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  • 1995-1999
  • 1975-1979  (907)
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  • 1977  (907)
  • Cell & Developmental Biology  (573)
  • Computational Chemistry and Molecular Modeling  (192)
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  • 1995-1999
  • 1975-1979  (907)
  • 1905-1909
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  • 101
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 895-895 
    ISSN: 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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  • 102
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 931-941 
    ISSN: 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: One of the variants of Löwdin's partitioning technique that makes use of a Brillouin-type perturbation expansion for the study of lower bounds to the eigenvalues of a Hamiltonian has not been applied to any practical quantum mechanical problem so far. To illustrate how powerful this method can be, an application is made to the rigid rotator in an electric field, which has already been studied by Choi and Smith using the bracketing function of an intermediate Hamiltonian. It turns out that for a given order of the basis set of the Bazley space the Brillouin-Löwdin perturbation expansion gives closer bounds than the method of Choi and Smith, except for the case l = m, where the procedures can be shown to be mathematically equivalent. Especially for high l - m the number of basis functions needed to attain the same accuracy is by far larger for the method of Choi and Smith than for the Brillouin-Löwdin method.
    Additional Material: 2 Tab.
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  • 103
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    International Journal of Quantum Chemistry 11 (1977), S. 991-1000 
    ISSN: 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 solution of the quantum-mechanical one-particle problem involving a Coulomb potential with a cut-off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier.
    Additional Material: 1 Ill.
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  • 104
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    International Journal of Quantum Chemistry 11 (1977), S. 380-380 
    ISSN: 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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  • 105
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 1005-1015 
    ISSN: 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 explored two areas of approximately rigorous calculations for computing nonempirical wave functions for heavy and/or large molecules orders of magnitude faster than with conventional ab-initio methods but with the same chemical accuracy.First, we have developed and used a series of programs (starting from our new fast sets of ab-initio Gaussian SCF and SCF-CI programs) incorporating ab-initio effective core model potentials (MOD-POT) which allow one to treat only the valence electrons explicitly, plus a charge conserving integral prescreening, which cuts down significantly on the number of integrals that have to be calculated, stored, or processed for a large molecule. We have named this latter procedure VRDDO (variable retention of diatomic differential overlap). With these MODPOT and MODPOT/VRDDO methods we have explored a variety of small, medium, and large systems ranging from electron affinities of atoms through to molecules of biological interest and large boron hydrides. The results compared to ab-initio SCF or SCF/CI calcuations are very good, usually within 0.001 to 0.002 a.u. for orbital energies and gross atomic populations (GAPS) and even better along potential energy curves.Secondly, we have explored the use of the MS-Xα method for less conventional molecules and properties than those for which it is customarily employed.
    Additional Material: 6 Tab.
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  • 106
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    International Journal of Quantum Chemistry 12 (1977), S. 11-17 
    ISSN: 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 AMO function of the hydrogen molecule ψ = ψc + η ψi, where ψc is the covalent part and ψi the ionic part, is investigated for small internuclear distances R. We found η → -1 as R →,-1 as R → 0, contrary to the intuitively expected limit η → 1. However, near R = 0 an analytical expression of ψ is derived, showing that ψ reduces to the helium ground state as R → 0. We have proved that the empirical concept „covalent and ionic character“ should be replaced by the symmetry argument in the case of small R.
    Additional Material: 2 Ill.
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  • 107
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    International Journal of Quantum Chemistry 11 (1977), S. 561-576 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is known that the 2l+1 spherical harmonics Ylm can be transformed into cyclically equivalent orbitals, of which only a few examples have so far been given explicitly. In this article the totality of such cyclic sets is derived.It is demonstrated that other kinds of equivalent spherical harmonics do not exist.Finally a set of five equivalent d orbitals related to icosahedral symmetry is introduced.
    Additional Material: 1 Tab.
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  • 108
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    International Journal of Quantum Chemistry 11 (1977), S. 605-611 
    ISSN: 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 parameter optimization method of Part I is applied to the exponents of real STOS of first row atoms. In addition to minimum basis ground states, some independently optimized excited states are discussed in the case of Be. Local minima on the energy versus parameter surface are found in 4-configuration functions for the ground state of N. They are not present in either the simpler minimum basis function or in a more complete 8-configuration function.
    Additional Material: 4 Tab.
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  • 109
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    International Journal of Quantum Chemistry 11 (1977), S. 849-867 
    ISSN: 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 time independent diagrammatic technique based on the Wick theorem and graphical methods of spin algebras, as outlined in Part I, is applied to a simple open shell case having one unpaired electron in addition to the pure singlet closed shell. Compact explicit expressions for the matrix elements of a spin independent Hamiltonian between conveniently chosen spin symmetry adapted states are given for the ground, mono- and bi-excited configurations.
    Additional Material: 7 Ill.
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  • 110
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    International Journal of Quantum Chemistry 11 (1977), S. 885-894 
    ISSN: 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: Gaussian orbitals are used to calculate Temple lower bounds for H2+, HeH++, and H3++. Molecular orbitals are constructed from individual Gaussian-type orbitals (GTO) and from GTO contractions adapted for either upper or lower bounds of the hydrogen atoms. The MOS are optimized by minimizing either the upper bound, 〈H〉, or the variance, 〈(H - E)2〉. The best Temple lower bounds achieved by these methods are -0.60336 a.u. for 2+, - 1.06224 a.u. for HeH++, and -0.13003 a.u. for H3++. Comparison is made with other types of molecular orbitals and with the exact wave functions for 2+, HeH++. Analysis of the nuclear cusps is given. A prescription for constructing lower bound molecular orbitals is offered.
    Additional Material: 1 Ill.
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  • 111
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    International Journal of Quantum Chemistry 12 (1977), S. 1-9 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper static dipole polarizabilities and shielding factors of 3p open-shell atomic systems from A1 to C1 are presented using coupled Hartree-Fock theory in the Roothaan scheme. The calculation was made for the ground as well as for some valence excited states of the ions. A variational approach was adopted to obtain the polarizability values and the results are compared with the existing data wherever possible. The shielding factor values are in good agreement with the theoretical N/Z ratio.
    Additional Material: 1 Ill.
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  • 112
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    International Journal of Quantum Chemistry 12 (1977), S. 61-81 
    ISSN: 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, more accurate, Hartree-Fock limit energies (EHF) for ethane and ethylene are obtained from SCF total molecular energie using Ermler and Kern's procedure. These results, together with EHF values for other small closed shell molecules, are employed to calculate correlation energy (Ec) contributions to reaction heats. Cancellation to within 98% of the total Ec involved, and often to more than 99%, is found for a wide variety of chemical reactions, which strongly suggests that there are systematic regularities in the contribution to Ec from the different kinds of electron pairs in the valence shell. Assuming trictly localized pairs occupying orbitals having strongly directional character, Ec for the valence shell is evaluated in terms of Ec per lone pair, Ec per X—H bond, and Ec per X/X shared pair for Ne and for molecules containing first row atoms, where X is C, N, O, and F.
    Additional Material: 9 Tab.
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  • 113
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    International Journal of Quantum Chemistry 12 (1977), S. 83-92 
    ISSN: 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 Hartree-Fock and first natural spin determinants were compared as reference determinants for calculating various one-electron properties such as ρ(0), 〈½∇〉, 〈r-2〉,…, 〈r3〉, and r-112〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree-Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one-particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one-electron expectation values accurately.
    Additional Material: 2 Tab.
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  • 114
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    International Journal of Quantum Chemistry 11 (1977), S. 1021-1033 
    ISSN: 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 describe an attempt to use the AMO method for the investigation of insulator metal transitions. One of the main features of the calculation is that it permits an extension of the AMO method to finite temperatures.The ability of the model to account for such transitions is emphasized for the special case of linear antiferromagnetic systems. We discuss possible generalizations by pointing out that there exists a connection with Peierls' model.
    Additional Material: 2 Ill.
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  • 115
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    International Journal of Quantum Chemistry 12 (1977), S. 19-28 
    ISSN: 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 for treating exchange interactions between atoms or molecules as a perturbation, which was first propoed by Jansen, is extended to general cases by the use of the group algebraic technique and a nonorthogonal basis set. As a result, a new expresion for the perturbation ket and energy of each order is obtained. A comparion of the expression with those presented by other investigators is made.
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  • 116
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    International Journal of Quantum Chemistry 12 (1977), S. 105-113 
    ISSN: 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: Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H2. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.
    Additional Material: 1 Tab.
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  • 117
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    International Journal of Quantum Chemistry 12 (1977), S. 161-191 
    ISSN: 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 unitary group formulation of the many-electron problem is employed to give explicit representations of state vectors which are convenient for the discussion of progerties derived from propagatorcalculations. New results are obtained concerning the nature of various random-phase-like approximations and ground state representatives are generated from consistency requirements for the spectral resolution of the polarization propagator. The explicit solution admits the calculation of ground state average values for arbitrary operators and a variational upper bound to the ground state energy.
    Additional Material: 1 Tab.
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  • 118
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    International Journal of Quantum Chemistry 12 (1977), S. 215-223 
    ISSN: 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 invariance question int he CNDO and INDO levels of approximation is discussed with particular reference to one-center and two-center two-electron integrals and rotation of molecule-fixed coordinate axes. It is shown that asufficient condition for rotational invariance for the cone-center two-electron integrals is Jμμ = Jμμ, +2Kμμ, where J and K are the Coulomb and exchange integrals over orbitals μ μ′ with the same azimuthal quantum number. CNDO and INDO procedures, which explicitly employ Löwdin's orthogonalized basis set of atomic ortbitals (OAO) and differentiate between s-, p-, and d-orbitals on an atom in calculating various integrals, have also been examined in relation to the rotational invariance requirement. An expression which satisfies rotational invariance for two-electron Coulomb repulsion integrals over OAOS is also given.
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  • 119
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    International Journal of Quantum Chemistry 12 (1977), S. 227-229 
    ISSN: 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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  • 120
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    International Journal of Quantum Chemistry 12 (1977), S. 291-303 
    ISSN: 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 investigate the total spin structure of an approximate localized-site wave function for a collection of paramagnetic sites interacting so as to favor a singlet ground state. As the number of sites becomes infinite we obtain the distribution of weights of the different symmetry components of the localized site wave function; further, although only a very small fraction of such nonsymmetric wave functions is actually singlet, we find that it generally yields the same bulk property expectation values as its singlet-projected component.
    Additional Material: 6 Ill.
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  • 121
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    International Journal of Quantum Chemistry 12 (1977), S. 317-326 
    ISSN: 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 use of the pseudo-inverse matrix technique the generalization of the Löwdin orthogonalization, given by Kashiwagi and Sasaki, is shown to be valid in a case of singular metric matrices for two basis sets of functions. The application of the same idea to the inverse vibrational problem brings about new procedures for solving this problem in an iterative way.
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  • 122
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    International Journal of Quantum Chemistry 12 (1977), S. 431-431 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 123
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    International Journal of Quantum Chemistry 12 (1977), S. 397-426 
    ISSN: 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: Klein has pointed out that des Cloizeaux's orthonormalization is just another formulation of Löwdin's symmetric orthonormalization. We demonstrate that des Cloizeaux's formulation is convenient for theoretical discussions and that it is intimately connected with polar decomposition--which is a generalization to operators of the fact that any complex number z can be written r exp (iθ) where r is positive and θ real. We generalize two other properties for z and find an interpretation of the Carlson-Keller theorem. Recently Lathouwers found that Löwdin's canonical orthonormalization leads to the eigenvectors of a positive operator. This operator is des Cloizeaux's. We discuss some variational theorems on this background and find the Courant-Hilbert-Löwdin “measure of linear independence” from a simple least squares consideration, closely related to Lathouwers' results.An orthonormalization due to Schweinler and Wigner (1970) is observed to be Löwdin's canonical. The Schweinler-Wigner maximum characterization is referred to a simple general theorem, which also implies a new maximum characterization.In Sections 6 and 7 we consider transformation to an effective Hamiltonian from the point of view of polar decomposition and symmetric orthonormalization. It turns out that the polar part of Bloch's transformation is des Cloizeaux's. The characterizations of this by both Klein and Jørgensen are visualized in a simple way.
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  • 124
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    International Journal of Quantum Chemistry 12 (1977), S. 457-469 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of fractional parentage is extended to the general case of mixed configurations in arbitrary nonsimply reducible groups, G ⊂ SO(3). Particular attention is devoted to the calculation of coefficients of fractional parentage (CFP) and expressions are provided for the matrix elements of F and G type operators between N electron functions.
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  • 125
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    International Journal of Quantum Chemistry 12 (1977), S. 495-503 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum-mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).
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  • 126
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Further developments of a recent semiempirical, variable effective charge MO theory for calculation of ionization potentials (IP) and electron affinities (EA) as energy differences between separately minimized ground and ionized states are reported. The method is extended to adiabatic as well as vertical IPS and EAS by including core repulsion and σ bond compression energies in the total energy. The method is generalized to heteroatomic systems and is simplified by neglecting penetration integrals. As before, only two molecular parameters, the vertical IPS of benzene and naphthalene, are required to set the magnitude of the σ changes associated with the polarization of the core during loss or gain of a π charge. Twenty-seven aromatic molecules are studied, including polyacenes, condensed ring compounds, nonbenzenoids with five and seven member rings, nonplanar molecules, and heteroatomics with N+, as in pyridine, N+2, as in pyrrole, and O+2, as in furan. The results are within 0.2 eV of the photoelectron spectroscopic vertical IPS and the predicted vertical-adiabatic separation is consistent with the shape of the first band. The calculated EAS are within 0.2 eV of the observed values.The calculation is used to predict the IP and EA of the ionic photosensitizing cyanine dye, pinacyanol. The values obtained are consistent with the latest measured IP and EA of the adsorbed dye, corrected for surface and aggregation polarization effects.
    Additional Material: 3 Ill.
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  • 127
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    International Journal of Quantum Chemistry 11 (1977) 
    ISSN: 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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  • 128
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    International Journal of Quantum Chemistry 11 (1977), S. 21-47 
    ISSN: 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 full set of harmonics which are at the basis of all irreducible representations of the cubic point group and having order l ≤ 16 has been calculated in terms of Cartesian coordinates. Due to their complication, former calculations of harmonics in Cartesian coordinates for half of the irreducible representations did not exceed l = 6. The method presented in this paper is a modification of that originally given by Von der Lage and Bethe; it can be readily applied to the calculation of harmonics of arbitrary order for any irreducible representation of the cubic point group.
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  • 129
    ISSN: 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: Following Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh-Ritz method in the replacement of the usual kinetic energy operators T̂(μ) with operators T̂′(μ) = T̂(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ∇Ψ · ∇Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ∇Ψ and the change of ∇Ψ across surfaces of discontinuity.
    Additional Material: 5 Ill.
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  • 130
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    International Journal of Quantum Chemistry 11 (1977), S. 149-161 
    ISSN: 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 the vertical ionization potentials and electron affinities according to their fundamental definition as differences between energies of the singlet ground and doublet ionized states is developed for cyclic hydrocarbons. The method adopts a new approach based on the central idea of a recent ab initio IP and EA calculation in which orbital exponents are optimized for both ground and ionized states. Hence, all the semi-empirical parameters of the MO theory are written as functions of the effective nuclear charge which, in turn, is made self-consistent with the molecular electronic charge distribution of the species. Although the MO theory is developed in the π electron approximation, the changes in the σ electron density, resulting from the loss or gain of a π electron, are explicitly considered in the calculation. The theory is compared to the earlier work of Hoyland and Goodman and tested against the first five polyacenes and on the condensed ring aromatics phenanthrene, pyrene, and perylene. Except for perylene, the results are in close agreement with the latest photoelectron spectroscopic measurements.
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  • 131
    ISSN: 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 computational procedure which introduces some electron correlation into quantum mechanical calculations is described. Diverse applications are given. Among these, the method gives values of 65.6 kcal/mole for the dissociation energy of LiH, 62.0 kcal/mole for the ring-opening energy of cyclopropane, and 9.123 × 155 dynes/cm for the O-H stretching force constant of H2O. These results, and others given, suggest that our procedure has great potential and provides a very economical method for introducing electron correlation into a wave-function.
    Additional Material: 4 Ill.
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  • 132
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    International Journal of Quantum Chemistry 11 (1977), S. 277-281 
    ISSN: 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: Parseval's identity for orthonormal bases in Hilbert space is generalised to characterise uniquely biorthonormal bases among biorthonormal systems.
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  • 133
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    International Journal of Quantum Chemistry 11 (1977), S. 301-315 
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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: This paper studies the decay, due to the spin-lattice coupling, of two ½ spins with slightly different Zeeman energies when the lattice is thermally excited. The analysis is based on obtaining, by means of the Nakajima-Zwanzig projection operator technique, an equation for the evolution of the reduced density operator of the spin system which manifests the influence of one spin on the relaxation process of the other. The zero-order solutions obtained for the evolution of the expectation values of the spin dynamics operators are essentially equivalent to the Bloch equations; higher order solutions are also obtained.
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  • 134
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    International Journal of Quantum Chemistry 11 (1977), S. 349-358 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new algorithm for the computation of the density of states distributions of stereoregular polymers is presented. It is related to the Gilat-Raubenheimer technique for three dimensional systems. Its application to polyethylene is briefly described.
    Additional Material: 3 Ill.
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  • 135
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    International Journal of Quantum Chemistry 11 (1977), S. 1-15 
    ISSN: 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 influence of errors in molecular integrals on the calculated RHF energy values is considered for two models which correspond to round-off and shift errors. The energy variations induced by errors in elements of one- and two-electron matrices and the overlap matrix are represented in a quadratic approximation and the same degree of accuracy is maintained for mean values and standard deviations. The formulas given point out that mean values are less than zero when some of the errors are non-shifted. Special care is required when Gaussian lobe functions are used.
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  • 136
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    International Journal of Quantum Chemistry 11 (1977), S. 17-20 
    ISSN: 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 derivation of most general existence conditions for surface states of a semi-infinite Kronig-Penney crystal is reported. They reduce to Steslicka's conditions under a subsidiary restriction and also indicate that the surface-state energies may lie in the allowed bulk bands. Numerical computations supporting the qualitative conclusions are provided.
    Additional Material: 2 Ill.
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  • 137
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    International Journal of Quantum Chemistry 11 (1977), S. 59-71 
    ISSN: 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 goodness of the local fit of an approximate wave-function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ0, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. From this quantity the global accuracy of \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. The relative global accuracies of eight wave-functions for H2 are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z2, r2, x2 + y2, 3z2 -; r2, ξ, rA-1, r12-1, and EL (the reduced local energy). The success rate is high (〉90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave-function.
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  • 138
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    International Journal of Quantum Chemistry 11 (1977), S. 137-147 
    ISSN: 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 have been performed on selected first-row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO'S) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO, and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy-size relationship exists for core LMO'S but only approximately holds for bond LMO'S.
    Additional Material: 4 Ill.
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  • 139
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    International Journal of Quantum Chemistry 11 (1977), S. 163-178 
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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 Thomas-Fermi-Dirac equation for the electron density in a homonuclear diatomic system is solved numerically. The problems arising and methods of dealing with them are discussed and attention is given to the accuracy of the calculated energies. Comparisons are made to previously published work employing approximations, permitting a discussion of their utility.
    Additional Material: 3 Ill.
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  • 140
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    International Journal of Quantum Chemistry 11 (1977), S. 701-701 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 141
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    International Journal of Quantum Chemistry 11 (1977), S. 695-700 
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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: Relativistic symmetry orbitals are given for the double group D3h. For atomic orbitals at the symmetry center a general expression is presented. The atomic orbitals of the s, p½, and p3/2 variety outside the center are also considered. The representation matrices are given in explicit form.
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  • 142
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    International Journal of Quantum Chemistry 11 (1977), S. 704-704 
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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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  • 143
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    International Journal of Quantum Chemistry 11 (1977), S. 733-741 
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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 use a variation-perturbation method to calculate the electric polarizabilities and the electric dipole moment of the LiH molecule. We obtain 4.455 for the perpendicular polarizability and 4.001 (×10-24 cm3) for the parallel polarizability. Our result for the electric dipole moment at equilibrium nuclear distance is 5.866, which is in excellent agreement with the experimental value 5.828 debye units.
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  • 144
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    International Journal of Quantum Chemistry 12 (1977), S. 35-59 
    ISSN: 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 semi-analytical solution for the nucleus and the internuclear midpoint centred partial wave equations representing the Schrödinger equation for the H2+-like molecule is discussed. Explicit proton and internuclear midpoint centred results for the interaction energy and the wave function for the 1sσg state of H2+ are obtained as a function of the internuclear distance R and the number of coupled differential equation N N ≦ 14 used to represent the Schrödinger equation for the molecule. These, together with some energy optimized floating one centre results for the interaction energy, are used to (1) discuss the convergence of the partial wave calculation as a function of R,N, and the position of the expansion centre, (2) discuss the concept of Coulomb versus electron exchange interaction energies, and (3) discuss briefly the convergence problems of analogous one centre perturbation theory treatments for the ground state H2+ molecule. The electron exchange H2+ (1sσg) molecule provides a severe test for the uefulness of partial wave methods.
    Additional Material: 6 Ill.
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  • 145
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    International Journal of Quantum Chemistry 12 (1977), S. 115-131 
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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: Three simplifying methodds are discussed and applied to the four lowest valence states of CH2(3B1, 1A1, 1B1 and 1Σg+(1A1*)) and to the two lowest of CH2+(2A1 and 2∏u(2B1)). These methods concern: (1) the development of polarization functions for Gaussian-lobe basis sets by least-square fitting of numebrical multiconfigurational atomic fuinctions (this approach is tested also on (C2H2, (2) the use of intermediate Hamiltonians to calculate avoided crossings between potential hypersurfaces, and (3) thecalculation of correlation energies using an atoms-in-molecule approach.The calculated equilibrium geometries of the CH2 States are within 0.02 Å and 5° of available experimental data. The calculated term values and ionization potentials, Te(1A1 = 0.35 eV, Te (1B1) = 1.22 eV, Te (1Σg+(1A1*)) 2.48 eV, I.P. (2A1) = 10.39 eV and I. P. (2∏u(2B1)) = 10.58 eV, are in agreement with some recent theoretical studies, and are very close to existing experimental information.
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  • 146
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    International Journal of Quantum Chemistry 12 (1977), S. 193-205 
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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 focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the 3P → 1D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.
    Additional Material: 1 Ill.
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  • 147
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    International Journal of Quantum Chemistry 12 (1977) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 148
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    International Journal of Quantum Chemistry 12 (1977), S. 273-289 
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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 localized-site cluster expansion technique is applied to the infinite linear Heisenberg model with both nearest-neighbor and next nearest-neighbor interactions. These cluster ansätze are systematically studied and improved, up to the so-called 5-site approximation. Generally we find the present cluster ansätze yield the most accurate variational results yet available.
    Additional Material: 20 Ill.
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  • 149
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    International Journal of Quantum Chemistry 12 (1977), S. 327-334 
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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: For orbital optimization within the MC SCF theory a modification of the OEH method is proposed with the direction of descent determined according to the Fletcher-Reeves gradient method. The combined method developed on this basis ensures the convergence of the iterative process when the Hessian singularities occur. The convergence properties of the method proposed are studied by performing the ab initio water molecule calculations using two types of multiconfigurational wave functions.
    Additional Material: 1 Ill.
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  • 150
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    International Journal of Quantum Chemistry 12 (1977), S. 369-382 
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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: Branching diagram and Serber-type spin functions are ordered according to their diagrams. The method of Graebenstetter et al. is slightly modified; it provides an effective algorithm for the construction of genealogical spin functions. A counterpart of the method is developed for Serber-type spin functions. Special properties of branching diagram functions and Serber-functions are established.
    Additional Material: 7 Ill.
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  • 151
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    International Journal of Quantum Chemistry 12 (1977), S. 427-429 
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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: A comparison of experimental and theoretical values for Δα = αe - αg, assuming no sigma-electron contribution, shows a great distortion by π-electron calculations. We analyze existing electrochromic data, using this assumption, and report Δα values of 44 Å3 for coronene and 43 Å3 for triphenylene. Some general properties of Δα are discussed in terms of potential energy curves which suggest interesting calculations to relate excited matrix elements with experimental measurements.
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  • 152
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    International Journal of Quantum Chemistry 12 (1977), S. 433-441 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy spectrum of localized states in a simple cubic crystal is analysed, using the next-nearest neighbor approximation. The main distinguishing feature between the nearest and next-nearest neighbor approximation is the energy distribution of the localized states. Contrary to the tight-binding approximation, a non-symmetric distribution is found for clean surfaces, and split energy bands are found for surfaces completely covered by adsorbed atoms.
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  • 153
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    Topics: Chemistry and Pharmacology
    Notes: MS-Xα calculations have been performed for the neutral species and the transition states for the positive and negative ions of the heavy metal atoms Mo, W, Re, Ir, Pt, and U and their diatomic hydrides and fluorides. Both nonspin-polarized and spin-polarized calculations were performed. The main purpose of this study was to gain insight into which negative ion species might be preferable to try to prepare for use in ion sources for tandem accelerators.
    Additional Material: 7 Tab.
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  • 154
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    Topics: Chemistry and Pharmacology
    Notes: We formulated a pharmacological-physiological systems analysis and control theory based on interactive neuronal feedback loops (the effects of endogenous neurochemical diseases and exogenous psychotropic and other CNS drugs on neurotransmitter synthesis and release, reuptake, and metabolism) for normal, abnormal, and catastrophic situations.We were concerned primarily with the problems of stability or instability which might lead the system to exhibit catastrophic behavior. We set up the systems diagrams for the neurotransmitter systems and in that single framework were able to describe endogenous neurochemical disorders, the effect their drug treatment modalities had on the dynamic neurochemical balance, the effect psychotropic or other CNS drugs such as narcotics and narcotic antagonists had on neurotransmitter balance, and the interactive effect that multiple drug administration would have on neurotransmitter balance. Endogenous neurochemical disorders such as schizophrenia, Parkinsonism, depression, and mania should show up mathematically either as overly damped solutions if there is too little normal neurotransmitter or as catastrophically divergent instabilities if there is too much normal neurotransmitter. Improper mixed drug therapies, as well as the devastating effect of eating foods such as cheese (which contains sympathomimetic amines which potentiate the release of catecholamines from the presynaptic nerve endings) while on MAOI therapy also show up as mathematical, usually catastrophic, instabilities. We also indicated how this systems analysis and control theory could be put on small interactive computer terminals for use in clinical management and proper drug therapy of patients with neurochemical disorders.
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  • 155
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    International Journal of Quantum Chemistry 11 (1977), S. 543-559 
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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: Quasi-relativistic (QR) versions of the CNDO and Mulliken-Wolfsberg-Helmholz (MWH) semiempirical methods based on the SCF-QR-MO-LCAO method given earlier are worked out. For the CNDO method only the basic formulas and matrix element expressions are given, while for the MWH one, the parametrization as well as the basis functions and group spinor overlap integral calculation were discussed. (PtCl6)2- complex was chosen for a test calculation. The energy level values and LCAO coefficients were obtained and compared with the nonrelativistic calculations. One of the results was the occurrence of a very strong reduction of the spin-orbit interaction due to covalency. The calculation proves the semi-empirical versions of the QR-MO-LCAO method to be quite realizable in practice.
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  • 156
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    International Journal of Quantum Chemistry 11 (1977), S. 613-625 
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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: For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two-electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre-Elder procedure. We compare SCF calculations on the phosphorus molecule using Td symmetry with those using various subgroups of Td. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry-related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.
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  • 157
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 158
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    International Journal of Quantum Chemistry 11 (1977), S. 715-723 
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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 report in this work SCF atomic calculations for Li, Be, B, C, and Ne using a basis set of completely loge-localized functions. For these second row atoms the total volume R3 was partitioned into a spherical loge of radius R and its volume complement. The loge-localized basis functions were constructed as a product of Slater-type orbitals and a cut-off factor. The energy values obtained differ significantly from the Hartree-Fock ones indicating that the delocalization effects - not included in these calculations - are important.
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  • 159
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    International Journal of Quantum Chemistry 11 (1977), S. 1045-1045 
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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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  • 160
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    International Journal of Quantum Chemistry 12 (1977), S. 875-896 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A very general realization of the so(2, 1) algebra, which easily follows from the basic commutation relations that are satisfied by any pair of mutually conjugate generalized coordinates and momenta, is constructed. Using special cases of this general realization, and closely following the well known derivation of the eigenvalue spectra of the angular-momentum operators, based on the so(3) algebra, we derive the energy spectrum for the N-dimensional isotropic harmonic oscillator, and for both the nonrelativistic and the relativistic N-dimensional hydrogen atom. Special attention is given to a simple derivation of the form of these Hamiltonians in terms of the so(2, 1) algebra generators. In particular, the usually exploited tilting transformation is avoided, and the whole derivation is presented in an extremely simple and straightforward way. The present approach stresses the similarity and mutual relationship between the systems studied and, in addition to introducing some novel techniques and providing considerable insight into the overall structure of these problems, also has a definite pedagogical value.
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  • 161
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    International Journal of Quantum Chemistry 12 (1977), S. 967-967 
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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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  • 162
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    International Journal of Quantum Chemistry 12 (1977), S. 969-969 
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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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  • 163
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    International Journal of Quantum Chemistry 11 (1977), S. 381-391 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A quantum calculation of the optical activity and gyrotropic birefringence is used in a molecular crystal to deduce symmetry properties. A study of the variation of the components of these tensors, when a change of origin occurs, is used to account for the formula for the electric excitation proposed by Landau and Lifchitz. It is shown that the results obtained are valid in the case of crystals with nonlocalized electrons.
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  • 164
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    International Journal of Quantum Chemistry 11 (1977), S. 435-440 
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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 FSGO model has been used to make ab initio calculations of the geometry of B2H5+ ion. The results indicate that the acetylenic structure has the lowest energy (-43.881 a.u.) and the planar structure has the highest energy (-43.838 a.u.). The energy of the non-symmetric structure is only slightly higher (-43.879 a.u.) than that of the acetylenic one. Results of CNDO/2 calculations reported here also predict the acetylenic structure to be the most stable one.
    Additional Material: 1 Ill.
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  • 165
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    International Journal of Quantum Chemistry 11 (1977), S. 524-524 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 166
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    International Journal of Quantum Chemistry 11 (1977), S. 869-880 
    ISSN: 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: Green's functions and the symbol manipulative computer language LISP have been used to obtain exact, closed form, first-order functions and second-order energies for the first fourteen states of the hydrogen atom in electric and magnetic fields.
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  • 167
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    International Journal of Quantum Chemistry 11 (1977), S. 917-929 
    ISSN: 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: Löwdin has presented his angular momentum projection operators in two forms, the sum form deduced from the product form. A direct proof of the sum form is presented here, together with a brief account of application of the technique to the pd configuration.
    Additional Material: 1 Ill.
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  • 168
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    International Journal of Quantum Chemistry 11 (1977), S. 959-970 
    ISSN: 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: Presenting a relatively simple ab initio method to calculate full van der Waals interaction potentials between molecules, we give rules for the optimization of basis functions which permit the reliable evaluation of second order long range interactions. Closed expressions for the long range interaction energy are derived in which the orientational dependence is simplified to the utmost. Calculations show that even for molecules which have no dipole moment, such as ethylene, the strongly anisotropic electrostatic interactions are of the same magnitude as the dispersion interactions, but also that the anisotropic (“cross”) terms in the dispersion energy are about equal in size to the corresponding “quadratic” terms. Even though these anisotropic forces cancel to a large extent in the cohesion energy of the ethylene crystal, they can have important effects on some of the other crystal properties.
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  • 169
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    International Journal of Quantum Chemistry 11 (1977), S. 971-978 
    ISSN: 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 chemical methods employed by us to investigate the stabilities, charge densities, and bonding characteristics of atomic and molecular anions are briefly reviewed. The results of our work on chemically interesting species are surveyed, as are our initial results on the treatment of solvation effects in anionic systems. Finally, a simple-minded approach to the problem of finding shape resonances for electron-atom scattering processes is outlined.
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  • 170
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    International Journal of Quantum Chemistry 11 (1977), S. 1017-1020 
    ISSN: 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 tunneling transfer probability has been considered within the framework of the time dependent perturbation theory. It has been found that the probability of proton transfer may be enhanced by several orders when a dynamic potential barrier is assumed.
    Additional Material: 1 Ill.
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  • 171
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    International Journal of Quantum Chemistry 12 (1977), S. 207-213 
    ISSN: 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 SCF scheme for excited states of closed-shell systems based on the direct minimization technique is discussed. The utility of the scheme is tested for several excited states of H2O. The contribution of various tyeps of optimization of orbitals occupied in the excited state is discussed using the example of H2 O and FNO. It was found that relaxation of doubly occupied orbitals always gives a significnat contribution to the lowering of the excited state energy in the SCF process. Unexpectedly, on the other hand, optimization of the excited orbital in many cases gave negligible results.
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  • 172
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    International Journal of Quantum Chemistry 12 (1977), S. 233-246 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the framework of the path-integral formalism of nonrelativistic quantum theory the perturbation method is developed. This is based on the cumulative expansion of the partition function in powers of the difference between the classical actions of the exact and trial system. The trial system is constructed by replacing the Coulomb interactions by elastic ones, with parameters defined by Feynman's variational principle. The second order corrections to the ground-state energy of the hydrogen and helium atoms, the hydrogen molecule, and molecular ion have been evaluated. The results have been found to coincide with the actual values with an accuracy of 4-6%, whereas the corresponding error of the variational solution is of the order of 15-20%.
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  • 173
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    International Journal of Quantum Chemistry 12 (1977), S. 247-254 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By applying the powerful direct optimization technique of conjugate gradients as adapted for the optimization of an open shell energy functional, a uniformly balanced (15s 10p) Gaussian basis set was obtained for the silicon atom. The quality of this basis set, as defined in terms of “exponent forces” or energy gradient |g|, is compatible with the quality of suitably chosen (10s 5p) carbon and (5s) hydrogen basis sets. Contractions better than double zeta were determined for all three bases of Si, C, and H. Using the primitive and contracted bases, ab initio SCF MO calculations were carried out on molecules of SiH4, CH4, and H2. Some of the computed results obtained for H2C = SiH2 are also included as an illustration for organo-silicon compounds.
    Additional Material: 6 Tab.
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  • 174
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    International Journal of Quantum Chemistry 12 (1977), S. 343-353 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A reduced first order density matrix for the Be ground state is computed from an extensive configuration interaction (CI) wave function. A sequence of increasingly accurate CI wave functions Φq converging towards the exact Ψ is used to assess the quality of the results which include approximate bounds for the overlaps 〈Φq|Ψ〉, electron-nuclear coalescence cusp data, Weinhold's overlap between density matrices, virial ratios, occupation number spectra, and some expectation values. The nuclear magnetic shielding constant and the molar diamagnetic susceptibility are determined with 2.0 and 1.5% of uncertainty, respectively.
    Additional Material: 6 Tab.
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  • 175
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    International Journal of Quantum Chemistry 12 (1977), S. 335-342 
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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: In theories of the potential of an impurity ion in semiconductors, the common starting point is an expansion of the Fermi-Dirac integral F1/2 appearing in the screening-charge density. In the present paper, a formal test of the convergence of the series for F1/2 is carried out. The results show that, in the physically important limits of complete degeneracy and complete nondegeneracy, respectively, the series for F1/2 do converge. This establishes the validity of nonlinear Poisson equations for the impurity-ion potential, which can be solved approximately by making use of a variational principle.
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  • 176
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    International Journal of Quantum Chemistry 12 (1977), S. 383-396 
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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 SCF-MSXα method is used to determine the electronic structure of [Fe(CN)6]-3. Optical transition energies and valence electron ionization potentials are calculated and compared with experimental measurements. The electronic charge density at the Fe nucleus is calculated; this result and available electron densities at the Fe nucleus obtained by the same method for other Fe complexes are used to discuss the mechanisms involved in the interpretation of Mössbauer isomer shift values.
    Additional Material: 5 Ill.
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  • 177
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    International Journal of Quantum Chemistry 12 (1977) 
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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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  • 178
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    International Journal of Quantum Chemistry 12 (1977), S. 449-456 
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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 LCAO SCF MO CI calculations of naphthalene are carried out with a minimal basis set to test an integral approximation scheme proposed in a previous paper. When 71.3 and 53.0% of the two-electron integrals are neglected, the errors in the SCF total energy are only -0.0534 and -0.0006 a.u., respectively. In the latter case, the maximum absolute errors of the orbital energy and the gross AO population are 0.007 a.u. and 0.001, respectively. Even in the former case the errors of the excitation energies are less than 0.0004 a.u. Errors of oscillator strengths are also examined and are found to be tolerably small.
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  • 179
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    International Journal of Quantum Chemistry 12 (1977), S. 505-514 
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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 reaction of the transition metal ion Cu(II) with nucleic acid bases - adenine, guanine, uracil, and cytosine - has been investigated by conformation energy calculations (CEC) and molecular orbital (MO) methods. Various binding sites, e.g., N7-C6NH2, N7-C6O, N3-N9, and N1 in purines and N3 and O8 in pyramidines, have been considered. It was found that the energy minima for different binding sites had different values. In addition to the energy minima in the nucleic acid base plane, we have observed out-of-plane energy minima, differing in energy by a few kcal/mol in most of the cases. The MO calculations were performed on the most favorable planar positions obtained. It was found that the presence of Cu(II) alters the charge distribution pattern of practically all the atoms of nucleic acid bases. Its main effect is to withdraw electrons from the negatively charged nitrogens and positively charged carbons. The oxygen charge did not alter significantly. The results are compared with the experimental electron spin resonance and x-ray diffraction studies and their biological significance is discussed.
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  • 180
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    International Journal of Quantum Chemistry 12 (1977), S. 549-559 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Energy-shifted perturbation theory is studied in connection with corrections to Koopmans' theorem. The first three vertical Ionization potentials of N2, C2H2, and HCN are computed with basis sets of double-zeta Gaussian-type orbitals and double-zeta GTO plus polarization functions. The average absolute deviation of calculation ionization potentials from the observed values is found to be 0.4 eV, whether one uses Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory.
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  • 181
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    International Journal of Quantum Chemistry 12 (1977), S. 591-591 
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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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  • 182
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    International Journal of Quantum Chemistry 12 (1977), S. 609-622 
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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: Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X1 σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: re = 1.125 Å (1.128 Å), Be = 1.943 cm-1 (1.9312 cm-1), aBe = 0.0156 cm-1 (0.0175 cm-1), We = 2247 cm-1 (2170 cm-1), WeXe = 12.16 cm-1 (13.29 cm-1), where the experimental values are given in parenthesis.
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  • 183
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    International Journal of Quantum Chemistry 12 (1977), S. 623-637 
    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: Functions of several variables, such as the electron density and the nuclear Born-Oppenheimer potential, may be analysed very effectively using orthogonal trajectories. In particular the behaviour of these trajectories at critical points of the functions is investigated in detail. The use of orthogonal trajectories in the virial partitioning of Bader and in the definition of reaction coordinates is extended. A chemical interpretation of the critical points is suggested. The relevance of catastrophe theory is illustrated.
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  • 184
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    International Journal of Quantum Chemistry 12 (1977), S. 683-705 
    ISSN: 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: Approximate numerical linear dependence among the columns of the two-electron integral matrix and the positiveness of the Coulomb operator are exploited in order to reduce the number of integrals that need to be calculated when a numerical accuracy is given by the machine in use or by the choice of the investigator. Numerical results presented indicate that the method leads to an algorithm for carrying out the two-electron integral four-index transformation which in practice can be achieved in a small fraction (˜1/5-1/3) of the time required to generate the integrals by one of the fastest available Gaussian integral programs, Almlöf's MOLECULE. This effectively removes one of the major bottlenecks of computational quantum chemistry.
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  • 185
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The potential energy curves of the bending mode of PH2 in the ground 2B1 and the excited 2A1 states have been calculated using ab initio SCF-MO wave-functions. The radical is found, in agreement with experiment, to be bent in the two states. The calculated results clarify the interpretations of the anomalous behaviour of observed vibrational intervals, and offer an explanation of the ‘quasilinearity’; of the radical in the 2A1 state.
    Additional Material: 1 Ill.
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  • 186
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    International Journal of Quantum Chemistry 11 (1977), S. 129-135 
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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 investigate whether or not a previously proposed variation-perturbation method for calculating static polarizabilities can be used also to calculate dynamic polarizabilities. We find that the method can be used for frequencies below the first excitation frequency of the system. By amending and supplementing the procedures for solving the second-order equations we can obtain the same accuracy for dynamic polarizabilities as in the previous procedure for static polarizabilities.
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  • 187
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    International Journal of Quantum Chemistry 11 (1977), S. 179-179 
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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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  • 188
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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
    Additional Material: 2 Ill.
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  • 189
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    International Journal of Quantum Chemistry 11 (1977), S. 259-269 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In order to elucidate certain controversies in interpreting the π-electronic structure of some simple quinone and indigo dyes the Pariser-Parr-Pople SCβ,γ-wave-functions have been subjected to configuration analyses. Whereas 2,5-diamino-quinone (1) can be excellently represented by coupling of two trimethine-merocyanine chains, the analogous consideration is less appropriate with bispyrrolindigo (2). In this case the results of the configuration analyses indicate clearly the limited applicability of the Longuet/Higgins-Murrell-method.
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  • 190
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    International Journal of Quantum Chemistry 11 (1977), S. 293-300 
    ISSN: 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 PCILO method was used to calculate intermolecular interactions using fixed polarities. In this way our calculations are without any iteration cycle.The investigated supermolecules involve London-van der Waals type, hydrogen bonding type, and charge transfer type interactions, respectively. Both stabilization energies and equilibrium distances are in good agreement with the calculated values using optimized wavefunctions.Also the analysis of the individual contributions to the energy reflects well the mechanism of the intermolecular interactions.
    Additional Material: 4 Ill.
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  • 191
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    International Journal of Quantum Chemistry 11 (1977), S. 341-348 
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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: With the basic equivalent transformation Pσ = ∊(P)(Pr)-1 the dual bases of symmetric groups can be constructed. The importance of the double antisymmetrization is shown. The advantages of the use of the m basis as compared to the Wigner (matric) basis are discussed.
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  • 192
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    International Journal of Quantum Chemistry 11 (1977), S. 427-433 
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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 equilibrium distances of the complex components and the stabilization energies were calculated for the molecular complexes ethylene-fluorine, ethylene-chlorine, tetracyanoethylene-benzene, tetracyanoethylene-durene, and quinone-hydroquinone using the PCILO method. The results are compared with the experimental values and the theoretical predictions of the CNDO/2 method.
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  • 193
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    International Journal of Quantum Chemistry 11 (1977), S. 473-484 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper an application of a reaction field theory of solvent effects has been made to study proton transfer mechanisms in hydrogen bonded systems coupled to an environment. The latter is simulated with reaction fields having variable strength and direction (defined with respect to the supermolecule's total dipole moment direction), together with superposed uniform external electric fields. Changes in proton potential curves and some other properties of a model water dimer and a water trimer are reported. The results are discussed in relation to relevant phenomena in biology and biochemistry, namely proton relay systems in enzymatic catalysis.
    Additional Material: 5 Ill.
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  • 194
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The relation between the completeness condition for an appropriate one-particle basis set and the occupation number representation (second quantization) is shown for the time-independent case. The explicit expressions for the basic symmetric operators are derived in the Dirac bra-ket notation. The physical meaning of these operators, the algebra as well as the connections with the one-electron density matrix and with the projector on the Fermi sea in the one-electron approximation, follow directly from these expressions. The generalization for a nonorthogonal basis and the algebra for corresponding basic operators are formulated. The connection with the notion of the molecular diagrams of different kinds for the nonorthogonal atomic orbitals is shown. The Mulliken populations and the Chirgwin-Coulson bond orders are equal to the diagonal and offdiagonal elements of the molecular diagram 1, respectively. The matrix elements of the projector on the Fermi sea in the one-electron approximation in the representation of nonorthogonal atomic orbitals are elements of the molecular diagram 2.
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  • 195
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    International Journal of Quantum Chemistry 11 (1977), S. 577-589 
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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 problems of permutational symmetry of the density matrices in reduction are studied. Some necessary and sufficient conditions for N, [λ1], [λ2]-derivability problem are given.
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  • 196
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    International Journal of Quantum Chemistry 11 (1977), S. 665-683 
    ISSN: 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 double-zeta quality molecular orbital calculations have been carried out on an extensive series of ten-electron hydrides. The Edmiston-Ruedenberg energy-localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms of dipole moments, contour plots, and a simplified model for the orbital density involving analysis of the first and second moments. The simplified moment analysis model may be easily visualized in terms of threedimensional geometric objects, spheres, and ellipsoids. The model summarizes the information on the effective functional distribution inherent in the more detailed orbital contour plots in a clear and concise manner.
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    International Journal of Quantum Chemistry 11 (1977), S. 703-703 
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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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  • 198
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    International Journal of Quantum Chemistry 11 (1977), S. 705-713 
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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 proved that in general the INDO approximation to the full Roothaan theory does not lead to expressions which are invariant under a rotation of local atomic axes. However, when only s- and p-functions are used in the atomic basis set, the equations obtained are invariant due to the special properties of the p-functions. When d-orbitals are included into the basis set, rotational invariance is lost but can be restored if a supplementary approximation is introduced.
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    International Journal of Quantum Chemistry 11 (1977), S. 753-758 
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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 additivity model as suggested by Moss et al. has been used for predicting spin densities in methyl-substituted radical anions. Linderberg's relation has been employed for evaluating the core-resonance integrals (βrs) and a heteroatom model for the methyl group has been used.
    Additional Material: 1 Ill.
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  • 200
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 813-848 
    ISSN: 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 time independent diagrammatic technique based on the mathematical methods of quantum electrodynamics (second quantization, Wick's theorem, Feynman-like diagrams) is combined with graphical techniques of spin algebras to derive general expressions for the matrix elements of spin independent one- and two-particle operators between spin symmetry adapted ground, mono- and bi-excited configurations of a closed shell system. Two coupling schemes are considered for bi-excited states and their relative merits are discussed. Finally, the results are used to derive compact expressions for the coupling coefficients of the direct configuration interaction from molecular integrals (CIMI) method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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