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  • 1975-1979  (156)
  • 1970-1974  (59)
  • 1920-1924
  • 1978  (156)
  • 1971  (59)
  • Computational Chemistry and Molecular Modeling  (215)
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  • 1975-1979  (156)
  • 1970-1974  (59)
  • 1920-1924
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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
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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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    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.
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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.
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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.
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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) 
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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
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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.
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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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  • 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.
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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 of Quantum Chemistry 5 (1971), 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 finite Gaussian Expansion method for molecular integrals proposed by Taketa, O-ohata and Huzinaga has been extended to the integrals of molecular properties. The integral formulas of so-called moment, field and field gradient integrals have been derived. It has been numerically shown that in order to evaluate the field and the field gradient integrals based on Slater type orbitals, eight- or ten-term Gaussian expansions are sufficient but this method fails to attain sufficient effective numbers for the moment integrals.
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  • 158
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    International Journal of Quantum Chemistry 5 (1971), S. 239-263 
    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
    Notes: A one-dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass-springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second-order, and it is shown that the perturbation series converges in this range.An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut-off frequency of the linear crystal is determined to be very small, λ ≦ 104 sec -;1.The rate for the lattice relaxation process corresponds to a line-width λ = 6 cm -1 at 0K.An explanation for the thermal quenching of the low-temperature luminescence of SO2 is based upon induced cascade-phonon emission.
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  • 159
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    Topics: Chemistry and Pharmacology
    Notes: A new interpretation of the ordinate in a Walsh diagram for a polyatomic molecule is suggested in terms of the Hellmann-Feynman theorem. This makes use of the fact that in a single-configurational MO wave function the total one-electron density is the sum of individual densities in the occupied orbitals. Walsh-type diagrams have been constructed for three different molecules, water, ammonia and hydrogen peroxide.In H2O and NH3 calculation of the force, and thus of the energy, in terms of the valence angle, is made on the assumption that the central (heavy) atom is kept fixed while each of the lighter atoms moves in a plane containing the principal symmetry axis and the relevant bond, in a totally symmetric fashion; for H2O2 the two oxygen atoms are kept fixed.The angular correlation diagrams obtained reproduce the general features of those obtained by plotting Hartree-Fock MO energies as functions of the valence angles. The conclusion emerges that the force formulation provides a satisfactory pictorial basis for understanding molecular geometry in terms of the balance between the electron-nucleus attractive forces resulting from the charge densities in the occupied MO'S, and the nuclear repulsive forces. However, in the absence of highly accurate charge distributions such an approach is unsuitable for the quantitative prediction of molecular quantities such as valence angles, force constants or energy barriers.
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  • 160
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    International Journal of Quantum Chemistry 5 (1971) 
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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
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    International Journal of Quantum Chemistry 5 (1971), S. 477-478 
    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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  • 162
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    International Journal of Quantum Chemistry 5 (1971), S. 557-563 
    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 work, we report an all-electron SCF-LCGO-CO computation for the ground state wave-function of an infinite polyenic chain. This work demonstrates that ab initio calculations on the electronic structure of polymers become actually feasible. Our results are compared with previously obtained semi-empirical ones.
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  • 163
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    International Journal of Quantum Chemistry 5 (1971), S. 549-556 
    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 Casimir-Polder retarded dispersion energy is calculated for non-symmetric molecules and the energy is expressed in terms of body fixed axes for the dipole transition moments on each molecule. In the special case of molecules with cylindrical symmetry the potential energy is given in terms of the transverse and longitudinal polarizabilities and in terms of the angles defining the orientation of the axes of the molecules with respect to the intermolecular direction. In the limit of no retardation (R ≪ λ) the result becomes that of London and in the opposite limit of full retardation at large R the potential energy tends to that of Craig and Power.
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  • 164
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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: A kinetic model employing calculated atom and bond localization energies to approximate relative activation energies of reaction is used to analyse previously obtained experimental results for in vitro and in vivo chemical binding of polycyclic aromatic hydrocarbons to nucleic acids. It is found that in vitro linkage of hydrocarbons to DNA induced by a microsomal hydroxylating system is compatible with mechanisms involving either attack at the most reactive hydrocarbon center or attack at the most reactive hydrocarbon bond. Independent evidence leads us to favor the former mechanism. Further, the limited experimental data for in vivo linkage of hydrocarbons to DNA is found to be consistent with a model involving attack at the most reactive bond of the molecule: the “K region”. This model is supported by a close parallelism found between extent of hydrocarbons bound to DNA in vivo and the experimentally determined relative reactivities of their K regions.
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  • 165
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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 Separated Electron Pair (SEP) model (Strongly Orthogonal Geminals) and methods for its systematic extension has been applied to the series: NH4+, NH3, NH2-, NH2- and N3-. On going from NH4+ to N3-, the SEP model, in its most general form, recovers 85-75% of the intrapair correlation energy and 60-55% of the interpair correlation energy obtainable with the given basis set. The best wave functions for each species recovered about 45-50% of the total empirical correlation energy which is expected to be very close to the basis set limit. It was apparent that the SEP model yields a set of one-electron functions that are very useful for further improvement of the wave function. This fact apparently remains true even when the SEP model itself gives very poor energies.
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  • 166
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    International Journal of Quantum Chemistry 5 (1971), S. 273-296 
    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 intermolecular interaction is examined by using spatial wave functions and the theory of permutation groups. In the special case of interacting 2-electron systems it is proven that the Rayleigh-Schrödinger perturbation method, when starting from the ground state of the unperturbed system, could only give the physically inadmissible mathematical ground state of the complex (totally symmetric spatial eigenfunction). Then this property is considered in the case of arbitrary interacting systems and a general proof is proposed. From these results a general explanation of the inadequacy of the Rayleigh-Schrödinger expansion for the treatment of short range intermolecular interaction is proposed.
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  • 167
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    International Journal of Quantum Chemistry 5 (1971), S. 319-333 
    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: Hartree-Fock wave functions for the He and Be isoelectronic sequences of ions are calculated using orbitals which are linear combinations of simple exponential functions. By a full optimization of the exponents and coefficients close approximations to the HartreeFock energies were obtained. To the same order of accuracy the resulting Hartree-Fock orbitals require fewer basis functions than used previously. A number of difficulties which arise in the numerical procedures as the size of the basis set is increased are analysed in detail. Similar results are obtained for the Li sequence using the Unrestricted HartreeFock method with and without projection.
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  • 168
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    International Journal of Quantum Chemistry 5 (1971), S. 497-503 
    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 MO-LCAO-SCF treatment is performed on water, ammonia and methane using a recently proposed approximate method.The procedure is found capable of predicting total and orbital energies in close agreement with the results of accurate computations using double ζ basis sets of Slater type orbitals.A comparison is made with the results of similar approximate ab initio procedures.
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  • 169
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    International Journal of Quantum Chemistry 5 (1971), S. 505-512 
    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 various multicenter exchange, hybrid and Coulomb electron repulsion integrals that occur in molecular quantum mechanics are shown to satisfy a Poisson equation in which an overlap integral plays the role of a source distribution function. Two-, three-and four-center exchange integrals arise from four-center source functions; two- and three-center hybrid integrals arise from three-center distributions; and one- and two-center Coulomb integrals have two-center sources.
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  • 170
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    International Journal of Quantum Chemistry 5 (1971), S. 539-548 
    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 use of natural orbital iterations in limited CI calculations is discussed. This method is then applied to the ground X2II state of the nitric oxide molecule at its experimental equilibrium internuclear separation to yield the total energy, dipole moment, spin densities at each nucleus, and approximate natural spin orbitals for this molecule.
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  • 171
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    International Journal of Quantum Chemistry 5 (1971) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 172
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    International Journal of Quantum Chemistry 5 (1971), S. 13-34 
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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: A function analogue of the formal operator theory of Goldberger and Watson for the decay of prepared states is developed with a modification that permits treatment of degenerate, interacting intermediate states. The theory is applied to the problem of absorption of radiation by an absorber in a very intense monochromatic beam. In particular, a simple two-level absorber in a resonant monochromatic beam of sufficient intensity to induce transitions from the ground state at a rate exceeding the spontaneous emission rate from the excited state, but still lying well below the optical frequency characterizing the transition, is investigated with the conclusion that the absorption cross-section falls off with the one-half power of the incident intensity. Conditions for the possible experimental verification of this result are presented.
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  • 173
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    International Journal of Quantum Chemistry 5 (1971), S. 111-113 
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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
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  • 174
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    International Journal of Quantum Chemistry 5 (1971), S. 119-130 
    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 relation between the cluster expansion theory of many electron wave functions and the correlated wave functions method is established. In this way, the theoretical basis of the method is elucidated and the approximations involved in its application become apparent. General forms of the correlated wave function, differing in certain important respects from that form usually assumed, are derived.
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  • 175
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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 electron density and the Fermi hole of the ground states of the atoms He, Be, Ne, Mg, Ar, Ca, Zn, and Kr are studied in the restricted Hartree-Fock approximation. The use of single Slater-type orbitals for the free atoms is also discussed.
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  • 176
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    International Journal of Quantum Chemistry 5 (1971), S. 221-234 
    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 absorption and emission spectra of a diatomic “molecule” connected to an unstrained linear crystal are calculated for the circumstance where the diatomic undergoes a change of equilibrium internuclear separation in the electronic transition. The expansion (or contraction) of the diatomic results in a frequency dependent line-width in the customary Lorentzian expression, and is manifested in the absorption spectrum as an asymmetric tailing to the blue, and in the emission spectrum as an asymmetric tailing to the red. The interaction of the diatomic with the lattice also produces a blue-shift of the absorption spectrum and a red-shift of the emission spectrum. An important consequence of the asymmetry is the apparent loss of integrated intensity of the line. The striking similarity, both in the width and the over-all shape, of the emission line calculated here with those observed in the Vegard-Kaplan band of N2 dissolved in rare gas crystals is discussed.
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  • 177
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    International Journal of Quantum Chemistry 5 (1971), S. 297-309 
    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 optimum projection technique is the determination of the best function in the space spanned by a set off f(N, S) linearly independent antisymmetric space-spin eigenfunctions of S2 obtainable from a spatial function made of a product of N-independent orbitals. This is formulated in the spin-free framework. We consider several sets of predetermined orbitals for the lithium 2S state. Both the energy and spin-density are determined for each optimum projected function. The behavior of certain results is explained in terms of the “closeness” of the ls and ls′ split-shell core orbitals.
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  • 178
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    International Journal of Quantum Chemistry 5 (1971), S. 335-357 
    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: Wave functions of the 1S (ground state), 3P and 1P states for the beryllium isoelectronic sequence have been obtained in various approximations.The HF 2p orbitals for the 1P and 3P states are similar except for Be, where the 2p orbital is quite diffuse for the 1P state.The difference between the experimental E(1P) - E(3P) and the HF E(1P) - E(3P) is 0.62 eV for Be and 1.17 ∼ 1.40 eV for B+ ∼ F5+. The disagreements are attributed to the correlation effects between the 2s and 2p electrons. This is confirmed by ci calculations.It is shown that a limited basis SCF calculation reproduces the above feature of the HF results if we treat the orbital exponents as the variational parameters. The use of the Slater values for the orbital exponents is shown to be inadequate especially for the Be 1P state.The conclusions of this paper will be useful for discussing the V-T separations of H2 and C2H4.
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  • 179
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    International Journal of Quantum Chemistry 5 (1971), S. 395-409 
    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 model of complete loge localization is employed here to develop a practical method for handling correlation effects in atomic and molecular many electron systems. Intraloge correlation is dealt with by an independent variational treatment of pair functions which are continuous and vanish outside a given loge. It is shown that in the context of the model it is possible to compute pair correlation energies for localized single and double bonds in molecules by evaluating only modified atomic integrals. We bypass in this manner the evaluation of multicenter integrals necessary in other formalisms. In addition, the corrections to the model are discussed and in particular it is shown that part of the interloge correlation effects are already described by the loge localized wave function.
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  • 180
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    International Journal of Quantum Chemistry 5 (1971), S. 455-467 
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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 infinite summation of intermolecular ring diagrams is extended to any pair of interacting molecules with isotropic polarizabilities. The calculation no longer requires the use of a minimal basis set. The polarizabilities α,α′ may be factorized at all orders, and an expression is derived, which gives modified Van der Waals energies. For heavy atoms the series converges if αα′/R6 is smaller than 1, R being the interatomic distance. This inequality is easily satisfied for the Van der Waals distances, and in practice the correction due to the high orders of the perturbation expansion remains weak. The role of the EPV diagrams and the connection with a configuration interaction treatment are discussed.
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  • 181
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    International Journal of Quantum Chemistry 5 (1971), S. 583-598 
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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 singly-excited two-electron states 1s2s 3S and ls3s 3S have been investigated by means of the variational perturbation theory procedure. The wave functions have been constructed as linear combinations of Hylleraas terms with hyperbolic factors in t, and the results obtained by carrying the computations through to 10th perturbation order and with 36(37)- 57(58)- and 85(86)-term basic sets, respectively, are reported. These results compare favourably with the corresponding best values from previous conventional variational calculations.
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  • 182
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    International Journal of Quantum Chemistry 5 (1971), S. 637-646 
    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 fully coupled variation-perturbation theory has been introduced for handling open-shell atomic systems in the presence of static perturbations. The static dipolar and quadrupolar polarizabilities and shielding factors for Li, Be+, B2+, B, C+, Na and Al have been calculated and compared with available results. Important sources of discrepancies in previous calculations of shielding factors have been noticed and critically examined. The dipolar shielding factors calculated in this paper show satisfactory agreement with the theoretical N/Z ratio. In the absence of any theoretical test for the quadrupolar shielding factor, the accuracy of the calculations of γ∞, should be judged in the light of the accuracy of the corresponding β∞ values.
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  • 183
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    International Journal of Quantum Chemistry 5 (1971), S. 435-453 
    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 classical intermolecular Rayleigh-Schrödinger perturbation expansion is used with a finite basis of simple products of single determinants. For two hydrogen molecules with a minimal basis set, one shows that the ring and ladder diagrams dominate the perturbation series. The contributions of the purely intermolecular convex and concave ring diagrams are summed at all orders. The mixed ladder-ring diagrams are also included. The series converges if the norm of the first order perturbed wave function is smaller than ½. The summation multiplies the Van der Waals-London forces by an explicit factor.
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  • 184
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    International Journal of Quantum Chemistry 5 (1971), S. 475-475 
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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
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  • 185
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    International Journal of Quantum Chemistry 5 (1971), S. 479-495 
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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 molecular orbital configuration for the ground-state of O2 generates the valence formula . “Increased-valence” formulae for triatomic and polyatomic molecules have been developed recently. In them, more electrons participate in bonding than is possible for the familiar valence-bond formulae. Using oxyhaemoglobin as an example of an oxygen carrier, various increased-valence formulae are generated for the FeO2 groups. In the low-energy formulae, the iron is bonded to the above valence formula for O2. Therefore, in contrast to the bonding schemes of Pauling and Coryell, Griffith and Weiss, little reorganization of O2 need occur on formation of HbO2. This conclusion is independent of the mode of co-ordination of iron to the O2.
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  • 186
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    International Journal of Quantum Chemistry 5 (1971), S. 525-537 
    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: Upper and lower bound expressions are derived to the second-order energy relating to an unperturbed degenerate excited state in those cases where both the first-order energy and the off diagonal matrix elements in the secular equation vanish, making use of the partitioning technique, operator inequalities and inner projection approach. These expressions, which involve an arbitrary basis, are then developed to yield reasonably good bounds to van der Waals dispersion energies for systems of the type H (first excited state)  -  other atom b (ground state). The particular choice of basis used in the development yields the latter bounds easy to evaluate by expressing them in terms of the ground state sum rule values, S(k) of atom b. This same choice is also utilized in Lindner and Löwdin's expressions [1] to obtain bounds to systems of the type H (ground state)  -  other atom b (ground state) that are comparable to those found by other more elaborate semi-empirical methods.
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  • 187
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    International Journal of Quantum Chemistry 5 (1971), S. 565-574 
    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 expressions for the time-dependent probability amplitudes of the quantum states of two arbitrary, interacting atoms are calculated when one atom is initially in an excited p state and the other atom is in an s ground state. The lifetimes of the excited states and the line shape of the emitted radiation are obtained as functions of both the atomic separation and the energy difference between the excited states of the two atoms. The emission line shape is shown to be doubly peaked and to agree with the line shape of the radiation scattered by a system of two interacting atoms. The expressions for the lifetimes of the excited states are found to be identical to those obtained for the radiation scattering situation.
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    International Journal of Quantum Chemistry 5 (1971), S. 599-603 
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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: By means of second quantization formalism and angular momenta coupling techniques, we show the reason why the irrational part of the coefficients of the Slater integrals Rk(ab, cd) in the expression \documentclass{article}\pagestyle{empty}\begin{document}$ (\Psi |\sum\limits_{i 〈 j} {e^2 /r_{ij} |\Psi } ') $\end{document} is common to all values of k, a, b, c, d, and depends only on (Ψ∣ and ∣Ψ′).
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  • 189
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    International Journal of Quantum Chemistry 5 (1971), S. 657-668 
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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 maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.
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  • 190
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    International Journal of Quantum Chemistry 5 (1971), S. 683-697 
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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 energy-localization method is examined for continuous degeneracy using a grouptheoretic approach. Conditions for the degenerate orbitals are obtained and an enumeration of symmetry groups where continuous degeneracy may occur is given. It is found that the orbitals may be equivalent under operations not contained in the total symmetry group. An alternative explanation for the free rotation of the lone pairs in F2 is offered.
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  • 191
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    International Journal of Quantum Chemistry 5 (1971), S. 115-115 
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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
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  • 192
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    International Journal of Quantum Chemistry 5 (1971), S. 101-110 
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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 Variable Electronegativity Pariser-Parr-Pople method has been successfully applied to calculate the potential energy curve for the formation of a 1: 1 complex between quinone and hydroquinone. A consistent evaluation of core and electronic repulsion integrals is important to obtain a meaningful curve. A computationally simple procedure has been suggested for separating interactions due to electron exchange between the components from other intermolecular interactions. In agreement with experimental deductions the preferred configuration for the quinone-hydroquinone complex is found to be one in which the molecules are in parallel planes with their C - O bonds parallel. The equilibrium separation between the molecular planes is found to be 2.3 Å and the stabilization energy in this position is 1.2 eV. In this equilibrium position forces due to electron exchange constitute the major contributing factor to the stability of the complex.
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  • 193
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The [N, M] Padé approximants to functions formally associated to power series expanssions are expressed in terms of expectation values of inverse matrices. These formulae, which can be derived by the inner-projection technique, lead to a simple analysis of the properties of serveral approximation methods and their inter-relationships, in particular Gaussian integration, continued factorization and Padé approximations, which are of current interest in the calculation of physical properties. A relation with Fredholm integral equations and expansions of the resolvent is also discussed.The use of operator inequalities in a systematic fashion is particularly convenient when both the function being approximated and the coefficients of the power series have physically meaningful expressions as moments of operators.
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    International Journal of Quantum Chemistry 5 (1971) 
    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
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  • 195
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 387-394 
    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 Schrödinger equation for helium is written as a generalized eigenvalue equation which is solved for the ground state using perturbation theory. Two zero order equations are used and defined implicitly by specifying their eigenvalues and eigenfunctions. In both cases the eigenfunctions are taken to be the complete discrete set of products of eigenfunctions of the generalized eigenvalue equation for the hydrogen atom. To complete the definition the zero order eigenvalues are needed and two different intuitive choices are made. In the better of our two calculations an energy of -2.9014 a.u. is obtained for helium using the perturbation theory to second order.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 196
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 469-473 
    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 relativistic long-range intermolecular interaction energy term of Mavroyannis and Stephen is estimated for some amino acids by using optical rotatory dispersion data and for hexahelicene by using theoretical values of excitation energies and rotational strengths. The result shows that the interaction energy may be significant for the interaction between some essentially dissymmetric chromophores such as hexahelicene, but that it is unimportant for other cases.
    Additional Material: 1 Tab.
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  • 197
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 478-478 
    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
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  • 198
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 647-655 
    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 variation perturbation method in the Hartree-Fock scheme has been described to calculate excited 3P state wave functions of atoms. The starting wave functions are obtained from a study of the singularities in the dynamic polarizability calculation [1]. The 23P, 33P and 43P states of He, Li+, Be2+, B3+ and C4+ are studied. The results obtained are in satisfactory agreement with experimental values and with other accurate theoretical estimates.
    Additional Material: 4 Tab.
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  • 199
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 699-702 
    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: The super-secular-equation has been introduced by Löwdin to discuss the Schrödinger equation in terms of a linearly dependent basis. The method is shown to be particularly simple when the basis is a symmetry adapted one. By expanding the secular equation a formula giving a good estimate of the eigenvalue is obtained.
    Type of Medium: Electronic Resource
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  • 200
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 513-524 
    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 results of the calculations of π-π* transition energies of some free hydrazyl radicals, their ionic forms and initial hydrazines by the SCF-MO-LCAO method with restricted configuration interaction are presented. The comparison of the data obtained with the electronic spectra experimentally found, revealed that the absorption of radical solutions in the visible area was due to the electronic structure of radical molecules, the contribution of ionic forms to the absorption being negligible.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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