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  • 1970-1974  (408)
  • Computational Chemistry and Molecular Modeling  (408)
  • Nuclear reactions
  • 101
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 1203-1220 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The expressions for matrix elements of spin-independent operators F and G with the use of Young operators are obtained in the case of arbitrary nonorthogonalized orbital configuration, including both singly and doubly filled orbitals and corresponding to the definite value of total spin. The formulas obtained do not require a preliminary construction of linear combinations of determinants and turn into known Löwdin formulas in the particular case of fully antisymmetric spatial states.
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  • 102
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 1221-1225 
    ISSN: 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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  • 103
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973) 
    ISSN: 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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  • 104
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 1-13 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The treatment of electrostatic interactions between molecular groups is based on quantum mechanical electron density distributions. A general method is suggested using tesseral harmonic multipole expansions and representing each set of point multipoles by a cluster of discrete charges small with respect to atomic dimensions. The procedure is carried out for the amino group with an electron density derived from the wave function of ammonia. We evaluate the optical rotation of two aminopyrrolidones as a test case. Expansions are compared for several approximate wave functions for ammonia.
    Additional Material: 8 Ill.
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  • 105
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 15-25 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that gauge terms can be introduced into the Gaussian functions used as the basis functions for an ab initio calculation of the energy of a molecule in the presence of a uniform magnetic field so that all the integrals become independent of the origin of the vector potential. The perturbation treatment of the diamagnetic susceptibility is considered in the molecular orbital approximation. The results show that the susceptibility can be calculated using only the unperturbed orbitals and their first-order corrections. All the integrals that arise can be expressed in terms of known functions.
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  • 106
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 51-62 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy terms arising in the water calculation by the FSGO method are analyzed as a function of the bond angle in order to gain insight into the reasons for the particular equilibrium configuration. The analysis is made in terms of symmetrically orthogonalized orbitals so as to exclude three- and four-orbital electron repulsion terms.
    Additional Material: 5 Ill.
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  • 107
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 63-73 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The exchange polarization energy and higher-order exchange corrections arising in the second order of the Murrell-Shaw and Musher-Amos (MS-MA) theory are evaluated analytically for the hydrogen molecule ion. At large internuclear distances the second-order exchange energy predicted by MS-MA theory behaves like \documentclass{article}\pagestyle{empty}\begin{document}$- \frac{1}{{18}}Re^{ - R}$\end{document}. It represents only 80% of the difference between the exact result of Holstein and the asymptotic value of the first-order exchange energy. The same result holds for the case of Hirschfelder-van der Avoird (HAV) and Hirschfelder-Silbey (HS) theories.
    Additional Material: 3 Tab.
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  • 108
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    International Journal of Quantum Chemistry 7 (1973), S. 127-130 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 109
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    International Journal of Quantum Chemistry 7 (1973), S. 131-132 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 110
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 135-135 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 111
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 133-134 
    ISSN: 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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  • 112
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 173-186 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The equation for the screened potential in the RPA has been derived by using the method of functional differentiation of Martin and Schwinger. The contribution of the “oyster” diagram has been contained in this equation.
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  • 113
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    International Journal of Quantum Chemistry 7 (1973), S. 155-171 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exchange perturbation theory of the Rayleigh-Schrödinger type is applied, in first and second orders, to the problem of bonding in rare-gas halides. The basic model is that of a four-electron, three-center system with one effective electron replacing the unpaired electrons of a halogen atom, and two spin-paired electrons representing the closed shells of the rare-gas atom. On the basis of exchange perturbation theory, the model verifies a direct parallelism between bonding in rare-gas compounds and the phenomenon of super-exchange in ionic solids with paramagnetic cations. It is found that the observed stability and specific geometric configuration of the xenon and krypton fluorides are readily reproduced by the model. In addition, the model explains why other dihalides cannot exist. The two principal components of the interaction energy are found to be indirect exchange between halogen atoms via the rare-gas atoms (attractive in the stable configurations) and, in compounds with coordination higher than two, simultaneous interactions between three halogen atoms (always repulsive). The observed approximate constancy of the binding energy per bond in xenon fluorides with increasing coordination is accounted for.
    Additional Material: 4 Ill.
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  • 114
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    International Journal of Quantum Chemistry 7 (1973), S. 223-232 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Approximate and ab initio molecular wave functions are obtained using Gaussian expansions of different length for the Slater orbitals. The expectation values of several one-electron operators are obtained and the accuracy of different wave functions discussed.
    Additional Material: 6 Tab.
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  • 115
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    International Journal of Quantum Chemistry 7 (1973), S. 253-284 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Tensorial sets adapted to sequences of finite subgroups are applied to the crystal field problem, and a general method for generating sequence-adapted molecular tensors using finite group algebra is formulated. All subgroup sequences of the abstract finite group G(24), isomorphic to the octahedral, O, tetrahedral, Td, and symmetric, S(4), groups are tabulated with explicit isomorphisms provided. The sequences fall into eight equivalence classes. A catalog of irreducible representations of G(24) adapted to a member of each of the eight sequence classes is given together with the transformations which generate representations adapted to all other sequences. With this data it is possible to systematically generate tensorial sets adapted to any sequence of a realization of G(24). Unitary transformations which adapt conventional forms of first- and second-rank irreducible tensorial sets of the rotation group to the eight sequences of the octahedral group are provided. Forms suitable for use with magnetic fields are included. The problem of a d1 ion in a trigonal crystal field is treated with sequence-adapted molecular tensors, and the utility of different sequences for descent in symmetry is discussed.
    Additional Material: 13 Tab.
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  • 116
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Slater orbital r12-1 integrals are calculated with a numerical Fourier-transform method based on a formulation first given by Bonham, Peacher and Cox. Spherical wave expansions are introduced that decouple the Feynman integrations for the charge distribution Fourier transforms. The Feynman integrals are evaluated semianalytically, and their properties are analyzed in detail. The final computational step involves a numerical integration over charge distribution quantities. Results for (coplanar) multicenter exchange integrals over 1s orbitals are given. As long as the charge distributions are overlapping considerably, the method gives good results, even when these distributions are highly asymmetric. The method as presently implemented fails when highly disconnected charge distributions are involved.
    Additional Material: 4 Tab.
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  • 117
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    International Journal of Quantum Chemistry 7 (1973), S. 285-300 
    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: Formulae are presented for the evaluation of some definite integrals in which the Laguerre orthogonal functions are contained. In some cases mechanical quadratures are to be preferred, and a scheme is presented for generating such a quadrature as it is needed.
    Additional Material: 1 Tab.
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  • 118
    ISSN: 0020-7608
    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 proposed recently for the generation of modified Hartree-Fock virtual orbitals has been tested by performing a simple configuration-interaction calculation for the ground state of the He atom. A very compact truncated basis set was constructed by using an a priori criterion based on the probability density within the region of the occupied orbital. The best results were obtained by making the virtual orbital energies more positive.
    Additional Material: 2 Tab.
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  • 119
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    International Journal of Quantum Chemistry 7 (1973), S. 383-404 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: After a discussion of different concepts of anisotropy with reference to the icosahedron, the unusual problems surrounding the construction of icosahedral irreducible tensors are discussed. Tables of these tensors are then presented and applied to orbital problems, molecular polarization phenomena and to the construction of projection operators.
    Additional Material: 1 Ill.
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  • 120
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    International Journal of Quantum Chemistry 7 (1973), S. 365-381 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A mathematical analysis is presented of molecular integrals of relativistic interactions in molecules. The integrals are based on Gaussian-type orbitals and include those arising from variation of electron mass with velocity, one-electron Fermi contact interaction, electron spin-same-orbit interaction, electron spin-nuclear spin interaction, electron spin-spin contact interaction, electron spin-other-orbit interaction, electron spin-spin dipolar interaction and electron orbit-orbit interaction. The integrals are expressed in suitable forms for use in computer. It is also pointed out that the integrals are written essentially in terms of the overlap, nuclear attraction, electron repulsion, or field integrals.
    Additional Material: 1 Tab.
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  • 121
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    International Journal of Quantum Chemistry 7 (1973), S. 537-546 
    ISSN: 0020-7608
    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 is given for accurate calculation of the expectation value of the Hamiltonian of a crystal with respect to a single-determinant wave function of LCAO type. The method is partly based on numerical integration over one Wigner-Seitz cell. In principle, the calculations involve infinite summations over lattice sites; suitable truncation methods are devised.
    Additional Material: 1 Ill.
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  • 122
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    International Journal of Quantum Chemistry 7 (1973), S. 951-958 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various optimization criteria are compared for the hydrogen atom to find orbitals which improve lower bounds computed from the Weinstein, Temple, and Stevenson-Crawford formulas. Minimization of squared energy deviation, “variance,” is recommended because the resulting lower bound orbitals give excellent lower bounds, converge to the exact wave function, are relatively easy to optimize, and are insensitive to the estimated energy eigenvalue. New linear combinations of Gaussian orbitals which minimize the variance are presented for the 1s, 2s, 2p, 3s, 3p, and 3d orbitals. These orbitals are compared with previous linear combinations with regard to their expectation values and local properties.
    Additional Material: 3 Tab.
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  • 123
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    International Journal of Quantum Chemistry 7 (1973), 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: Very often only “diagonal” second order energies, varying as an even power of R-1, occur in the multipole expansion of the interaction energy. However for many molecular interactions important “nondiagonal” second order energies, varying as an odd or even power of R-1 can arise. This point is emphasized by a general discussion and by a detailed specific example, the interaction of an ionized dipolar molecule with a nondegenerate atom. Also some useful theorems, on the orientation average of various types of second order energies, are derived.
    Additional Material: 2 Tab.
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  • 124
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    International Journal of Quantum Chemistry 7 (1973), S. 971-984 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The 1P and 3P states arising from the configuration (1s)2(2s)(2p) of the Be isoelectronic sequence are investigated. In the single configuration approximation, the energies of the two states are expressed as E0 + K2s2p and E0 - K2s2p, respectively. K2s2p is the exchange integral between the 2s and 2p electrons and E0 is the energy of a model in which K2s2p is deleted. First we calculate the 2s- and 2p-orbitals in this model. Second, by taking account of K2s2p in this model, effects of this term on the 2p-orbitals in the 1,3P states are investigated. In this manner, an explanation is given for the following facts which are obtained from a minimal Slater-type orbital set; (1) for Be and B+, the 2p-orbital of the 1P state is broader than that of the 3P state; (2) for C2+, the extension of the 2p-orbital in the two states is almost the same; (3) for O4+ and Ne6+, in contrast to Be and B+, the 2p-orbital of the 1P state is tighter than that of the 3P state.
    Additional Material: 6 Ill.
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  • 125
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    International Journal of Quantum Chemistry 7 (1973), S. 985-989 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The spin rearrangement of π-electrons in the ground state of a conjugated molecule in a strong magnetic field H is discussed. The spin S of the molecule increases as the field H increases (intramolecular paramagnetism). The dependence S(H) for linear and cyclic conjugated molecules in the free-electron model and in the Hückel-London approximation is derived. For the cyclic molecules the diamagnetic effects are taken into account.
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  • 126
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    International Journal of Quantum Chemistry 7 (1973), S. 991-998 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The third-order interaction between two nonpolar molecules due to the instantaneous induced dipole effect of an infinitely long linear molecule is assessed following arguments similar to earlier research on three-body effects. It is found that an attractive force favors small polar angles in approach to the linear molecule; such behavior could be of interest to processes such as those involved in replication of DNA.
    Additional Material: 1 Ill.
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  • 127
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    International Journal of Quantum Chemistry 7 (1973), S. 1029-1031 
    ISSN: 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 7 (1973), S. 1021-1028 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The general formula for the electron-electron repulsion integral in the modified Cartesian Gaussian basis set derived in Ref. [1] is simplified. A general relation between the standard and modified CG functions is given. A possible use of the modified CG functions to quantum chemical calculations which include the correlation factor rij2 is indicated.
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  • 129
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    International Journal of Quantum Chemistry 7 (1973), S. 999-1019 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron spin dipole-dipole contribution to the zero field splitting has been evaluated for the 3A2 (n → π*) and 3A1 (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian-lobe functions. The values D = 0.539 cm-1 and E = 0.031 cm-1 were obtained for the 3A2(n → π*) state and D = -0.588 cm-1 and E = 0.058 cm-1 were obtained for the 3A1 (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the 3A2 (n n → π*) state of formaldehyde and the 3B1 ground state of methylene. Numerical results are given which show that internally consistent self-consistent field orbitals (ICSCF) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the 1A1 ground state gave an energy of -114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C+O-) in good agreement with the experimental value of 2.33 ± 0.02 Debye.
    Additional Material: 5 Ill.
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  • 130
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    International Journal of Quantum Chemistry 7 (1973), S. 1033-1035 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
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  • 131
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    International Journal of Quantum Chemistry 7 (1973) 
    ISSN: 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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  • 132
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    International Journal of Quantum Chemistry 7 (1973), S. 1037-1037 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 133
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    International Journal of Quantum Chemistry 7 (1973), S. 1039-1043 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
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  • 134
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    International Journal of Quantum Chemistry 7 (1973), S. 1045-1050 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The general problem of the transfer of the representation of a set of orthonormal functions from one basis to a different, nonequivalent one is considered and specialized to a matrix formulation convenient for use in molecular electronic structure calculations. A procedure is suggested for treating problems where the transfer of representation breaks into a subset of most interest and one of less interest as for example the occupied and virtual orbitals of a Hartree-Fock SCF calculation. These techniques are then applied to obtain a representation of a methyl group from an SCF wave function for methane.
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  • 135
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    International Journal of Quantum Chemistry 7 (1973), S. 1063-1075 
    ISSN: 0020-7608
    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 obtained the Bloch spin wave dispersion formula using the methods of spin-free quantum chemistry. The spin-free eigenvectors are waves in spin-free space. This development makes the point that Bloch spin waves are dynamically spin-free. The neutron diffraction transition moment for spin waves is calculated employing the antisymmetrized projections of vector products of spin-free eigenkets and spin kets and is found to be agreement with results of Moorhouse.
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  • 136
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    International Journal of Quantum Chemistry 7 (1973), S. 1139-1144 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A general method is given for finding the complete set of linearly independent crystal field parameters from symmetry arguments. No recourse is made to expansions of the crystal field in terms of spherical harmonics. The core of the method lies in an extension of the known zero-trace property of tensor operators, to the case of irreducible operators.
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  • 137
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    International Journal of Quantum Chemistry 7 (1973), S. 1099-1116 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The importance sampling method of point selection has been used in the local energy framework to obtain least-squares solutions of the Schrödinger equation for a variety of H2 functions. It is shown that good results are obtainable with relatively small samples, and that the method is rather insensitive within broad limits to the nature of the weighting function employed. Expectation values for a number of operators besides the energy are examined. The energy variances are likewise scrutinized and attempts are made to rationalize their behavior in terms of how and to what extent sample points are chosen.
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  • 138
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    International Journal of Quantum Chemistry 7 (1973), S. 1145-1158 
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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 Schrödinger equation of an N-electron closed-shell system is reduced to that for the spatial wave function Ψ∥[λ] by the aid of the theory of the symmetric (permutation) group SN. The first-order perturbation equation based on the Hartree-Fock-SCF model as the zero-order solution is then solved by decomposing it into a set of soluble 1/2(N/2)[(N/2) + 1] equations for the pair-correlation (first-order) spatial wave functions. These spatial functions give the spatial parts of the pair functions in the spin orbital basis formulation, reducing also the number of independent pairs needed in the first order.
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  • 139
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    International Journal of Quantum Chemistry 7 (1973), S. 1159-1174 
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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 formulation developed in Paper I for a closed shell system is extended for a system with one nonclosed shell. Roothaan's restricted Hartree-Fock (RHF) open-shell wave function is taken as the zero-order solution. The first-order Schrödinger equation is then solved for the spatial part of the wave function by reducing it to a set of one- and two-electron equations, using the properties of the symmetric group SN.
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  • 140
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    International Journal of Quantum Chemistry 7 (1973), S. 1183-1192 
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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: Selected valence electron split-shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split-shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.
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  • 141
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    International Journal of Quantum Chemistry 7 (1973), S. 1193-1201 
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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: Padé approximants of type II have been applied to solve equations of the type F(z) = 0. The method is compared with the first-order iteration procedure, the Aitken-Samuelson formula, and the Newton-Raphson tangential method. As a test example the partitioning technique in its most simple form is applied to the Hamiltonian of a rigid symmetric-top molecule in a static electric field. The proposed algorithm is found to be superior to the first-order procedure and the Aitken-Samuleson formula, and at least as effective as the Newton-Raphson method.
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  • 142
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    International Journal of Quantum Chemistry 7 (1973), S. 1221-1221 
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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 7 (1973) 
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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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  • 144
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    International Journal of Quantum Chemistry 7 (1973), S. 139-153 
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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 theoretical study of the spin-optimized self-consistent field methods is given in a second quantization formalism using the occupation-branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman. A diagrammatic presentation can then be introduced. Further investigation will be thus facilitated.
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  • 145
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    International Journal of Quantum Chemistry 7 (1973), S. 187-193 
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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 theorem is proved which demonstrates the relationship between a product of group functions describing the correlated motion of a particular group of electrons in an N-electron system and a wave function obtained from the exact wave function which describes the correlation of the same group of electrons. By considering such products of group functions as elements in a variational wave function, an expansion for correlated wave functions is suggested, which emphasizes the correlated motion of groups of electrons in the whole system.
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  • 146
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    International Journal of Quantum Chemistry 7 (1973), S. 195-213 
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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 Green functions and Kubo linear-response theory are used to calculate the absorption coefficient of a collection of diatomic molecules embedded in a one-dimensional lattice. The effect of the environment is restricted to the coupling between the molecular internal vibration and lattice vibrations. For the molecular oscillators, both harmonic and anharmonic models are considered. The absorption line shape is expressed in closed form whether the molecular frequency falls outside or within the allowed phonon frequency range. In both cases a frequency shift is found. In the anharmonic case there is a broadening of the absorption lines. Expressions for the shift and line width are given.
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  • 147
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    International Journal of Quantum Chemistry 7 (1973), S. i 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 148
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    International Journal of Quantum Chemistry 7 (1973), S. 27-34 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: SCF-LCAO-MO-CI calculations made on 2- and 4-amino-, and 2,4-diaminopteridines indicate that the most favorable site where the protonation can take place is N-1.
    Additional Material: 3 Ill.
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  • 149
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    International Journal of Quantum Chemistry 7 (1973), S. 35-49 
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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: One-center core integrals for valence orbitals are determined from the experimental average energies of neutral atomic configurations from Li through Zn. These values are compared with those estimated from CNDO/1, “INDO/1”, CNDO/2, “INDO/2” and with theoretical values calculated from a pseudo-potential method. The agreement is good between values obtained from neutral atoms and from the psuedo-potential calculation except for the 3d orbitals of the transition elements where the theoretically calculated integrals over single ξ functions are not realistic. These two methods reproduce both term and average configuration energies for the first two rows of atoms; the semiempirical method reliably reproduces them for the third row. The CNDO/1 and INDO/1 methods underestimate atomic energies, while the CNDO/2 and INDO/2 procedures fail rather poorly.The propriety of using core integrals estimated semiempirically in molecular orbital calculations is discussed.
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  • 150
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    International Journal of Quantum Chemistry 7 (1973), S. 75-85 
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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 method is described whereby molecular symmetry properties may be used to reduce the numbers of one- and two-electron integrals that need to be calculated and stored in the course of a molecular SCF calculation. The method is a generalization of a previously reported procedure, extending the earlier work to cover those molecules belonging to point groups which have complex representations. The practical application of the method is discussed and an illustrative example given. The quite extensive tables of molecular symmetry properties which the method uses may be computer generated in a straightforward manner. A procedure for doing this using a minimum amount of input data is presented.
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  • 151
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    International Journal of Quantum Chemistry 7 (1973), S. 87-108 
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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 instabilities of the solutions to the Hartree-Fock equations for the nonalternants in the pentalene, heptalene, etc., series and in the azulene, etc., series are examined. The systems are found to have symmetry-adapted solutions which are unstable for values of the core integral β close to the standard (spectroscopic) value; for example, the pentalene solution is unstable with β equal to 75% of its standard value. The “broken” symmetry solutions although exhibiting only a very slightly lower energy (0.01 eV) may exhibit dramatically different values for other properties, e.g., 30% changes in bond orders. The off-diagonal charge-density wave (CDW) appearing in the “broken” symmetry solutions at the onset of instability is amplified as the cooperative phenomena dominate, until in the “fully correlated” limit, the linked-ethylenic (bond alternating) structure is obtained.
    Additional Material: 10 Ill.
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  • 152
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    International Journal of Quantum Chemistry 7 (1973), S. 109-125 
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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 method of direct treatment of valence electrons is proposed for the various 2S, 2P,2D, 2F states of the lithium, sodium, and potassium atoms and the corresponding isoelectronic ions. The function describing the outer electron, which is orthogonal to the wave functions of the electrons in the core, is given as a linear combination of generalized Laguerre functions, with effective charges Q = 1, 2 … equal to the charges of the core.A simpler analytical STO function, with non-integer principal quantum number n is then proposed.
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  • 153
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    International Journal of Quantum Chemistry 7 (1973), S. 309-318 
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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: SCF calculations utilizing a basis of all s-type Gaussians have been performed to investigate the dimerization of BH3 to B2H6. Localized molecular orbitals and pseudonatural orbitals are calculated. The dimerization energy obtained (11.5 kcal/mole) supports the assumption that the non-Hartree-Fock interactions (electron correlation) play a dominant role (Exp = 40-60 kcal/mole).The energy of the principal type of resonance structure based on the SCF-MO's of the separated-but-distorted BH3 systems is rigorously calculated and found to be 150 kcal/mole higher in energy than the SCF energy of B2H6. Thus, resonance stabilization (delocalization) is shown to be extremely important to the stability of the “three-center” bonds in B2H6, as has been suspected for many years.
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  • 154
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    International Journal of Quantum Chemistry 7 (1973), S. 319-332 
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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 tunneling of a hydrogen atom through the barrier of a three-dimensional double-well potential is considered. From the time-dependent Schrödinger equation, expressions are derived for the ensemble-averaged probability density and for the probability that the hydrogen atom is in the reactant region, in the barrier region, or in the product region. It is found that when thermal vibrations are not taken into account, the ensemble-averaged probability density may oscillate with time about its equilibrium value. When thermal vibrations are included, the oscillations become damped and the probability density approaches equilibrium. The tunneling rate is found to decrease considerably for increasing barrier thickness and barrier height.
    Additional Material: 3 Ill.
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  • 155
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    International Journal of Quantum Chemistry 7 (1973), S. 333-344 
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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: Consideration is given to the problem of interactions between molecular systems (magnetic couplings being neglected) by highlighting the fact that the main difficulty of a perturbation theory that takes into account the exchange effects, resides in the differentiated symmetry of the unperturbed state and of the state of interaction (at an overlap other than zero). This difficulty has been overcome by choosing for the Schrödinger equation of the interacting systems a particular representation on the set of unperturbed functions and by reversing the symmetry properties onto the operators. This will lead to a new equation no longer presenting any difficulties for the symmetry interconnection. This equation is used for a double perturbational expansion both in Coulomb and in exchange terms, thus obtaining general perturbation equations. Explicit solutions are provided (up to the second total order) which are briefly discussed.
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  • 156
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    International Journal of Quantum Chemistry 7 (1973), S. 345-355 
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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: Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.
    Additional Material: 1 Tab.
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  • 157
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    International Journal of Quantum Chemistry 7 (1973), S. 357-364 
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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 describe a method to optimize simultaneously Slater orbital exponents. The procedure is based on Newton's method and requires the derivatives of the energy as a function of the exponents. The calculation of these derivatives is described explicitly. The method has been applied to the hydrogen molecule.
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  • 158
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    International Journal of Quantum Chemistry 7 (1973), S. 405-406 
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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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  • 159
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    International Journal of Quantum Chemistry 7 (1973), S. 569-581 
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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: Applying an extended form of the Mulliken approximation and a monopole approximation for the Coulomb integrals the Hartree-Fock nonorthogonal energy expression is decoupled. Thus, the total energy splits into a sum of one-electron increments. The increments are minimized directly with respect to the linear coefficients and orbital exponents. Further, the ZDO approximation is used in the decoupled energy expression to avoid difficulties arising in connection with the evaluation of multicenter integrals. “Rigid core” calculations were carried out for the valence electrons of first-row diatomics. In case of nonpolar molecules good results are obtained for equilibrium distances and force constants. The method fails for molecules with atoms having very different nuclear charges.
    Additional Material: 1 Ill.
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  • 160
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    International Journal of Quantum Chemistry 7 (1973), S. 583-608 
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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 (spin projected) extended Hartree-Fock equations are derived and discussed in the general (“many λi”) case. The derivation is based on the corresponding generalized Brillouin theorem, substituting in its expression the spin projected DODS Slater determinant as a linear combination of determinants. The expressions obtained for the elements of the different matrices εcd (c = a or b, and d = a or b) occurring in the equations are analyzed. The transformation of the equations into the form of a pseudoeigenvalue problem and the LCAO form of the equations are given, too. Finally the relation to the Goddard's GF equations is discussed in detail.
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    International Journal of Quantum Chemistry 7 (1973), 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: Various molecular properties have been calculated for pyridine and pyrazine from Gaussian lobe ab initio SCF molecular wave functions. Values are compared with available experimental data. In general, agreement is satisfactory with the exception of the rather sensitive asymmetry parameter of the quadrupole coupling tensor. The distributions of total electronic charge, and of selected molecular orbitals have been displayed as plots of the charge density contours in two dimensions.
    Additional Material: 8 Ill.
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    International Journal of Quantum Chemistry 7 (1973), S. 623-634 
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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 modified Gaussian function g(u, v, w, a, R) = const s(a, R) is considered where l = u + v + w, s (a, R) is a 1s-type Gaussian function centered at R, a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R. General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.
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  • 163
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    International Journal of Quantum Chemistry 7 (1973), S. 635-636 
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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: 1 Tab.
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    International Journal of Quantum Chemistry 7 (1973), S. 637-637 
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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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  • 165
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 166
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    International Journal of Quantum Chemistry 7 (1973), S. 647-665 
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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 computational approach for general Heisenberg spin Hamiltonians for a finite number of interacting doublet species is described. Maximum use of permutation and point group symmetry is incorporated in factorizing the secular equation. Associated problems in the computation of symmetric group characters, related frequencies, and selection of linearly independent kets from a large linearly dependent set are also solved.
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    International Journal of Quantum Chemistry 7 (1973), S. 667-674 
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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 simple, “nearly free electron” model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in second-order pseudopotential perturbation theory. The stability of three probable crystal structures is investigated, and lattice parameters are calculated for two different choices of the pseudopotential.
    Additional Material: 2 Ill.
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  • 168
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    International Journal of Quantum Chemistry 7 (1973), S. 641-646 
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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 an estimation of the pair correlation the interelectronic distance r12 in geminal ψk(12) is introduced. The calculations are carried out by the local energy method [1, 2]. The influence of other electrons are taken into consideration with the help of the one- and two-electron integrals depending upon r1 and r2 as parameters. If the strong orthogonality condition is satisfied all two-electron integrals and most of the one-electron integrals vanish. All atomic orbitals are expressed in terms of Gaussian functions. A trial calculation is made for the beryllium atom.POUR tenir compte de la corrélation, on introduit la distance interélectronique r12 dans la géminale ψk(12). Le calcul est réalisé par une méthode des énergies locales [1, 2]. L'influence des autres électrons est décrite par des intégrales à un et deux electrons, dépendantes de r1 et r2 comme paramètres. Dans les conditions de l'orthogonalité forte, toutes les intégrales à un électron et la plupart des intégrales à deux électrons disparaissent. Pour simplifier l'algorithme du problème, toutes les orbitales sont exprimées par les fonctions de Gauss. Le calcul est réalisé sur le modèle de l'atome Be.Für Berechnung der Korrelation wird der Interelektronenabstand r12 in Geminal ψk(12) eingeführt. Die Berechnung wird mit der Lokalenenergiemethode durchgeführt [1, 2]. Die Einwirkung der anderen Elektronen wird durch 1- und 2-Elektronenintegrale berücksichtigt, die von Parametern r1 und r2 abhängen. Bei Erfüllung der starken Orthogonalitätsbedingung verschwinden alle 2-Elektronen- und die Mehrzahl der 1-Elektronenintegrale. Alle Orbitale werden durch Gaussfunktionen ausgedrückt. Eine Berechnung für das Atom Be wird durchgeführt.
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  • 169
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    International Journal of Quantum Chemistry 7 (1973), S. 675-686 
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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: As until now proposed in the literature, in the local energy calculations we can distinguish “few-points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many-points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many-points” calculation M points/N functions (M 〉 N) can be connected in a simple way with the errors of the (MN) partial calculations N points/N functions.This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.
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    International Journal of Quantum Chemistry 7 (1973), S. 699-705 
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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 discussion of Hartree damping in closed-shell Hartree-Fock theory is given indicating when the method might force convergence of intrinsically divergent cases. An alternative, but closely related principle, “level shifting” is described, and the advantages of the latter procedure discussed.
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  • 171
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    International Journal of Quantum Chemistry 7 (1973), S. 687-698 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The half-projected Hartree-Fock function (HPHF) for singlet states is defined as a linear combination of two Slater determinants, which contains only spin eigenfunctions with even quantum number. Using a self-consistent procedure based on the generalized Brillouin's theorem, the RHF, HPHF and PHF functions are deduced for the ground states of the Li-, Be, B+, and C2+ systems, in a limited basis set. It is found that the HPHF function yields better energy values than the RHF function, very close to that of the PHF one. The HPHF scheme seems thus to be useful as a substitute for the PHF model, specially in the case of large electronic systems in which the latter method becomes unmanageable.
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  • 172
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    International Journal of Quantum Chemistry 7 (1973), S. 707-715 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH3 as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N - D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single-center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.
    Additional Material: 4 Tab.
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  • 173
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    International Journal of Quantum Chemistry 7 (1973), S. 717-723 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown how to obtain pseudonatural orbitals directly from the equations of motion. A sample calculation on the ground state of the Be atom is given.
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  • 174
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    International Journal of Quantum Chemistry 7 (1973), S. 725-737 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio self-consistent computation has been performed on the permanganate ion (MnO4-) in a large basis set of contracted gaussian functions. The ground state description as well as those of the first two excited states are discussed and compared with those obtained experimentally from photoelectron spectroscopy, ESCA, optical spectroscopy and magnetic circular dichroism.
    Additional Material: 11 Tab.
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  • 175
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure for the use of the plethysm operation for classification of the permitted electronic terms of impurity complexes in a crystal is presented. The cases of polyatomic symmetrical complexes are discussed as examples.
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  • 176
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    International Journal of Quantum Chemistry 7 (1973), S. 759-777 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron spin dipole-dipole interaction in CH2 has been calculated as a function of bond angle with configuration-interaction wave functions built from contracted gaussianlobe basis functions. The values D = 0.781 cm-1 and E = 0.050 cm-1 were obtained for the spin dipole-dipole contribution to these parameters for the best CI wave function at the equilibrium geometry. The angular dependence of D shows that the assumption of perfect orbital following is not valid. Based on previous estimates of the spin-orbit contribution to D, the total D is estimated to be 0.9 ± 0.1 cm-1 which is higher than the current experimental value 0.76 ± 0.02 cm-1.
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  • 177
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    International Journal of Quantum Chemistry 7 (1973), S. 745-757 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The exchange polarization energy for the H2+ ion is expressed as an infinite sum of its angular components. At large internuclear distances R, a particular l-component, referred to as induced 2l-pole exchange energy, behaves asymptotically like \documentclass{article}\pagestyle{empty}\begin{document}$$- \frac{4}{{\left({l + 1} \right)\left({l + 2} \right)\left({l + 3} \right)\left({l + 4} \right)}}Re^{ - R}$$\end{document}For larger R this suggests a rather slow l-4 rate of convergence of the series. However, as contrasted to the analogous expansion for the induction energy the convergence speeds up considerably with decreasing internuclear separation.It is also shown that at sufficiently large R a given induced 2l-pole exchange energy can be computed with a high accuracy using a polarization function obtained with neglect of charge overlap effects. Near the bottom of the van der Waals minimum over 99% of the exchange polarization energy can be produced using this simplified form of the polarization function.
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  • 178
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    International Journal of Quantum Chemistry 7 (1973), S. 779-783 
    ISSN: 0020-7608
    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-dependent variational principle due to Frenkel is derived from Hamilton's principle using a suitable general expression for the variational wave function. The connections with a recent comment of P. O. Löwdin and P. K. Mukherjee on the same subject are discussed.
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  • 179
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    International Journal of Quantum Chemistry 7 (1973), S. 807-817 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By performing calculations on H2 O similar to the calculations of Dunning and McKoy on C2H4 and HCHO [1a], it is shown that the singlet excited states of the water molecule cannot be adequately represented by an ab initio calculation (no semiempirical elements) using a valence-like basis set (either minimum basis or double zeta) of Slater-type orbitals. The triplets which are the lowest states of their symmetry appear to be described more accurately than the other states, and the lowest four triplet excitation energies are calculated to be 8.1, 8.4, 9.5, and 10.3 eV. The implications for the applicability of simple molecular orbital theory of the type commonly applied are discussed.
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  • 180
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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: Expressions are derived for the n-dependent, hydrogen-like relativistic corrections to the magnetic dipole and electric quadrupole radial hyperfine integrals of an arbitrary atomic state.Good agreement has been obtained earlier between these corrections and the relativistic Hartree-Fock results for s1/2 states. The agreement remains good for the p1/2 states. For the p3/2 states in heavier atoms the hydrogenic corrections still reproduce the Hartree-Fock trend. For the higher l values the agreement is poor. Numerical tables are given for 1 ≤ Z ≤ 100 for the s1/2, p1/2, and p3/2 magnetic dipole cases and the p3/2 quadrupole case.
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  • 181
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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: Several schemes are discussed for partitioning the second-order reduced density matrix Γ into two parts, Γ0 and Γ′.The Γ0s are based on the independent particle model and the Γ′s are corrections due to electron correlation. The difficulties of choosing a Γ0 that will serve as a suitable reference point for studying electron correlation are discussed.In order to compare alternative partitioning schemes, an atomic wave function for the 1S ground state of the Be atom in the configuration-interaction approximation was selected. A fifty-two configuration wave function was computed and contour graphs were made of the total pair density Γ(1 2) and of the “correlation pair density” Γ′(1 2) for several choices of the reference Γ0.
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  • 182
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    International Journal of Quantum Chemistry 7 (1973), S. 877-892 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The dispersion interaction between two nonoverlapping atoms (or molecules) is expressed in terms of single-atom “polarizabilities.” The formulation is valid even if one atom (or both) is in an excited state. To illustrate the procedure, the dispersion interaction between a 1s and a 2s hydrogen atom is computed accurately through order R-10 (R = internuclear separation).
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  • 183
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    International Journal of Quantum Chemistry 7 (1973), S. 893-903 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An ab initio valence bond (VB) method for calculating energies and wave functions for simple electronic systems is described and the results of its application to methylene are given together with extensive comparisons with previous theoretical results.
    Additional Material: 2 Ill.
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  • 184
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    International Journal of Quantum Chemistry 7 (1973), S. 905-925 
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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: Hydroxyl diffusion and interhydroxyl binding in hydroxyapatite has been studied. LCGO-MO-SCF calculations have been carried out on groups of hydroxyl ions in a perfect and a vacancy-containing crystal.Electrostatic crystal effects were accounted for by including the crystal potential field in the SCF calculations. Nearest-neighbour interactions were calculated to first order. Effects exerted by fluorine impurities were considered for the vacancy-containing crystal.The calculations indicate that narrow bandwidths obtained in nmr experiments on biological hydroxyapatite may be caused by a hydroxyl displacement mechanism and that no interhydroxyl hydrogen bonds exist in hydroxyapatite. The suggestion that the caries-inhibiting properties of fluorine impurities in human dental enamel is caused by a diffusion-binding mechanism is supported by the results.
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  • 185
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    International Journal of Quantum Chemistry 7 (1973), S. 927-944 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An interpretation of degenerate symmetry spaces associated with a given atomic or molecular configuration is presented, and the theory necessary for atomic applications is discussed in detail. Löwdin's symmetric projection operator for spin and orbital angular momentum is applied on a well-defined sequence of Slater determinants. In this way a degenerate LS space is divided into orthogonal invariant subspaces which can be classified according to internal couplings of angular momentum. A procedure is found which permits expression of each of these LS eigenfunctions as the smallest possible number of successively orthogonalized projected Slater determinants. In particular, minimum size Hartree-Fock interacting spaces (important in rapidly convergent correlation energy calculations) are obtained in their most compact form. An optimum partition of degenerate spaces of three and four excited (atomic or molecular) configurations is obtained in general. Interpretations, simplifications, and systematizations in atomic configuration interaction calculations are discussed in light of present results.
    Additional Material: 5 Tab.
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  • 186
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Un procédé de minimisation directe de l'énergie d'une molécule par rapport aux coefficients des orbitales atomiques des fonctions moléculaires est utilisé en vue de déterminer les fonctions de l'état fondamental et des états excités. L'orthogonalité entre les divers états est obtenue par des conditions moins restrictives que celles de Roothaan, si bien que l'énergie obtenue pour la première transition électronique est abaissée: de 0,1 à 0,2 eV pour les transitions π → π* des polyènes.
    Additional Material: 3 Tab.
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  • 187
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    International Journal of Quantum Chemistry 7 (1973), S. 1051-1061 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The coarse structure magnetic theory presented here is a reformulation of conventional magnetic theory which emphasizes the spin-free (i.e., the coulombic) nature of the electron-electron interaction. We show that the magnetic properties of a system for which fine and hyperfine structure can be neglected depend only on the energy spectrum of a spin-free Hamiltonian. As an example, we treat the Heisenberg linear chain.
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  • 188
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    International Journal of Quantum Chemistry 7 (1973), S. 1077-1090 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The infinite interaction range model (IIRM) for ferromagnetic systems is presented in its spin-free formulation. In this formulation the states are labelled by partitions which provide a natural variable for thermodynamic computation. We have extended the calculations of Kittel and Shore by computing to a practical thermodynamic limit (N ∼ 100,000). The heat capacity, magnetic susceptibility and the magnetization of the first two functions exhibit a critical temperature while the magnetization is zero at zero field for all temperatures. Spontaneous magnetization is obtained by linear extrapolation from high field or equivalently by a polarized partition function. Relationships are explored among IIRM, the Heisenberg model and the mean field model. Application to IIRM of the Yang-Lee condition for a phase transition yields a critical temperature identical to that obtained by the direct calculation.
    Additional Material: 5 Ill.
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  • 189
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    International Journal of Quantum Chemistry 7 (1973), S. 1091-1097 
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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 restriction on a method for computing irreducible representations of finite groups, requiring that in the irreducible representation to be constructed, at least one group element has at least one nondegenerate eigenvalue, is removed. The method is thus shown to be applicable to an arbitrary finite group and constitutes a practical algorithm for handling groups of order less than 400.
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  • 190
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    International Journal of Quantum Chemistry 7 (1973), S. 1117-1137 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The application of Lie algebras in quantum chemistry is considered. Particular attention is devoted to their application to high symmetry problems especially where icosahedral symmetry prevails. A general programme for implementing the theory of Lie algebras in the analysis of symmetry problems is outlined.
    Additional Material: 9 Tab.
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  • 191
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    International Journal of Quantum Chemistry 7 (1973), S. 1175-1182 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical electronic wave functions, potential curves, and expectation values of some one-electron properties are given for the c3IIu state of the hydrogen molecule. The calculations are carried out by the matrix Hartree-Fock method and use a 2-center basis of Slater-type orbitals. A total energy of -0.7292 a.u. is obtained in the best calculation. Our potential curve is reasonably consistent with that calculated by Browne, but we have examined the region of small internuclear distances (those at and below Re for the ground state) more extensively than any previous calculation. At R ≦ 1.6 a.u. our calculated potential curve is in excellent agreement with experiment.
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  • 192
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    International Journal of Quantum Chemistry 7 (1973), S. 1227-1228 
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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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  • 193
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    International Journal of Quantum Chemistry 7 (1973), S. 215-222 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A theoretical study of π-electron spin density distributions has been made for a series of fluoro-substituted hydrocarbon radical cations using unrestricted Hartree-Fock theory. Although some of the predicted proton splittings are not in very good agreement with experiment, the overall agreement with experiment can be passed as fairly satisfactory considering the approximate nature of the theory used. The experimental fluorine splittings can be well predicted by using a one-parameter relationship between the isotropic fluorine splitting (aF) and the π-electron spin density (ρCC) on the attached carbon. It has been further shown that both ρCC and the proportionality constant (Qeff) in the linear relation, are fairly insensitive to the parameter choice.
    Additional Material: 1 Ill.
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  • 194
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    International Journal of Quantum Chemistry 6 (1972), S. 125-130 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Feenberg-Goldhammer change of scale, whereby the H0 in perturbation theory is replaced by (1/μ)H0 with μ a scaling parameter, is shown to be equivalent to a change of variable for the perturbation parameter. A more general change of variable is shown to lead to a perturbation series with perturbation energies E3, …, E2n+1 equal to zero. The resulting energy through (2n + 1)th order has the same form as that found from the Brillouin-Wigner series by different methods.
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  • 195
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    International Journal of Quantum Chemistry 6 (1972), S. 131-142 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Two different perturbation series (the polarization expansion and a united-atom expansion) of the ground state energy of the delta-function model for one-electron diatoms are studied and the radii of convergence are determined. For both expansions the singularity in the energy which limits the radius of convergence is a branch point with exponent one-half. The physical significance of the branch point is that for particular values of the perturbation parameter, two different energy eigenvalues coalesce. The positions of the branch points are computed as a function of the internuclear separation R. For all values of R, both series converge for all physical values of the perturbation parameters. A lower bound to the radius of convergence of the polarization expansion has been computed previously by Claverie. It is proved in the present paper that the lower bound calculation is in fact an exact determination of the radius of convergence. The results of the model study are applied to real one-electron diatoms to suggest the possible location of a branch point singularity in the energy of the ground state.
    Additional Material: 3 Ill.
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  • 196
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    International Journal of Quantum Chemistry 6 (1972), S. 167-179 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The bond exciton model, developed originally for alkane molecules, is applied here to a range of alkene molecules and diene polymers. The necessary empirical parameters are derived by comparison of the theory with the vacuum-ultraviolet absorption spectra of ethylene and a number of alkyl-substituted ethylenes, and these values are used to predict the energies, intensities and polarizations of the lower energy allowed valence transitions of fine diene polymers. Despite its simplicity the bond exciton model is found to give results in quite reasonable agreement with the available experimental data, and suggests that considerable excitation energy transfer may occur along the main chains of certain diene polymers.
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  • 197
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    International Journal of Quantum Chemistry 6 (1972), S. 181-192 
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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 problem of evaluating the radial electron-electron distribution function P0(r12) from the spin-free 2-particle density matrix P(2)(r1, r2Ir'1, r'2) is considered in detail. The analysis is first applied to 2-electron S-type functions built from l2 configurations. For the special case l = 0, the expression for P0(r12) reduces to the result obtained by Coulson and Neilson.For non-spherically symmetric states of N-electron atoms, the angular integrations are handled by a procedure used by Calais and Löwdin in their evaluation of atomic integrals containing functions of r12. Consideration is also given to the evaluation of necessary radial integrals.
    Additional Material: 2 Tab.
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  • 198
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    International Journal of Quantum Chemistry 6 (1972) 
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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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  • 199
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    International Journal of Quantum Chemistry 6 (1972), S. 211-224 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A variational formulation of the Hartree-Fock-Roothaan (HFR) theory for open shell ions in presence of time dependent perturbations is presented. The theory has been used to calculate the dynamic polarizabilities of the first three ions of the Li sequence. The polarizability values, extrapolated to zero frequency, show good shell by shell agreement with the corresponding static results. The polarizability graphs display resonance behaviour at the transition frequencies of the ions, and a study of these points leads to analytic HF wave functions for their low lying excited states. The calculated transition frequencies are in excellent accord with the experimental values. The calculated oscillator strengths for the 2s → np transitions are in reasonable agreement with the extensive multiconfiguration calculations of Weiss and the available experimental results.
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  • 200
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    International Journal of Quantum Chemistry 6 (1972), S. 263-269 
    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: The paramagnetic properties of one-dimensional macromolecules with conjugated C=C bonds are discussed on the basis of low-lying quasi-homeopolar triplet excitations. A good agreement with the experimental results is shown.
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