio after breakthrough. The effect of lumping the mass matrix is then examined with a view to reducting the surge in the values obtained for the capillary pressure. Finally an optimum method is suggested for use as a starting algorithm for more sophisticated time-stepping schemes.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 384-384 
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    Keywords: Engineering ; Engineering General
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  • 195
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 415-428 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A Finite Element Method using rectangular elements is applied to solve Burgers' non-linear equation in one space dimension. The non-linear algebraic equations thus obtained are solved by an iteration which is equivalent to the generalized Newton method. Numerical experiments indicate that the order of accuracy is equal to 2. In two space dimensions, the method is more efficient than other methods we have tested.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 471-477 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A global variational method (GVM) not requiring the boundary conditions to be incorporated in the trial functions is described. The method is outlined for a linear differential equation and the extensions necessary to handle the non-linear problem of the indirect design of a compressible fluid channel described. The method requires a suitable estimate of a parameter, but the results obtained for the non-linear problem indicate that the actual value of this parameter is not critical (provided that a sufficeintly large number of trial functions is used). Comparisons are made with the results from an alternative GVM approach described in Davies and Hendry.1
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 479-486 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of confined seepage of water under a hydraulic structure, through a porous medium, is considered in an appropriate abstract space. Existence and uniqueness of the solution are proved. The numerical solution is derived by means of the finite element method. An error estimate is given. A sample problems in included.
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1485-1486 
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1487-1488 
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    International Journal for Numerical Methods in Engineering 12 (1978) 
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