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  • Atomic, Molecular and Optical Physics
  • 1995-1999  (370)
  • 1985-1989
  • 1980-1984
  • 1975-1979  (291)
  • 1940-1944
  • 1995  (370)
  • 1977  (192)
  • 1975  (99)
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  • 1995-1999  (370)
  • 1985-1989
  • 1980-1984
  • 1975-1979  (291)
  • 1940-1944
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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 1-8 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this paper a calculation of the static quadrupole polarizabilities and the shielding factors of the atoms and ions of the 2p open shell systems is presented. A fully coupled Hartree-Fock method using the Roothaan formalism is adopted. Calculations have been done for the ground as well as for some valence excited states. An antishielding effect is observed for all the atoms and ions under study.
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  • 2
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    International Journal of Quantum Chemistry 9 (1975), S. 67-74 
    ISSN: 0020-7608
    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 integral transform function: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm exp }\left({{\rm - }\zeta {\rm r}} \right)\int_0^\infty {s(n)r^n dn} $$\end{document} where s(n) is a positive definite shape function, is proposed and investigated. A test on H2+ shows that it does not suffer from the inadequacies of earlier integral transform functions, of the form: \documentclass{article}\pagestyle{empty}\begin{document}$$ r^n \int_0^\infty {c(\zeta ){\rm exp}({{-}\xi r})d\zeta } $$\end{document} where c(ζ) is a positive definite shape function.
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  • 3
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    International Journal of Quantum Chemistry 9 (1975), S. 103-117 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Weyl's eigenvalue theory for ordinary second-order differential equations is discussed for the case of a continuous spectrum. It is demonstrated that the spectral density function obtained from a suitably averaged Green's function, equal to the Weinstein function, can be directly related to the Weyl-Titchmarsh m-function. The explicit connections with scattering theory are derived and it is found that the Weyl and Jost solutions are proportional; the proportionality factor being the reciprocal value of the latter at the origin. The physical interpretation of the complex poles of the spectral density is discussed in relation to Gamow's exponentially growing functions. The advantage of using a formulation that allows for a “perturbation” of boundary conditions is pointed out.
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  • 4
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    International Journal of Quantum Chemistry 9 (1975), S. 149-156 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Combined CI-HY method techniques have been employed in obtaining a 57-term CI-HY wave function with an energy of -14.66632 a.u. A method due to Brown has been adopted for obtaining this wave function and various shorter expansions. A 44-term expansion with an energy of -14.66606 a.u. is analyzed in terms of various pair effects, and qualitative arguments are presented for understanding these effects.
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  • 5
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    International Journal of Quantum Chemistry 9 (1975), S. 229-236 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Mø-Plesset theory, in which electron correlation energy is calculated by perturbation techniques, is used in second order to calculate energies of the ground states of atoms up to neon. The unrestricted Hartree-Fock (UHF) Hamiltonian is used as the unperturbed system and the technique is then described as unrestricted Mø-Plesset to second order (UMP2). Use of large Gaussian basis sets suggests that the limiting UMP2 energies with a complete basis of s, p, and d functions account for 75-84% of the correlation energy. Preliminary estimates of the contributions of basis functions with higher angular quantum numbers indicate that full UMP2 limits give even more accurate total energies.
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  • 6
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    International Journal of Quantum Chemistry 9 (1975), S. 789-795 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A smooth interpolation method for the calculation of Fourier transforms of numerical atomic orbitals is presented and the method is used to calculate two-center overlap integrals. Examples applying various definitions of smoothness are given.
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  • 7
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    International Journal of Quantum Chemistry 9 (1975), S. 825-834 
    ISSN: 0020-7608
    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 variational principle for transition and density matrices is proposed. The principle is closely related to Rowe's variational treatment of the equations-of-motion method. It permits the simultaneous construction of coupled approximations for two eigenstates, and it is a straightforward extension of the usual variational method.
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  • 8
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    International Journal of Quantum Chemistry 9 (1975), S. 887-900 
    ISSN: 0020-7608
    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 we discuss an extension of the standard multiple scattered wave method for molecular electronic structure calculations to the case of arbitrarily shaped molecules. A general theory is presented where the difficulties arising from the matching problem across an arbitrary boundary are avoided. The secular equation to determine the energy spectrum is obtained and the wave functions are calculated in all regions.
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  • 9
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    International Journal of Quantum Chemistry 9 (1975) 
    ISSN: 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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  • 10
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    International Journal of Quantum Chemistry 9 (1975), S. 969-973 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Reformulation, generalization, and application of Löwdin's symmetric orthonormalization, of orthogonalization of two sets of vectors, and of McWeeny's variational method of a density matrix, etc., by means of an operator for forming ket vectors on which are imposed some conditions, are presented.
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  • 11
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    International Journal of Quantum Chemistry 9 (1975), S. 1055-1067 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical formulas are derived for integrals of the orbit-orbit operator in the Breit-Pauli Hamiltonian. The present method differs from an earlier one in the introduction of a new auxiliary function Gn(a) which is an integral of Shavitt's Fm(t) function. A method for its evaluation is discussed and some numerical examples are given.
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  • 12
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    International Journal of Quantum Chemistry 9 (1975), S. 1109-1112 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new method is presented for obtaining the spin eigenfunctions of 2n electron systems in the spin state S and MS = 0. Using a modified Young operator the function for the state S, MS ( = S) of the system is first projected out. The projected function is then symmetrized over the last n particles and the weight lowering operator Š-S is then applied to it, resulting in a projection of the state S, 0. To within a multiplicative factor, the resulting function is identical with the one resulting from the vector coupling methods.
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  • 13
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    International Journal of Quantum Chemistry 9 (1975), S. 379-381 
    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
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  • 14
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    International Journal of Quantum Chemistry 9 (1975), S. 385-392 
    ISSN: 0020-7608
    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 communication we discuss a method of incorporating corrections to the coupled Hartree-Fock (CHF) formalism by introducing the so-called “rearrangement effect.” In this we take account of the relaxation of the core orbitals when excitations from a starting Hartree-Fock wave function occur. The magnitude of this correction numerically is found to be quite significant for the polarizabilities of two-electron atomic systems, results for which are reported.
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  • 15
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    International Journal of Quantum Chemistry 9 (1975), S. 431-443 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A perturbation approach based on resolvent technique and Padé approximants is proposed. The eigenvalue of interest is part of a solution of two nonlinear algebraic equations. The nonlinear equations are arrived at by considering two different expression of the expectation value of the resolvent of an outer projection of the Hamiltonian. The first expression is based on the spectral resolution of the resolvent, and the second one is obtained by a power series expansion analogous to that applied in the derivation of the energy expression in the Brillouin-Wigner perturbation theory. The truncated power series is extrapolated by Padé approximants of type II. The method is tested on a CI calculation of the energy of the lowest 1Σ state of the B2 molecule.
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  • 16
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    International Journal of Quantum Chemistry 9 (1975), S. 479-487 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Complementary variational functionals are derived which impose upper and lower bounds on transition probabilities. These functionals are used to yield bounds in terms of sets of sum rules, and illustrative calculations are presented for hydrogen, helium and krypton atoms.
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  • 17
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    International Journal of Quantum Chemistry 9 (1975), S. 505-516 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Dynamical screening in π-electron systems is studied by the equations of motion method. By using a partitioning technique on the equations of motion we can obtain simple expressions for the effect of dynamical screening directly on the transition energies and transition moments in π-electron systems. These results are used to study the effect of such screening in the N → V transition in ethylene. This procedure can be used to extend the equations-of-motion method to larger π-electron systems.
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  • 18
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    International Journal of Quantum Chemistry 9 (1975), S. 557-557 
    ISSN: 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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  • 19
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report an attempt of ab initio computation for the ground-state wave-function of a few organic semiconductors (namely TCNQ salts and the PDC charge transfer complex) for which we show that electrical conduction appears to look strongly like that of a band-gap semiconductor.
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  • 20
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    International Journal of Quantum Chemistry 11 (1977), S. 189-211 
    ISSN: 0020-7608
    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 of pth-order singular differential equations is adaptable to the study of the system of recurrence relations occurring in the problem of a one-dimensional chain with pth-neighbor interactions. By using Green's formula, a mapping is defined between the space Vn of eigenvectors to the dynamical matrix and the symplectic space V2p of boundary conditions for the recurrence equations. The properties of the resolvent are obtained from an analysis of the solutions of a system of inhomogeneous equations and Green's matrix is constructed for the case of standard Sturm-Liouvilletype boundary conditions. The Weyl surface is discussed and its properties used for the construction of square summable sequences which in turn can be employed in expansion formulas. The generalization of Weyl's m-function in the second-order case (p = 1) becomes for p ≥ 2 a p × p matrix M(λ), where λ is a complex parameter. The imaginary part Im {M(λ)} is related to the spectral properties and serves as basis for the discussion of different concepts of spectral density for the normal modes of lattice dynamical problems. An important practical result is the equation M = -Ψa-1Φa valid in the limit point case, generalizing the corresponding second-order formula.
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  • 21
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    International Journal of Quantum Chemistry 11 (1977), S. 271-276 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An electrostatic correction to the energy of the EH method is deduced from the Hartree energy. A recent correction, due to Anderson and Hoffmann, is easily deduced as a particular case. Some calculations show how the correction can improve the description of stretching problems by EH calculations but poor results are obtained in bending and torsion problems.
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  • 22
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    International Journal of Quantum Chemistry 11 (1977), S. 317-324 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The basis set dependency of the core ionization potential of water was investigated for atomic optimized Cartesian Gaussian basis sets. Basis set parameters optimized for oxygen yielded better IP's than basis set parameters optimized for fluorine. Not much was gained by using different parameters for the ground state and for the 1s hole state.
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  • 23
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    International Journal of Quantum Chemistry 11 (1977), S. 325-339 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A recursive numerical integration scheme based on the method of Clenshaw and Curtis is proposed for the efficient implementation of the variation-iteration procedure for the computation of approximate energies and wave functions for atomic systems. Extensive numerical tests are carried out to assess the accuracy and efficiency of the method and inaccuracies in some earlier calculations are pointed out.
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  • 24
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    International Journal of Quantum Chemistry 11 (1977), S. 359-379 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The formalism described in the first paper of this series is applied to the chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2, the covering of SO(3) ⊃ D∞ ⊃ D4 ⊃ D2. The state vectors (|αJaΓγ) adapted to each link of the chain under consideration and the corresponding coupling coefficients \documentclass{article}\pagestyle{empty}\begin{document}$ f\left( {\begin{array}{*{20}c} {J_1 } & {J_2 } & J \\ {a_1 \Gamma _1 \gamma _1 } & {a_2 \Gamma _2 \gamma _2 } & {a\Gamma \gamma } \\ \end{array}} \right) $\end{document} are given in analytical form. The material reported here is very convenient for a quantum-mechanical description of molecular and nuclear systems with linear, tetragonal, or orthorhombic symmetry. In this respect, we present an outline for its applications to the electronic and vibrational-rotational spectroscopy of molecular aggregates and to the rotational spectroscopy of molecules or nuclei. In addition, we briefly show how the material may simplify the second-order non-Lie subgroup type approach to the representation theory of SU(2).
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  • 25
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    International Journal of Quantum Chemistry 11 (1977), S. 415-425 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The transferability of bonds in a set of small molecules has been explored. The molecular wave-functions have been calculated from the group (or loge) function method, via a construction based on Gaussian functions. The transferability is very good and the effect of lone pairs on adjacent bonds has been analysed. Furthermore, a very simple procedure has been proposed to estimate the frontiers of the bonds.
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  • 26
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    International Journal of Quantum Chemistry 11 (1977), S. 441-450 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of LCAO-MO-SCF calculations, using various basis sets of Gaussian-type functions, has been made in order to study the effects of p, d, and f polarization functions for a 10-electron isoelectronic series of oxygen hydrides and for an 18-electron isoelectronic series of sulfur hydrides. Conclusions from these results suggest that meaningful proton affinities cannot be calculated without the inclusion of a d function on the heavy atom and a p function on the hydrogen atoms.
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  • 27
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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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  • 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: Some applications of an optimization technique due to Levenberg in theoretical submolecular biology are described. This technique has proved a very useful tool for the generation of three-dimensional structures of molecules having cyclic components or other constrained regions. The generated molecular structures provide the starting point for quantum chemical calculations of great value in solving problems of biological interest. The mechanism of transport of alkali metal cations by valinomycin is one such example and this paper describes briefly how various conformations of valinomycin were obtained using the optimization technique. A variant of the same method has been suggested as a new technique for the detection of topographical similarities between apparently dissimilar molecules which are substrates for the same enzyme or receptor site. The technique is illustrated with a comparison of a tricyclic antidepressant with norepinephrine both of which have been postulated to compete for a common receptor site in the “amine pump” of peripheral adrenergic nerve cell membranes. Another area in which the optimization technique has proved useful is in developing an optimum separable localized bond function method designed for rigorous calculations on large saturated molecules. This method is briefly described.
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  • 29
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    International Journal of Quantum Chemistry 9 (1975), S. 459-471 
    ISSN: 0020-7608
    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 SCF-LCAO-MO calculations have been performed for TCNQ and its positive and negative ions in various electronic states. A basis set consisting of 412 primitive Gaussian type orbitals contracted to 180 was used in the investigation. The electron density distribution in TCNQ and the negative ions, and the redistribution upon ionization has been illustrated by plotting difference density contour maps. The quinone structure of the neutral TCNQ system undergoes a transformation to a benzenoid structure when electrons are added. Electronic transitions, ionization potentials and electron affinities have also been calculated.
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  • 30
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    International Journal of Quantum Chemistry 9 (1975), S. 517-526 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The extended Hartree-Fock equations of the spin-projected scheme are derived in a form suitable for the construction of a surely convergent method of solution using successive optimization of the individual orbitals. The derivation is based on a specific form of the generalized Brillouin theorem.
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  • 31
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    International Journal of Quantum Chemistry 11 (1977), S. 759-766 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A two-parameter ω-technique for MO calculations is proposed. The parameters ω and ω′ are chosen empirically to obtain a good agreement between calculated and observed bond lengths. The method amounts to an inclusion of the effect of nearest-neighbour electronic repulsion integrals into the conventional ω-technique.
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  • 32
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    International Journal of Quantum Chemistry 11 (1977), S. 907-916 
    ISSN: 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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  • 33
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    International Journal of Quantum Chemistry 11 (1977), S. 1001-1004 
    ISSN: 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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  • 34
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    International Journal of Quantum Chemistry 11 (1977), S. 1043-1043 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 35
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    International Journal of Quantum Chemistry 9 (1975), S. 1113-1129 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Valence-bond type wavefunctions based on contracted Gaussian atomic orbitals afford an adequate description of the potential of the ground 1Σg+ state of H2 for a wide range of internuclear separations. Semiempirical techniques for scaling the potential curve are evaluated. An efficient method for optimizing non-linear variables in the wavefunctions is explored.
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  • 36
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    International Journal of Quantum Chemistry 12 (1977), S. 593-608 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Floating spherical Gaussian orbital (FSGO) open-shell calculations have been made to determine the potential energy surface of planar square and rectangular arrangements of the four-electron system H4. This surface is discussed in relation to the bimolecular isotope exchange reaction H2+D2-→ 2HD. The changes in energy and geometry accompanying the coplanar approach of two hydrogen molecules interacting chemically have also been investigated. Calculations on the electronic energies of planar T-shaped and kite arrangements of H4 of various sizes show that it is unlikely that these configurations can serve as transition states for the exchange reaction. However, the energy curve for linear configurations of H4 (H—H—H … H), calculated as a function of the H3 … H distance with the symmetric linear H3 (H-H-H) unit fixed at the internuclear distance of 1.9080 a.u., is found to have a deep minimum (-1.9176 a.u.) at an r(H3 … H) distance of 1.5846 a.u. The overall results suggest that the following mechanism for the exchange reaction, H2+H2→H2+H+H→H3+H→H+H2+ H→H2+H2 could be advantageous as it requires a barrier height of 0.1604 a.u. which is significantly lower than that calculated from the saddle point energy (0.1950 a.u.). However, the problem of reconciling this with the experimental activation energy of 0.0685 a.u. still remains.
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  • 37
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    International Journal of Quantum Chemistry 12 (1977), S. 655-670 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Excitation energies and transition moments have been determined from a second order polarization propagator and the effect of including energy shifted denominators has been investigated. Results for Be and CH+ show a change of 2-5% for the transition moments and of 0-20% for the singlet excitation energies in a second order approach compared to a first order (time-dependent Hartree-Fock) approximation. Both Be and CH+ are triplet unstable in the time-dependent Hartree-Fock approximation. The triplet instability is removed for Be but not for CH+ in a second order polarization propagator approach.
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  • 38
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    International Journal of Quantum Chemistry 12 (1977), S. 759-763 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The spherical limit of a single particle in the field of three nuclei is shown to exhibit a variety of phenomena associated with the stability of the various extrema involved. Some consequences with respect to the general problem of detecting broken symmetry solutions of variational problems are pointed out.
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  • 39
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    International Journal of Quantum Chemistry 11 (1977), S. 895-895 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 40
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    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.
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  • 41
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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.
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  • 42
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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
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  • 43
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    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.
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  • 44
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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.
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  • 45
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    International Journal of Quantum Chemistry 9 (1975), S. 325-377 
    ISSN: 0020-7608
    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 is made of the states of nonrigid molecules, extending earlier work to apply Longuet-Higgins' symmetry group of feasible permutation/inversions in two previously untreated cases. The first involves nonrigid molecule processes between different stereoisomers, that is between molecular equilibrium configurations of different geometrical shapes. The second takes into account nonrigid molecule processes in linear molecules. The theory is applied to the specific case of nonrigid molecule effects in the butyl ion C4H9+ (case i), and the form of the nonrigid molecule energy levels and spectra are determined. The theory is also applied to determine the nonrigid molecule energy levels in linear H2F2 (case ii).
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  • 46
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    International Journal of Quantum Chemistry 9 (1975), S. 495-504 
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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 this paper we include the rearrangement correction (discussed in the preceding paper) in a coupled Hartree-Fock (CHF) calculation of atomic hyperpolarizabilities and other related properties. We have studied the effect of these corrections on properties like electric dipole hyperpolarizabilities, uniform electric field quadrupole polarizabilities and shielding factors in two-electron ions and have noticed significant changes in the computed values over the CHF results.
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  • 47
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    International Journal of Quantum Chemistry 9 (1975), S. 555-555 
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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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  • 48
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    International Journal of Quantum Chemistry 9 (1975), S. 545-554 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We introduce here a new partitioning of the Hamiltonian in calculating pair-correlation energies using many-body perturbation theory, by which we are able to eliminate the off-diagonal particle-hole (p-h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle-particle (p-p) and hole-hole ladders exactly to all orders. The effect of the off-diagonal p-p ladders has been estimated for each pair by computing the third-, foruth- and fifth-order energies. For highly symmetric systems the present partitioning yields in general symmetry-broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p-h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π-electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed.
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    Topics: Chemistry and Pharmacology
    Notes: The self-correlated field method is based on the insertion in the group product wave function of pair functions built upon a set of correlated “local” functions and of “nonlocal” functions. This work is an application to three-electron systems. The effects of the outer electron on the inner pair are studied. The total electronic energy and some intermediary results such as pair energies, Coulomb and exchange “correlated” integrals, are given. The results are always better than those given by conventional SCF computations and reach the same level of accuracy as those given by more laborious methods used in correlation studies.
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  • 50
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    International Journal of Quantum Chemistry 9 (1975), S. 669-681 
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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 modification of the concept of “seniority” for the classification of the permitted terms and the effective operators in complexes and molecules is presented. Tables of the states of complexes of impurity orbital nondegenerate ions (N = 3, 4) with spin S (\documentclass{article}\pagestyle{empty}\begin{document}$ S = \frac{1}{2} - \frac{7}{2} $\end{document}) and the corresponding tensorial operators are given.
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  • 51
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    International Journal of Quantum Chemistry 9 (1975), S. 711-719 
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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 first few terms of the perturbation expansions for the function and the energy shift of a degenerate state of an arbitrary quantum mechanical system are obtained using the adiabatic formula. It is shown how the expansion for the secular operator may be obtained from the expansion for the function. The results are used to calculate energies of the ground and some excited states and multiplet splittings of some beryllium-like ions.
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  • 52
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    International Journal of Quantum Chemistry 9 (1975) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 53
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    International Journal of Quantum Chemistry 9 (1975), S. 583-604 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Recent advances in the statistical exchange approximation to the one-electron potential and in the use of general potentials in multiple scattering are studied numerically and combined in a cellular multiple scattering calculation of the electronic structure of molecules. The particular examples of these calculations are SF6, H2+, and H2, the results being compared with those of previous approximations and other techniques. It is first seen that the Xαβ approximation or a similar one based on the use of a universal parametrization of the statistical exchange (and some effects of correlation) part of the potential will provide the maximum of freedom in the partition of the real space of the molecules into cells. This avoids arbitrariness in the assumed value of the parameters to be used in every cell. The usefulness of the Xαβ approximation in a muffin-tin and in a cellular calculation is discussed. It is also found that the usual limitation to muffin-tin-like potentials, while simpler as a first approximation, can be removed without unduly increasing the computing effort. However, an accurate evaluation of the real self-consistent potential in each cell (or even in a muffin-tin) will increase the length of the program, the storage necessities and the computing time by a factor estimated to be between three and ten according to the geometry considered. It is concluded that the cellular multiple scattering method offers the best possibilities for a systematic use of multiple scattering techniques in molecular calculations.
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  • 54
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    International Journal of Quantum Chemistry 9 (1975), S. 605-625 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electronic structure and collective excitations of long molecules with conjugated bonds in the main chain (linear polyene, cyclic polyene, polyphenylacetylene (PPA)) are considered. The electronic structure of these polymers is investigated by the generalized Hartree-Fock method. The first triplet collective excitations are derived using the compact technique of the Green's functions. This approach is shown to be equivalent to the random phase approximation. The problem of the triplet collective excitations in long cyclic polyenes is solved analytically and good agreement with the exact results is found. The effects of the free ends in a linear polyene are considered. The approach developed for PPA and polyene may be applied to an investigation of any polymer molecule with equivalent unit cells.
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  • 55
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    International Journal of Quantum Chemistry 9 (1975), S. 657-668 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The concept of a “multi-centered plethysm” for multinuclear problems is defined and studied. Schemes of links of atoms in molecules or complexes and corresponding schemes of the group reductions are considered.
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    International Journal of Quantum Chemistry 9 (1975), S. 701-710 
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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 different forms of perturbation theories, variational perturbation, finite perturbation and second-order, are evaluated regarding their value for calculation of electronic polarizabilities of small and intermediate size molecules. It is concluded that with the practical constraint of a small basis set the variational perturbation method is the most promising alternative for calculation of polarizabilities. For several small molecules, our calculated polarizabilities indicate that both IEHT and ab initio wave functions give values in close agreement with each other. Variational perturbation calculations of polarizabilities with IEHT wave functions also include the DNA bases.
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    International Journal of Quantum Chemistry 9 (1975), S. 755-757 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 9 (1975), S. 761-773 
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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: All the second-order density matrix spin components for the spin-projected Slater determinant are presented as expansions in direct products of powers of unprojected spin- and residual electron density matrices. Spin components of the second-order transition density matrices between spin-projected Slater determinants built of orthogonal orbitals are also obtained.
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  • 59
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    International Journal of Quantum Chemistry 9 (1975), S. 287-299 
    ISSN: 0020-7608
    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 test the effect of a removal of an “equivalence” restriction, some excited states of B, C+ and C arising from the configuration 1s22s2pn (n = 2, 3) are calculated by the use of a one-diffuse-electron model with the optimal spin coupling (DO), in which the freedom of the spin coupling is fully used. The configuration employed is 1s22s2pn-12p′ (n = 2, 3).The DO method gives a good agreement with the term energies especially for boron (4P → 2P) and carbon (5S° → 3S°). A diffuse 3p natural orbital with a large occupation number is found for boron 2P and carbon 3S° by DO. This result is confirmed by configuration interaction calculations.Using the same configuration as above, we also examine a one-diffuse-electron model with a fixed spin coupling for boron. This method almost reproduces the results of restricted Hartree-Fock and the effect of a removal of an “equivalence” restriction is not found.The importance of utilizing the freedom of the spin coupling in a one-diffuse-electron model is strongly indicated in this article.
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  • 60
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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.
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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.
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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.
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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.
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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.
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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.
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    International Journal of Quantum Chemistry 12 (1977), S. 83-92 
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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 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.
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    International Journal of Quantum Chemistry 9 (1975), S. 855-870 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A comprehensive review of the attempts to rephrase molecular quantum mechanics in terms of the particle density operator and the current density or phase density operator is given. All pertinent investigations which have come to our attention suffer from severe mathematical inconsistencies and are not adequate to the few-body problem of quantum chemistry. The origin of the failure of these attempts is investigated and it is shown that a realization of a local quantum field theory of molecular matter in terms of observables would presuppose the solution of many highly nontrivial mathematical problems.
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  • 68
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    International Journal of Quantum Chemistry 9 (1975), S. 901-916 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: We present a method for calculating the one-particle Green's function for molecules. The scheme is essentially that proposed by Schneider and Taylor [1]. The Green's function is obtained through the Dyson equation. Closed expressions result by using the functional derivation technique to truncate an infinite set of coupled equations. A physical interpretation of the approximation is given and a connection with the equations-of-motion method is pointed out. In a numerical application the ionization potentials are obtained for the molecules N2, H2O, NH3 and CH4.
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  • 69
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    International Journal of Quantum Chemistry 9 (1975), S. 923-940 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Results of semiempirical calculations (CNDO/2-FK and MINDO/2 methods) for the σ-π complex problem on protonated benzene are given and compared with previous ones. The semiempirical methods were chosen according to the agreement of their results with new theoretical energy data (EHF + Ekorrel) concerning the classical-nonclassical problem of protonated ethylene. By these methods the corresponding part of the energy surface of the benzene/H+ system is simulated. The stationary points of this surface are found by a gradient method with complete optimization of the geometry. On the basis of this method we determined the energy profile of a reaction coordinate between the classical (σ-complex) and nonclassical (π-complex) cation. The so called strong π-complex is a saddle point between two σ-complex minima and can be interpreted as transition state of 1,2-proton shifts. Hypotheses for possible minimum energy paths of electrophilic attacks in the given region of the surface are discussed.
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    International Journal of Quantum Chemistry 9 (1975), S. 975-980 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The convergence behavior of an iterative procedure proposed by Frost, Kellogg, and Curtis for solution of variance minimization equations is discussed. Use of particular sets of initial parameters in the iterative procedure is shown to yield rapid convergence.
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  • 71
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    International Journal of Quantum Chemistry 9 (1975), S. 1021-1031 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A computational technique within the Extended Hückel frame-work for the calculation of the hydrogen-molecule interaction energy is described. The procedure is ten times faster than the usual diagonalization procedure.The algorithm consists of transforming the generalized secular equation to give a bordered-diagonal matrix secular equation, which is solved by means of an efficient bisection technique.As an example, two problems are discussed: (i) glycine intra-molecular proton transfer process; (ii) interaction of the molecular fragments CH and OH.An atomic SCF Gaussian basis set was used instead of the usual Slater type basis set.
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    International Journal of Quantum Chemistry 9 (1975), S. 1069-1085 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Using the variational method advanced by McCavert and Rudge, we obtain the independent particle model variational principle for loge localized discontinuous wave functions. The transformation of the variational expressions into matrix form when the loge localized discontinuous orbitals are expanded in finite basis sets is discussed. The simplifications brought about by this new method in the evaluation of molecular integrals are indicated.
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  • 73
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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.
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  • 74
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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
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    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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  • 75
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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
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    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.
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    International Journal of Quantum Chemistry 12 (1977), S. 161-191 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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.
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  • 77
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    International Journal of Quantum Chemistry 12 (1977), S. 215-223 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    International Journal of Quantum Chemistry 12 (1977), S. 227-229 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 12 (1977), S. 291-303 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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.
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    International Journal of Quantum Chemistry 12 (1977), S. 317-326 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    International Journal of Quantum Chemistry 12 (1977), S. 431-431 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 12 (1977), S. 397-426 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    International Journal of Quantum Chemistry 12 (1977), S. 457-469 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    International Journal of Quantum Chemistry 12 (1977), S. 495-503 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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  • 85
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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.
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    International Journal of Quantum Chemistry 11 (1977) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 11 (1977), S. 21-47 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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  • 88
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    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.
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    International Journal of Quantum Chemistry 11 (1977), S. 149-161 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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  • 90
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    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.
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    International Journal of Quantum Chemistry 11 (1977), S. 277-281 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    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
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    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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    International Journal of Quantum Chemistry 11 (1977), S. 349-358 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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.
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    International Journal of Quantum Chemistry 11 (1977), S. 1-15 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    International Journal of Quantum Chemistry 11 (1977), S. 17-20 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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.
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    International Journal of Quantum Chemistry 11 (1977), S. 59-71 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    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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    International Journal of Quantum Chemistry 11 (1977), S. 137-147 
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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 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.
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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.
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    International Journal of Quantum Chemistry 9 (1975) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 9 (1975), S. 215-227 
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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 have calculated the energies of the (7s) and (8s) states of the valence electron in the K atom by making use of a pseudopotential based on recently obtained variational solutions of the Thomas-Fermi (TF) equation for neutral atoms, and positive ions. We have chosen trial wave functions, with appropriate parameters, for the valence electron and then minimized the energies of the respective states using the pseudoHamiltonian. The exchange interaction between the K+ core and the valence electron has also been considered as a perturbation. Comparison of the calculated (7s) and (8s) energies with the experimental values shows an agreement of about 6% for the former one and of about 5% for the latter one, respectively. With the exchange correction both of these discrepancies are reduced to less than 2%. We conclude that the procedure outlined here is a promising one in dealing with problems involving a highly excited electron outside of a closed-shell ion core, a system for which a more exact quantum-mechanical treatment would be much more difficult.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
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