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  • 1980-1984  (548)
  • 1982  (548)
  • Computational Chemistry and Molecular Modeling  (288)
  • Engineering General  (260)
  • Atomic, Molecular and Optical Physics  (206)
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  • 1980-1984  (548)
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  • 101
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 1105-1115 
    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 INDO-SCF method is used to provide electronic indices which are used as independent variables. These attempt to account for the variation in the antitumor activity and toxicity observed within a series of analogs of cis-diamino dichloro platinum(II).
    Additional Material: 1 Ill.
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  • 102
    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 formalism for a configuration interaction approach is presented, in which explicit introduction of interelectronic coordinates into individual configurations is accomplished through the use of spherical Gaussian correlation factors. Formulas for all required matrix elements over these configurations are derived, and a computationally convenient algorithm to evaluate the matrix elements is presented. In addition, analysis of the form of the correlation factor shows that both angular and radial correlation can be obtained using spherical Gaussian correlation factors.
    Additional Material: 1 Ill.
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  • 103
    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: Theoretical computations are performed with the stacking interactions of the 2-naphthylnitrenium ion, the ultimate metabolite of 2-naphthylamine and N-hydroxy-2-naphthylamine, with guanine and adenine. The most stable stacked complex of guanine with this compound is found to be distinctly more stable than that of adenine. The optimized stacking interaction of guanine with 1-naphthylnitrenium ion yields an energy close to that with 2-naphthylnitrenium. By contrast, the dinucleoside monophosphate cytidyl-(3′-5′)-guanosine held in two preselected intercalated conformations is seen to favor 2-naphthylnitrenium over 1-naphthylnitrenium by a significant amount of energy. The possible relevance of this finding to explain the difference in adduct formation with guanine in DNA by the isomeric naphthylnitrenium ions is discussed.
    Additional Material: 6 Ill.
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  • 104
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 101-114 
    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: Electronic energy level set topologies in the abstract nuclear charge space Z of molecular systems are defined and analyzed. Two theorems, one on the general convexity of level sets in Z, another on homotopies of boundaries of level sets, induced by nuclear geometry variations in the nuclear configuration space R, are proven. The applications of the two theorems are illustrated by examples of various molecules and ions.
    Additional Material: 2 Ill.
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  • 105
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 149-168 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The general extended geminal model is reviewed and two new approximate models EXGEM2 and EXGEM3 are introduced. In a test calculation on water using a double-zeta basis set, the approximate models recover 93.4% of the full CI correlation energy defined within the same basis set. A test calculation on the neon atom demonstrates that the performance of the models in comparison with the full CI, will improve as the basis set is increased. It is suggested that for basis sets of moderate and large size, and which include polarization functions, the extended geminal models are likely to recover 95%-97% of the correlation energy obtainable by the full CI.
    Additional Material: 3 Tab.
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  • 106
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 219-219 
    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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  • 107
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 223-239 
    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 complete list of expressions is given covering all possible types of nontrivial two-body operator matrix elements in the unitary group approach. The matrix elements are expressed in terms of factors which depend on the unique spin coupling chain indicated by each Weyl tableau. The method applies equally to pure and mixed orbital configurations. The results extend and clarify previous general treatments of Drake and Schlesinger and Paldus and Boyle. We worked out two examples of 3(ƒ4) matrix elements of V4. V4 interaction and of 4(ƒ5)→4([2(ƒ3)]d2) matrix elements of V1 · V1 interaction.
    Additional Material: 3 Ill.
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  • 108
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 275-288 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We present the first application of the coordinate rotation method, within the time-dependent Hartree-Fock framework, to calculation of positions and widths of metastable excited states. The method is briefly outlined and results of its application to 1P excited states of Li- are given. Comparison of our results to those obtained using electron scattering methods by other workers is also made.
    Additional Material: 3 Ill.
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  • 109
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    International Journal of Quantum Chemistry 22 (1982), S. 331-350 
    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 complete permutational analysis of the XeF6 dynamics is presented. The Longuet-Higgins group for each mode of rearrangement is obtained. On the basis of the splitting scheme of rigid molecule levels and statistical weights and selection rules for the non rigid molecule levels, it appears that transverse digonal twists and turnstile mechanisms have the same spectroscopic effects as the BPR-6 mechanisms. Hence, the previous interpretation of IR and Raman spectra is consistent with tunneling through transverse digonal twists and turnstile mechanisms as well as through BPR-6.
    Additional Material: 6 Ill.
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  • 110
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    International Journal of Quantum Chemistry 22 (1982), S. 397-414 
    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 show that spin projected unrestricted-Hartree-Fock (PUHF) wave functions are able to well approximate some low-lying covalent states of ring π systems. The UHF wave functions belong to either the axial or torsional spin density wave class. Their spin structures are found to be approximations for the spin correlation structures of the corresponding exact wave functions. The PUHF wave functions become close to exact eigenstates with homopolar valence bond characters in the strong correlation limit.
    Additional Material: 2 Ill.
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  • 111
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    International Journal of Quantum Chemistry 22 (1982), S. 433-434 
    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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  • 112
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982) 
    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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  • 113
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    International Journal of Quantum Chemistry 22 (1982), S. 485-496 
    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 detailed consideration of the kinetic aspect of the bridge process has allowed us to correctly write a kinetic equation beginning with knowledge of system microparameters. The solution of the equations makes it possible to elucidate the character of the relaxation process and to determine its typical constants as functions of those microparameters. Particular attention was given to kinetics in the presence of polaron effects. In this case the standard perturbation theory applied to derive the kinetic equations is not valid. The solutions obtained for this case are different both in the form of correlation functions and in the character of the interaction taken into account.
    Additional Material: 1 Ill.
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  • 114
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 557-573 
    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: Addition and subtraction operators defined on some subspaces of the full CI space are introduced. It is shown that the effect of these operators on Löwdin many-electron wave functions consists in adding or removing an electron without destroying spin symmetry. Upward and downward recurrence relations for the Sanibel-type coefficients are presented. A strategy for employing the Löwdin functions for the matrix element evaluation and some special decomposition of the fermion creation-annihilation operators are discussed.
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  • 115
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    International Journal of Quantum Chemistry 22 (1982), S. 631-637 
    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 configurations of the C2H4 · HF molecular complex were studied using the 4-31G basis set. The most stable configuration was found to be the π hydrogen bonded complex. For this structure the interaction energy was computed employing a double-zeta basis plus polarization functions. The changes in electronic properties of the components C2H4 and HF due to complex formation were discussed.
    Additional Material: 3 Ill.
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  • 116
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    International Journal of Quantum Chemistry 22 (1982), S. 639-647 
    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 calculations with an STO-3G basis have been performed to investigate the energetics and electronic properties of some 5-substituted uracils and their 4-OH tautomer forms with R including F, CH3, and OMe. In all cases, the diketo form is more stable. An excellent linear correlation between the calculated and experimental ionization potentials was found.
    Additional Material: 2 Ill.
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  • 117
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    International Journal of Quantum Chemistry 22 (1982), S. 663-663 
    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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  • 118
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    International Journal of Quantum Chemistry 22 (1982), S. 709-716 
    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 an attempt to account for the preferential binding to nonactin of K+ relative to Na+, theoretical computations are performed using the intermolecular interaction energies of the ionophore with the two cations. Both K+ and Na+ liganding conformations are considered, and an evaluation is made of the intramolecular energy expenditure caused by the reduction of the size of the cavity. The energy balance for the complexation of the two cations computed by taking into account the cation-ionophore interactions, the interactions between the liganding groups, as well as the desolvation enthalpies of the cations in methanol, favors K+ over Na+ by 4 to 5 kcal/mol, in fair agreement with the difference in the measured enthalpies of binding. The binding of NH4+ to nonactin is also investigated.
    Additional Material: 3 Ill.
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  • 119
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    International Journal of Quantum Chemistry 22 (1982), S. 691-707 
    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: Maps of electrostatic potential around a number of halocarbon anethetics have been obtained through Gaussian ab initio calculations. Information is obtained on the mode of association of these compounds with possible receptors. The positive potential found along the extension of the C—H bonds substantiates the role of the “acidic hydrogen.” The presence of fluorines on the carbon atom to which it is bound restricts the access to this positive site through the repulsive action of the fluorine lone pairs, an observation that explains the very different behavior of chloroform and fluoroform, for example, with respect to their anesthetic potencies and hydrogen bonding abilities. In the absence of an acidic hydrogen the chlorine atoms can serve as associative sites.
    Additional Material: 5 Ill.
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  • 120
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    International Journal of Quantum Chemistry 22 (1982), S. 739-752 
    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 adsorption of one or many silver atoms on a (111) silicon face (reduced to 61 dangling atomic orbitals) is investigated by means of a self-consistent Hartree-Fock method parametrized from atomic and thermodynamical data. The valley sites (above three Si atoms) are favored over the top sites (above one Si atom). The extrapolation of the results obtained for several structures corresponding to the adsorption of n = 1, 2, 3, 4, 6, and 7 Ag atoms allows us to conclude that the most stable structures correspond: for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{1}{3} $\end{document} to linear Ag chains (3 × 1 phase), for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{2}{3} $\end{document} to an honeycomb lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), and for θ = 1 to a centred hexagonal lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), the Ag atoms located at the centers of the hexagons being beneath the plan of the hexagons. The adsorption energies corresponding to the various θ are practically equal (ca. 3 eV/Ag). The net charges of Ag atoms are equal to 0.35.
    Additional Material: 5 Tab.
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  • 121
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    International Journal of Quantum Chemistry 22 (1982), S. 837-849 
    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 energies of the five lowest 4S and 4P0 states for three-electron ions for 3≤Z≤10 have been calculated by the Hylleraas method. The largest basis set used contained 97 terms with odd as well as even powers of rij. The change of scale r′ = Zr was applied to the Hamiltonian so that the same basis sets could be used for all the three-electron ions leading to great savings in computing time.
    Additional Material: 4 Ill.
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  • 122
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    International Journal of Quantum Chemistry 22 (1982), S. 889-902 
    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: Formulas are presented for the evaluation of the second-order reduced density matrix for correlated wave functions, including wave functions constructed from pairwise nonorthogonal orbitals. Numerical results are provided for the correlation holes and conditional nuclear spin densities for the water molecule.
    Additional Material: 4 Ill.
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  • 123
    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 a multilevel system excited by a laser pulse absorbs a cascade of photons, a second pulse of same frequency, equal duration but dephased by π takes it back to its initial state. This property can be inferred by studying the laser field system interaction matrix, using the rotating wave approximation.
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  • 124
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    International Journal of Quantum Chemistry 22 (1982), S. 1033-1036 
    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 simple and straightforward derivation of (in)stability conditions for projected Hartree-Fock solutions is carried out and compared to the existing approaches to the problem.
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  • 125
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    International Journal of Quantum Chemistry 22 (1982) 
    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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  • 126
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    International Journal of Quantum Chemistry 22 (1982), S. 1083-1084 
    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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  • 127
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    International Journal of Quantum Chemistry 22 (1982), S. 1189-1207 
    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 formalism has been developed to treat hydrogen-bonded A - H…B systems within the CNDO/2 and the MINDO/3 methodologies. In this formalism the interactions are divided into three distinct classes; those between (a) two hydrogen-bonded atoms, (b) one hydrogen-bonded and non-hydrogen-bonded atom, and (c) two non-hydrogen-bonded atoms. The last class of interactions is treated solely by the existing CNDO/2 or MINDO/3 method. For A -H…B systems, the core resonance integrals are individually parametrized depending upon the class of the interaction. Three types of A - H…B systems have been thus far parametrized. Nine hydrogen-bonded dimers have been studied using the new formalism and the current CNDO/2 and the MINDO/3 methods. MINDO/3 predicts very large interatomic (A -B) distances for the equilibrium geometry, and relatively small stabilization values for the hydrogen-bond energies. CNDO/2 predicts the reverse. The new formalism for both CNDO/2 and MINDO/3 predicts accurate geometries as well as energies for all nine dimers. The new formalisms are called CNDO/2H and MINDO/3H. A general discussion of the nature of hydrogen bonding as exhibited by CNDO/2H and MINDO/3H is presented.
    Additional Material: 12 Ill.
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  • 128
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    International Journal of Quantum Chemistry 22 (1982), S. 1249-1262 
    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 virial theorem has played an important role in applying quantum mechanics to chemical problems. It has served as one criterion of a satisfactory wave function and its consequences on chemical bonding, molecular structure, and substituent effects have been analyzed extensively. A common method of gaining compliance with the virial theorem is to introduce a “scale” factor which adjusts all distances by a factor η. Optimizing the scale factor through the variational principle produces a wave function satisfying the virial theorem. In the present paper it is shown that when this “scaling” procedure is applied to self-consistent wave functions, the virial theorem can be satisfied, but self-consistency is lost. Scaling generally has a small effect on the total energy, but the effects on the energy components (T, Vne, Vee, Vnn) can be two to three orders of magnitude larger and in the range of tens to hundreds of kcal. Consequently, for applications where the energy components are useful, it is highly desirable to obtain wave functions which satisfy the virial theorem and are self-consistent. In the present paper, a simple, inexpensive extrapolation technique is reported which requires one integral evaluation and two SCF cycles to achieve convergence. Applications to atoms and small molecules are reported.
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  • 129
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    International Journal of Quantum Chemistry 22 (1982), S. 1281-1305 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The first two members of the cyclic polyene homologous series are studied over a wide range of the coupling constant using the Hubbard and Pariser-Parr-Pople model Hamiltonians. The full and various limited configuration interaction (CI) correlation energies and wave functions are calculated exploiting the unitary group approach. The formalism for the cluster analysis of the exact wave function expressed through the unitary group formalism electronic Gelfand states is developed and applied to the full CI wave functions of the cyclic polyene models studied. It is shown that the connected tetraexcited clusters become essential in the fully correlated limit and that their contribution also significantly increases with electron number even for the coupling constant corresponding to the spectroscopic parametrization of the model Hamiltonians used.
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  • 130
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    International Journal of Quantum Chemistry 21 (1982), S. 711-716 
    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 within the PCILO framework for the study of periodic molecular systems involving impurities is described regarding a one-dimensional chain. The calculation of the whole system is reduced to the calculation of subsystem pairs only. By use of the first-neighbor approximation only one or two subsystem pairs must be considered for subsystems with identical or differing surroundings, respectively. The procedure described yields the ground state energies and charge distributions of the subsystems.
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  • 131
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    International Journal of Quantum Chemistry 21 (1982), S. 741-751 
    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 quantum-mechanical virial theorem is analyzed for those systems which obey nontrivial boundary conditions and for approximate wave functions. The conditions that trial functions have to fulfill are set up in order that every expression derived from the virial theorem can be properly used.
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  • 132
    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: Kekulé structures of 10 nonlinear acenes comprising 83 graphs are studied through the use of connectivities [M. Randić, J. Am. Chem. Soc. 97, 6609 (1975)] of their corresponding submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)]. In certain rare cases states were identified to have identical branching indices but different Kekulé indices [A. Graovac, I. Gutman, M. Randić, and N. Trinajstić, J. Am. Chem. Soc. 95, 6267 (1973)]. Such states are termed pseudodegenerate states. A method is described to forecast and another to remedy such situations. The method emphasizes the relation between VB (resonance) and MO theories using graph-theoretical concepts.
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  • 133
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    International Journal of Quantum Chemistry 21 (1982), S. 813-822 
    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: CNDO/2 calculations have been performed on the clusters X4H9 and X4Y9 modeling the [111] diamond and silicon surfaces. The X is either carbon or silicon atom and the Y is a pseudoatom containing one sp3 hybrid orbital. It is shown that in the CNDO/2 approximation in the foregoing pseudoatom models, the charge distribution of the cluster is better than the hydrogen atom, because the electronegativity of the hydrogen differs significantly from the electronegativity of the sp2 orbital of the silicon atom. Using the CNDO/2 parametrization, the electronegativity of the hydrogen is very near to the electronegativity of the sp3 orbital of the carbon atom, thus the hydrogen can be used for the saturation of the carbon clusters.
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  • 134
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    International Journal of Quantum Chemistry 21 (1982), S. 445-463 
    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: Quantitative structure-activity relationships have been developed to rationalize the experimental data obtained with a series of dibenzo-p-dioxins and dibenzofurans in the assays for receptor binding and aryl hydrocarbon hydroxylase (AHH) induction. Lateral substituents (in positions 2, 3, 7, and 8 of the tricyclic system) do not affect receptor binding and AHH induction in the same manner. Various hypotheses are suggested to explain this finding. Of special interest is the possibility that the lateral substituents are directly involved in the mechanism which transforms the receptor to the active state. The implications of this possibility are considered with regard to the design of an antidote for poisoning caused by the chlorinated congeners which occur as contaminants in certain commercial products.
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  • 135
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    International Journal of Quantum Chemistry 21 (1982), S. 511-513 
    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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  • 136
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    International Journal of Quantum Chemistry 21 (1982), S. 543-556 
    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 calculations by the diagonal and the off-diagonal hypervirial relations and by the sufficient conditions for these relations have been performed for the one-dimensional box potential and the harmonic oscillator models. In the case of the box potential model, the variation method gave the unsymmetrical wave functions for trial functions though it gave the best energies, but some of these hypervirial calculations gave the symmetrical functions and therefore they showed the exact expectation values of x, though they did not give the best energies. On the contrary, in the case of the harmonic oscillator model such a discrepancy for wave function and excitation energy did not happen. For the box potential model the expectation values of some operators were evaluated and compared with the results by the exact solution and the variation method. A weakness of the off-diagonal hypervirial calculation was pointed out and the removal of this weakness was tried. The effectiveness of these calculations were investigated.
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  • 137
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    International Journal of Quantum Chemistry 21 (1982), S. 967-991 
    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 calculating ab initio electronic excitation energies of molecular crystals, based on a many-electron tight-binding approximation, is described. The method follows Frenkel's model for excitons and allows a many-electron treatment of the band-structure problem of molecular crystals. The case of hole bands is studied in detail and various versions of the method are considered. A computational scheme is proposed, in which approximate correlation corrections to the HFR matrix equations of the one-electron LCMO method are calculated. The main effects contributing to these corrections are the effect of relaxation of a molecular ion, the effect of intramolecular electronic-correlation change, and the effect of polarization of the remaining molecules in a crystal. The method developed in the present paper is applied to calculation of the hole bands of the HCP helium crystal.
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  • 138
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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: An ab initio method for calculating the energies of excess-electron bands in a molecular crystal is developed. These energies represent the electron affinities of a crystal. The present method employs a tight-binding approximation to describe the molecules in a crystal and a set of local functions to describe the excess electron. One- and many-electron formulations of the method are given, the latter takes into account the effect of polarization of all the molecules in the crystal by the excess electron. A scheme for approximate determination of the electronic-correlation corrections to the one-electron bands is developed and applied to calculation of the excess-electron bands in the HCP helium crystal.
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  • 139
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    International Journal of Quantum Chemistry 21 (1982), S. 1041-1050 
    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 theory by which a wave function may be factorized into conditional and marginal amplitudes is extended to the domain of approximate wave functions. The approximate conditional and marginal factors are well defined, and the marginal factor satisfies a variation principle that is equivalent to a reduced Schrödinger equation having the same form as that derived in the case of exact wave functions. Of the two ways of calculating the effective potential in the reduced Schrödinger equation (which are equivalent in the case of exact wave functions), the integral method is demonstrated to be intrinsically more accurate than the differential method. The variation principle for the marginal amplitude leads to a technique for improving approximate wave functions within a subspace of the whole configuration space. These concepts are illustrated by calculations on the ground state of the helium atom.
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  • 140
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    International Journal of Quantum Chemistry 21 (1982), S. 1123-1125 
    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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  • 141
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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: Ab initio self-consistent-field and configuration interaction studies have been carried out on the ground state of the LiH molecule at its equilibrium distance. Floating spherical Gaussian basis orbitals (FSGO) were employed, along with spherical Gaussian correlation factors, using the procedure described in the preceding paper. A near-Hartree-Fock function was found using only 13 FSGO. Exploratory configuration interaction studies recovered approximately 73% of the inner shell correlation energy and approximately 56% of the total correlation energy with five configurations plus the Hartree-Fock configuration. These studies indicate that, by using spherical Gaussian correlation factors, direct introduction of interelectronic coordinates into trial wave functions can be accomplished for molecular systems. It was also shown that correlating configurations need not utilize the full Hartree-Fock basis, but may use substantially smaller bases and still recover correlation energy effectively. Finally, the results indicate that, in spite of their improper cusp behavior, FSGOS and spherical Gaussian correlation factors can be used for construction of high accuracy wave functions.
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  • 142
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    International Journal of Quantum Chemistry 22 (1982), S. 49-67 
    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 band theoretical calculation of angular distribution of annihilation photons (ADAP) and the positron lifetime, up to and including higher momentum components is reported. The results obtained using biquadratic quasianalytic integration schemes for all Brillouin zone integrals, compare favorably with existing experimental data. There are, however, significant structures in the ADAP curve obtained than in the experimental curves.
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  • 143
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    International Journal of Quantum Chemistry 22 (1982), S. 89-100 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have made a detailed analysis of the adequacy of different theoretical approaches to the study of uracil tautomerism. We have considered the effect of molecular relaxation and the ability of several methods to reproduce it. We have also considered their performance in predicting the tautomerization energy barrier. We found that semiempirical methods are not adequate for predicting the energy value but that they can be used for obtaining geometry optimizations. We also found a strong discrepancy between the energy values predicted by a minimal basis set and a 2ζ basis set, the last one being 24.9 kcal/mol. The implications of these findings are discussed and the results compared with experimental evidence.
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  • 144
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    International Journal of Quantum Chemistry 22 (1982), S. 169-182 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have applied the ab initio formulation of the perturbative configuration interaction using localized orbitals (PCILO) method up to third order to calculate intermolecular and intramolecular interaction energies going beyond the ab initio Hartree-Fock calculation. For the rotational barrier in ethane our results agree well with the experimental value and the cis- and even the trans-barriers in HOOH are at least qualitatively reproduced with the aid of the STO-3G basis set. In the case of the water dimer we obtain an equilibrium intermolecular distance and interaction energy which are confirmed by other calculations. We can further conclude from our studies that one has to include higher orders in the perturbation expansion as the system becomes more complicated. It is especially the last aspect which hinders the application of the ab initio PCILO to estimate the major part of the electron correlation energy for large molecules.
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  • 145
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    International Journal of Quantum Chemistry 21 (1982), S. 1091-1095 
    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 potential adaption procedure by means of polynomials is described for diatomic molecules. The conditions of the adaption and numerical results obtained on the basis of the model are presented.
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  • 146
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    International Journal of Quantum Chemistry 21 (1982), S. 647-663 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using a canonical numbering of vertices for the graph corresponding to a particular rearrangement of tetragonal-pyramidal complexes, all 120 permutations defining the symmetry for the rearrangement are derived. An examination of the permutations points to the symmetric group S5, which has previously been found for isomerizations of trigonal-bipyramidal complexes and in the rearrangement of homotetrahedryl cations.
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  • 147
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    International Journal of Quantum Chemistry 21 (1982) 
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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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  • 148
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    International Journal of Quantum Chemistry 22 (1982), S. 23-29 
    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: By using the vibration-rotation canonical functions, we show that the wave function for a vibration-rotation level (v, J) can be represented by ψvJ(r) = ψv (r)+Σl = 0∞ λlφl(r) with λ = J(J + 1). The radial Schrödinger equation can be written (Hv + λHJ)ψvλ = (Ev + Σl = 1∞ λlεl)ψvλ, where ε1, ε2, ε3,… stand for the rotational constants Bv, Dv, Hv,…. The radial equation being satisfied for any value of λ, the rotation “harmonics” φ1, φ2,… are found to be the solutions of a set of inhomogenous differential equations of the form Hφl = Evφl + fl(r)ψv. An analytic expression of the harmonics φi is given for any potential. The numerical application shows that, for a given r, the harmonics decrease in absolute values like Bv, Dv, Hv,… and that the agreement between the values of ψvJ deduced from the computation of the harmonics on one hand, and the direct computation on the other hand, is very satisfactory.
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    International Journal of Quantum Chemistry 22 (1982), S. 69-72 
    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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  • 150
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    International Journal of Quantum Chemistry 22 (1982), S. 127-148 
    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: Symmetry adaptation of spin-free multishell electron configurations in molecules to general non-Abelian point groups has been carried out. Using the basis spanning the irreducible representation [2N/2-S, 12S, 0n-N/2-S] of the unitary group U(n) as primitives, the Wigner operators for point groups were applied to generate the required basis. In the process it was found that the segments of the Weyl tableaux could be handled individually. Using this and the matric algebra of permutation group a viable procedure has been developed for point groups adaptation. A program based on the procedure has been generated and implemented.
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  • 151
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    International Journal of Quantum Chemistry 22 (1982), S. 217-217 
    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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  • 152
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    International Journal of Quantum Chemistry 22 (1982), S. 253-263 
    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: On the basis of the Heisenberg equation of motion and the Linderberg-Seamans approximations, useful formulas for, β-resonance integrals in the all-valence NDO-like semiempirical methods have been derived. The case of s, p, d basis sets of atomic orbitals has been considered.
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  • 153
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    International Journal of Quantum Chemistry 22 (1982), S. 595-630 
    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: Seventeen different computer experiments are presented and analyzed. In each experiment a three-turn B-DNA double helix fragment interacts with a variable number of water molecules (from 60 to 1200), with a variable number of sodium ions (from 30 to 63), at one or more temperatures (280, 300, 320 K). The experiments are performed with the Monte Carlo method using quantum-mechanically derived potentials. In the analysis of the experiments we partition the water molecules (and the corresponding interactions) as being either bound or in the first solvation shell or in the groove regions relative to DNA; for the former two cases, the number of water molecules and the water interaction energy are reported for selected atoms or groups of atoms. The entire study is condensed into eight tables. The use of these tables is exemplified by considering, in detail, some of the trends emerging from these experiments. The analyses are complemented by graphical representations presented either to elucidate the very complex pattern of hydrogen bonded water molecules, or to show the statistical distributions of the oxygen and hydrogen atoms of the water molecules.
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  • 154
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    International Journal of Quantum Chemistry 22 (1982), S. 657-659 
    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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  • 155
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    International Journal of Quantum Chemistry 22 (1982), S. 665-679 
    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 groups with local symmetries are employed to explore the intrinsic symmetries of various kinds of cycloadditions to become apparent ones. For the electrocyclic reactions, the concept of local symmetry can still be applied equivalently, but no new result can be achieved. Furthermore, the local symmetries are generalized to the systems as a many body treatment performed by Matsen.
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  • 156
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    International Journal of Quantum Chemistry 22 (1982), S. 717-738 
    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 general formula for angular integrations in many-dimensional spaces (derived in a previous paper) is applied to several problems connected with solution of the Schrödinger equation for many-particle systems. Matrix elements of the Hamiltonian are derived for cases where the potential can be expressed in terms of functions of the generalized radius multiplied by polynomials in the m coordinates. The theory of hyperspherical harmonics is reviewed, and a sum rule is derived relating the sum over all the harmonics belonging to a particular eigenvalue of angular momentum to the Gegenbauer polynomial corresponding to that eigenvalue. A formula is derived for projecting out the component of an arbitrary function corresponding to a particular eigenvalue of generalized angular momentum, and the formula is applied to polynomials in the m coordinates. An expansion is derived for expressing a many-dimensional plane wave in terms of hyperspherical harmonics and functions which might be called “hyperspherical Bessel functions.” It is shown how this expansion may be used to calculate many-dimensional Fourier transforms. A formula is derived expressing the effect of a group-theoretical projection operator acting on a many-dimensional plane wave. Finally, the techniques mentioned above are used to expand the Coulomb potential of a many-particle system in terms of Gegenbauer polynomials.
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    International Journal of Quantum Chemistry 22 (1982), S. 753-759 
    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: Sources of occasional convergence problems in our recently proposed algorithm for orthonormality constrained orbital optimization in SCF calculation, as well as in the partly equivalent orthogonal gradient method, are traced and remedial measures are suggested. A simple scaling technique for accelerating convergence in the related orthogonal gradient method is tested.
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  • 158
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    International Journal of Quantum Chemistry 22 (1982), S. 783-824 
    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 approach to the configuration interaction method based on symmetric groups (SGA) is developed. The formalism is an alternative of the unitary group approach (UGA). In many aspects the present formulation seems to be superior to UGA. In particular, in SGA the orbital and the spin parts of the configuration state functions may be processed separately. In consequence its graphical formulation is much simpler and the coupling constant expressions are more compact than the UGA analogs. A special emphasis is put on direct CI implementations. In addition to formulas for coupling constants, explicit expressions allowing for separation of external and internal space contributions are also presented.
    Additional Material: 6 Ill.
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  • 159
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Lifetimes of individual spin sublevels, vibronic intensities of phosphorescence, zero field splitting, hyperfine and nuclear quadruple tensors for the lowest triplet state, g factors, and dipole nature of microwave transitions have been calculated on the bases of CNDO and INDO methods taking into account spin-orbit, spin-spin, vibronic, and hyperfine interactions by perturbation theory. The results are in qualitative agreement with phosphorescence microwave double resonance data. Influence of intermolecular interaction on the zero field splitting are also investigated.
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  • 160
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    International Journal of Quantum Chemistry 22 (1982), S. 911-927 
    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 of direct calculation of lattice sums in three-dimensional crystals is reported. The method is based on annihilation of some lowest multipole moments of the unit cell by a redefinition of the unit cell content. As a result, properties of the infinite crystal can be calculated as usual by taking a finite cluster of unit cells, but surrounded by an additional surface layer of a charge density (e.g., a layer of point charges). This charge density distribution produces the electric field approximating that one of the rest of the infinite crystal. The method proposed is easily applicable in the SCFLCAO procedure as well as in any method using a cluster representation for an infinite crystal. The validity of the infinite crystal model for a finite crystal is also discussed.
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  • 161
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    International Journal of Quantum Chemistry 22 (1982), S. 929-938 
    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 recently developed procedure for calculation of tails of localized molecular orbitals is applied in order to obtain approximate rotational potential curves. In order to calculate reliable rotational barriers, tails, originating from direct interactions between bonding and antibonding strictly localized orthogonal orbitals, have to be determined. This finding permits us to develop a fast approximate SCF semiempirical procedure offering a reliable tool for studying conformational problems in rather large (bio)molecules. As a first example, a model of the active site of α-chymotrypsin was examined. According to our calculations, a hydrogen bond between Ser-195 and His-57 should exist.
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    International Journal of Quantum Chemistry 22 (1982), S. 989-997 
    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 provides an analysis of the reasons for the approximate validity of the relation \documentclass{article}\pagestyle{empty}\begin{document}$ E = \frac{3}{7}NV(0) $\end{document}, between the total energy E of a neutral atom, the number N of electrons, and the electronic potential at the nucleus V(0). Using the density functional formalism we find that the right-hand side of the above equation also appears (and is the leading term) in density functional approximations more sophisticated than the Thomas-Fermi (TF) approximation (the above equation is exact in the TF approximation). Systematic improvements to the equation appear to be difficult because the main corrections come from those terms which are more difficult to handle in the density functional formalism. After this analysis we propose a kinetic energy functional for neutral atoms in the Hartree-Fock approximation. The first term of this new functional is a rescaled Thomas-Fermi term \documentclass{article}\pagestyle{empty}\begin{document}$$ T_0^\gamma = (1 + \gamma)\int {\frac{3}{{10}}(3\pi ^2){}^{2/3}\rho ^{5/3} d{\rm r}} $$\end{document}, where γ = -0.0063 for light atoms and γ = 0.0085 for the others. The second term is the first gradient correction due to Kirzhnits \documentclass{article}\pagestyle{empty}\begin{document}$$ T_2 = \frac{1}{{72}}\int {\frac{{(\nabla \rho)^2 }}{\rho }d{\rm r}} $$\end{document}.For lithium to krypton atoms, this new functional gives an average error of 0.22%.
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    International Journal of Quantum Chemistry 22 (1982), S. 1083-1084 
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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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  • 164
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    International Journal of Quantum Chemistry 22 (1982), S. 1005-1011 
    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 importance of the Fermi-Amaldi correction for the Thomas-Fermi theory for ions is analyzed. An analytical trial electron density with a proper limiting behavior has been chosen and the Thomas-Fermi-Amaldi energy expression is minimized in a variational way for several closed-shell ions. The obtained optimum electron densities have been used for calculating the diamagnetic susceptibilities, and a comparison with other theoretical results and available experimental data is performed.
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    International Journal of Quantum Chemistry 22 (1982), S. 1049-1058 
    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 new properties of the Lagrange multiplier μ introduced through the normalization constraint on ρ in the variations of energy density functionals are determined. Through arguments concerning the homogeneity properties of these functionals with respect to μ, it is demonstrated that at the point of variation μ = μ0 = E0/N, where E0 is the ground state energy and N is the total particle number. It is also shown that the value of μ0 is independent of the normalization imposed on ρ. The interpretation of μ0 as a chemical potential is discussed in the light of these findings.
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    International Journal of Quantum Chemistry 22 (1982), S. 191-197 
    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 new concept of the stability of the quantum mechanical state is introduced for the study of the time-dependent process of the quasistationary state. A stable solution of the time-dependent Schrodinger equation predicts the presence of the new sharply localized long-living state at the most repulsive part of the effective potential.
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  • 167
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    International Journal of Quantum Chemistry 22 (1982), S. 199-215 
    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 procedure is given to derive an explicit charge-transfer contribution from the Murrell-Randic-Williams formula, and to implement it in the framework of an additive procedure for the computation of intermolecular interaction energies, as a sum of electrostatic, repulsion, polarization, dispersion, and charge-transfer terms. Comparisons are performed between the radial and angular dependence of this term in model hydrogen-bonded systems, and that of the charge-transfer term resulting from SCF supermolecule computations. The evolution of the derived term can be matched very satisfactorily to that of an SCF counterpart when the counterpoise correction is taken into account. The underlying features governing the radial and angular evolution of the counterpoise and charge transfer terms are underlined.
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  • 168
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    International Journal of Quantum Chemistry 22 (1982), S. 265-274 
    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: PCILO calculations on conformations of the C-17 side chains of three 20-oxopregnane hormones, progesterone, corticosterone, and cortisol, reveal that the calculated conformations are generally in close agreement with those observed crystallographically. Average deviation of the calculated rotation angle around the C(17) - C(20) bond from the experiment is 9°. The PCILO calculations also predict the intramolecular hydrogen bond between the 20-carbonyl group and the 21-hydroxyl for the three hormones. This is in accordance with experiment. It was concluded that the PCILO method is reliable in predicting conformations of the side chains of hormones whereas the extended Hückel theory (EHT) predicted wrong conformations. Based upon the PCILO calculations, biological activities of the hormones are discussed.
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  • 169
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    International Journal of Quantum Chemistry 22 (1982), S. 299-306 
    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 STO-3G calculations show that α-cyano- and α-isocyano-substitution on carbanions produce a significant approximately equal stabilization of these charged species. Evidence is presented which suggests that the mechanism of such stabilization is qualitatively different for the cyano and isocyano substituents. The former appears to act through an electron delocalization process while the latter may operate by an inductive effect.
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  • 170
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    International Journal of Quantum Chemistry 22 (1982), S. 367-383 
    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 stability of the possible ground states of an infinite linear equidistant polyene model has been discussed in the PPP approximation of the unrestricted-Hartree-Fock (UHF) method. The emphasis has been placed upon the investigation of nonsinglet (triplet) instabilities: the spin-density waves (SDW's) and the spin-bond-order alternation waves (SBAW's). For physically realistic parameter sets the SDW ground state of the infinite linear equidistant polyene has been shown to be lowest in energy. Whereas the symmetry-adapted restricted HF (RHF) solution (SAS) has been shown to be unstable to the formation of SDW's and SBAW's for all investigated parametrizations, the bond-order alternation wave (BAW) solution has been found to be unstable to the formation of SDW's, but stable to the formation of SBAW's; in fact, the BAW's and the SBAW's have been shown to yield identical gap widths and ground-state energies (at least in the PPP method). It has been shown that there exist such sets of semiempirical parameters for which the charge-density wave (CDW) ground state is nonsinglet stable irrespective of the existence of an energetically advantageous SDW solution for the same parameter set.
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  • 171
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    International Journal of Quantum Chemistry 22 (1982), S. 421-427 
    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: New psudopotentials of higher quality have been used in ab initio molecular calculations. Simple molecular systems like Li2, LiH, and BeH2 have been investigated with varying basis sets. Energy, geometrical parameters, and dipole moments have been determined. The convergence properties of the various quantities have been investigated. They show characteristic behavior, e.g., stationary value for the energy where such behavior may be expected.
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  • 172
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    International Journal of Quantum Chemistry 22 (1982), S. 445-457 
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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: Weyl's theory for a set of N-coupled singular second-order differential equations is analyzed in relation to S-matrix theory and a dilated version is presented. Applications of this theory to two single channel scattering model problems and a two-channel model problem are given. Some implications of the present theory are discussed.
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  • 173
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    International Journal of Quantum Chemistry 22 (1982), S. 497-535 
    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 localized bond model of Malrieu, Diner, and Claverie is extended to fourth order in perturbation theory. Single, double, triple, and quadruple replacements from the doubly occupied bonding reference function are included utilizing a symmetric form of diagrammatic perturbation theory. The fourth order theory derived executes on a computer as quickly as does the third order theory. Results are examined utilizing the Pariser-Parr-Pople and CNDO/2 model Hamiltonians, and are compared with third order results and with either exact results where they are known, or with a configuration interaction of all singles and doubles. The influence of the initial hybridization, localization, and bond polarization is discussed. In general, the fourth order corrections are of comparable size to third order. Improvement in results appears to be marginal in the Nesbet-Epstein scheme in passing to fourth order because of the oscillating nature of the series; for Moller-Plesset theory errors are approximately halved. The relative energies as a function of modest geometry change about minima is about the same at third order as it is at fourth for most cases examined.
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  • 174
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    International Journal of Quantum Chemistry 22 (1982), S. 583-594 
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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: MINDO/3 calculations have been performed on semiquinone and fully reduced lumiflavins and on hydroperoxy adducts of lumiflavin. Frontier orbital indices were calculated. Reduction of the flavin was studied in bent and planar flavin rings. The results suggest that the planar reduced flavin has a smaller ionization potential than the bent reduced flavin. This could account for the low redox potential of protein-bound reduced flavins.
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  • 175
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    International Journal of Quantum Chemistry 22 (1982), S. 649-655 
    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: Ab initio Hartree-Fock calculations are used to predict the effect of substituting one hydrogen on the guanidinium ion by a vinyl group. The results show no overlap between the π-electron system of the guanidinium moiety and that of the vinyl group.
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  • 176
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    International Journal of Quantum Chemistry 22 (1982) 
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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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  • 177
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    International Journal of Quantum Chemistry 22 (1982), S. 761-774 
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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: It is shown that the Peierls instability in conjugated polymers is modified by the interaction of π electrons. This modification gives rise to the absence of a soft mode of stretching C—C vibrations. Taking into account electron correlations we obtain reasonable agreement between the calculated and measured frequencies of the carbon skeleton of polyacetylene with all the C—C bonds being equal in length. It is shown that the conclusion for the bond length alternation in polyacetylene does not follow from the experimental data on the vibrations of polyacetylene.
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  • 178
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    International Journal of Quantum Chemistry 22 (1982), S. 825-835 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two possible effects - Peierls instability (bond alternation) and Mott-type correlation spin ordering - leading to metal-insulator transition (energy gap formation) in one-dimensional chains, have been considered using UHF treatment of the Hubbard-type Hamiltonian. It has been found that in the framework of approximations applied these two instabilities are mutually exclusive.
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  • 179
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    International Journal of Quantum Chemistry 22 (1982), S. 851-862 
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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: We analyze, in the Pariser-Parr-Pople (PPP) model of alternant hydrocarbons, how the charge and spin correlation functions (CF's) are related to the structure of a CI wave function and the MO's of the systems. The analysis is based on the fact that an uncorrelated electron present in an orbital does not contribute to the linked dynamically correlated parts of the CF's. By using the fact, simple rules are deduced predicting the covalent or ionic nature of the correlation structure in a low-lying state with two correlated electrons. The rules predict that the singlet minus and triplet plus states are covalent, while singlet plus and triplet minus states are ionic, where the plus and minus mean the alternancy symmetry. The rules also give a prediction for the unknown charge and spin correlation structures between different sites.
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  • 180
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    International Journal of Quantum Chemistry 22 (1982), S. 903-910 
    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 ab initio version of the Hartree-Fock-Slater method is applied to obtain molecular orbitals and eigenvalues for S5N6. The electronic structure, bonding, stability, and electronic spectrum are discussed.
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  • 181
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    International Journal of Quantum Chemistry 22 (1982), S. 1013-1031 
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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: Symmetry operators of generalized wreath product groups are formulated. Several applications of these operators to nonrigid molecular problems in chemical physics are outlined.
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  • 182
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    International Journal of Quantum Chemistry 22 (1982), S. 1041-1047 
    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 were performed on 2,4-pyridinediol, 4-hydroxy-2-pyridinone, and 2hydroxy-4-pyridinone at the HF/3-21G level with full geometry optimization. Two conformations of the hydroxyl group were considered for each tautomer. Corrections for polarization functions, electron correlation, and zero point energy were made by comparison with previous calculations on 2- and 4-pyridinone tautomerism which included these contributions. The most stable structure is 4-hydroxy-2-pyridinone, in agreement with experiment. Relative to 4-hydroxy-2-pyridinone, the energies of the other tautomers are estimated to be 1.9 kcal/mol for 2,4-pyridinediol and 8.9 kcal/mol for 2-hydroxy-4-pyridinone. These are in accord with the experimental values 0.3 ± 1.9 and 10.6 ± 1.9 kcal/mol, respectively, deduced from equilibration studies of the tautomeric methyl derivatives.
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    International Journal of Quantum Chemistry 22 (1982), S. 1059-1082 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A theory is outlined of the nature and origin of drug-induced visual hallucination patterns. It is shown that such patterns correspond to blobs or stripes of visual neo-cortical activity. A neuronal circuit is described that generates such patterns whenever its homogeneous resting state becomes unstable. Such a process is shown to be an example of spontaneous symmetry-breaking, similar to that occurring in electro-weak interactions, and in fluid convection. It is suggested that the neuronal instability is produced by the action of hallucinogens on monoamine secreting brain-stem neurons.
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  • 184
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    International Journal of Quantum Chemistry 22 (1982), S. 1085-1152 
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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: Techniques of diagrammatic spin algebra are employed to derive segment factorization formulas for spin-adapted matrix elements of one- and two-electron excitation operators. The spin-adapted basis is formed by the Yamanouchi-;Kotani geneological coupling method, and therefore constitutes an irreducible basis of the unitary group U(N), as prescribed by Gel'fand and Tsetlin. Several features distinguish this paper from similar work that has recently been published. First, intermediate steps in the derivation of each segment factor are fully documented. Comprehensive tables list the spin diagrams and phases that contribute to the possible segment factors. Second, a special effort has been made to distinguish between those parts of a segment factor that can be ascribed to a spin diagram and those parts which arise from the orbitals. The results of this paper should thus be useful for those who wish to extend diagrammatic spin algebra to evaluation of matrix elements for states built from nonorthogonal orbitals. Third, a novel graphical method has been introduced to keep track of phase changes that are induced by line up permutations of creation and annihilation operators. This technique may be useful for extension of our analysis to higher excitations. The necessary concepts of second quantization and diagrammatic spin algebra are developed in situ, so the present derivation should be accessible to those who have little prior knowledge of such methods.
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  • 185
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    International Journal of Quantum Chemistry 22 (1982), S. 1221-1247 
    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 correlation of the K-region carcinogenicity indices of Pullman and of Mainster and Memory with bay-region carbocation delocalization energy (BCDE) is displayed and shown to be maintained at the perturbational molecular orbital (PMO) level. PMO algebraic relations are examined to reveal the underlying relationships. Some correlation between BCDE and K-region indices exists simply because carbocation formation occurs preferentially on carbons which are bonded to positions α (adjacent) to ring fusion centers. Sampling a K region is synonymous with sampling such α carbons. However PMO analysis shows that a very strong correlation exists between BCDE and indices for a certain type of K region (called “primitive”). It is further shown that high BCDE is favored by a straight-line chain of benzene rings as one moves away from the bay region. Kinks in the chain will lower the BCDE, and the closer the kink is to the bay region, the greater is its effect. Effects of methylation upon BCDE are shown to correlate with K-region indices if the methylation occurs at a carbon which is in the opposite class as the carbon to which the bay-region carbocation is attached.
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    International Journal of Quantum Chemistry 21 (1982), S. 93-104 
    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: Reasons for understanding the general problem of perturbation theory in large order are discussed. It is shown that the behavior of perturbation theory in larger order is generally very simple because it reflects just the semiclassical content of the theory. Many simple examples are given, including some graph-counting problems. The behavior of mass-renormalized perturbation series for some very simple field-theory models is examined. It is shown that mass renormalization hardly affects the large-order behavior of a weak-coupling perturbation series. However, in a strong-coupling perturbation series mass renormalization has a dramatic effect.
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  • 187
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    International Journal of Quantum Chemistry 21 (1982), S. 119-124 
    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: A method for the asymptotics of the perturbation series (Bender-Wu formulas) which is not restricted to one dimension is outlined. The method has a classical mechanic flavor and involves computing classical trajectories using classical perturbation methods. The method applies also when the unperturbed eigenvalues are degenerate. It is illustrated for the Hydrogen Zeeman Hamiltonian which is not separable and has degeneracies.
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    International Journal of Quantum Chemistry 21 (1982), S. 153-171 
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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 representations of so(4,2) which are applicable to the perturbation treatment of one-electron Hamiltonians of the form H = H0 + λV are discussed, where H0 is a hydrogenic Hamiltonian. A unified construction of the representations of so(2,1) and so(3) is outlined and the representations of so(4) [and also so(3,1)] are then obtained using both the vector operator method and angular momentum recoupling techniques. The merging of so(2,1) and so(4) then leads in a natural way to so(4,2). An outline of perturbation theory applications such as the Stark and Zeeman effects is also given.
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    International Journal of Quantum Chemistry 21 (1982), S. 191-193 
    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: Asymptotic analysis of the energy levels of double-well potentials is discussed. Based on a previously developed method, the asymptotic behavior of the perturbation theory coefficients an for the 1/R expansion of the ground state of the hydrogen molecular ion H+2 is presented in analytic form. Nine terms in the expansion of an in powers of 1/n are obtained, and the first four agree with the four obtained by numerical fitting by Čížek et al. The one-dimensional oscillator double well and more complicated multiple wells are also discussed.
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    International Journal of Quantum Chemistry 21 (1982), S. 231-237 
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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 reasons for the surprisingly little contact between quantum chemists and materials scientists are discussed. Examples of areas where such contacts could be very beneficial are given.
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    International Journal of Quantum Chemistry 21 (1982), S. 269-273 
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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: Some results pertaining to the form of Γ(1) usually assumed in density functional theory, the properties of natural states of mixed states, their variational characterization, and a representation of pure states through reproducing kernels are given.
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  • 192
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    International Journal of Quantum Chemistry 21 (1982), S. 359-367 
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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 electronic energy bands in beryllium have been recalculated. The earlier work of Terrell [1] was found to contain a systematic error in the form of overlapping muffin tins. The new band structures give a density of states with the Fermi surface lying in the hole like portion, consistent with Hall measurements. All existing calculations misplaced the Fermi surface. As a further check on the new bands, the Hall coefficient AH was calculated. We obtained AH = (7.6 ± 0.8) × 10-24 cgs units for the easy axis or c direction, in excellent agreement with the experimental value of AH = 8.56 × 1024 cgs units.
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    International Journal of Quantum Chemistry 21 (1982), S. 419-429 
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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: Momentum expectation values (pk), values of the momentum density P(p) at selected points, and coefficients in the MacLaurin and asymptotic expansions of P(p) are used to test the quality of various orbital basis sets previously used for the atomic helium Hartree-Fock problem. The wellknown position-space defects of Gaussian-type orbital expansions are shown to have their momentum-space counterparts. Expansions of even-tempered Slater-type orbitals are found to be rather accurate. The exponentially damped rational function is found to be the outstanding two-parameter unconventional orbital.
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  • 194
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    International Journal of Quantum Chemistry 21 (1982), S. 431-443 
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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 structure of N,N'-dimethylnitrosamine (DMN) and its α-hydroxy derivative have been computed using the ab initio force method with a 4-21 basis set. The results are compared with experiment for DMN.
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  • 195
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    International Journal of Quantum Chemistry 21 (1982) 
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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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  • 196
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    International Journal of Quantum Chemistry 21 (1982), S. 487-509 
    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 linear-combination-of-bond-orbitals (LCBO) formulation of INDO-SCF-MO theory is employed to investigate the origin of rotation barrier coupling in propane and related molecules. The dominant contributions to rotor coupling in propane are identified to be (i) a direct steric (bond-bond) interaction, involving the close approach of two methyl CH bonds in the eclipsed-eclipsed geometry, and (ii) a nonvicinal bond-antibond effect, which arises when the side of a σCH bond orbital in an eclipsed methyl group comes into favorable overlap with the “backside” lobe of the coplanar σCH* antibond in the staggered-eclipsed geometry. A smaller nonadditive interaction of each methyl rotor with the central group is noted to be of importance when the central atom contains lone pairs. Aspects of this qualitative picture, and its dependence on geometry changes, are tested in applications to (CH3)2CHF, (CH3)2NH, (CH3)2O, (CH3)2C=CH2, (CH3)2C=O, and C(CH3)4.
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    International Journal of Quantum Chemistry 21 (1982), S. 515-542 
    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 term “crystal harmonic” is introduced to denote a symmetrized plane wave in the special case where the wave vector is a reciprocal lattice vector. Crystal harmonics, thus defined, have the translational symmetry of the lattice, and they also have the transformation properties of the irreducible representations of the crystal's point group. An expansion is derived expressing crystal harmonics in terms of spherical Bessel functions and in terms of the functions Yl,ξ (eigenfunctions of L2 which are also basis functions for IRS of the crystal's point group). A sum rule for the functions Yl,ξ is derived. Methods are given for expanding periodic functions of special symmetry in terms of crystal harmonics. Methods are also presented for calculating matrix elements of the potential in a crystal using crystal harmonics as a basis and for transforming to a STO basis. It is shown that the invariant component of the product of two crystal harmonics can be expressed as a sum of a few invariant crystal harmonics, and expressions for the coefficients in the sum are derived. Orthogonality with respect to summation over networks of points and normalization are also discussed. The properties mentioned above are illustrated in detail in the case of cubic crystals with point group Oh.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 198
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 617-632 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We continue to examine the connection between perturbation theory and the Van Vleck unitary transformation. Here we illustrate the formalism derived earlier by applying it to compute the stationary states of the perturbed harmonic oscillator. We find that each solution of the traditional Brillouin-Wigner perturbation theory equations gives rise to a different unitary transformation which, when operating on the unperturbed ground state, produces one or the other of the perturbed eigenstates. With any of the perturbed states able to be reached by a unitary transformation on the unperturbed ground state, we advise caution in using approximate solutions of the perturbation equations in general cases, lest an unexpected stationary state be obtained.
    Type of Medium: Electronic Resource
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  • 199
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 665-669 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 200
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 1-2 
    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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