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  • 1
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Molecular connectivities of submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)] corresponding to Kekulé structures of nine nonalternate hydrocarbons and four nonbenzenoid hydrocarbons containing four-membered rings are correlated with their Kekulé indices. In the latter class of compounds it was observed that the corresponding submolecules contain cut vertices and bridges in contrast to submolecules of benzenoid hydrocarbons which are devoid of such bridges. It was observed, furthermore, that the branching index goes up with the number of bridges in the submolecule. The results present an application to the abstract relation [D. Cvetković, I. Gutman, and N. Trinajstić, J. Chem. Phys. 61, 2700 (1974)] between resonance and MO theories.
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  • 2
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is well known that the CNDO and INDO methods fail in the field of theoretical conformational analysis of conjugated compounds. The NDDO approximation, however, can be applied very successfully to this problem. In this paper, a comparative analysis of these three approximations is performed to clarify the reasons for the failure of the former two methods. It is shown that the defects are inherent in their formalisms, and there is no reasonable possibility to compensate them (e.g., by reparametrization) at the level of the CNDO and INDO approximations. The central inadequacy is the oversimplified treatment of the two-center exchange interaction. In the case of molecules containing heteroatoms with lone-pair electrons the known defects concerning the description of Coulombic interactions of anisotropic charge distributions can additionally influence the results. To overcome these shortcomings, at least an extension of the formalism to the level of the NDDO method is necessary.
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  • 3
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    International Journal of Quantum Chemistry 21 (1982), S. 899-903 
    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: To calculate atom-atom interactions at high temperatures, one needs the electron densities of the interacting atoms. The present paper outlines an approach by which the temperature-dependent electron densities of compressed atoms may be obtained. The approach suggested makes use of the temperature-dependent Thomas-Fermi (TF) equation, and a variational principle by which this equation may be solved approximately.
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  • 4
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    International Journal of Quantum Chemistry 21 (1982), S. 905-915 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The performance of a recently proposed scaled one-electron Hamiltonian (SOEH) model is tested against parallel sets of restricted open-shell calculations by the method of Roothaan. It is found that the energy calculated by SOEH model, in general, lies slightly higher than the energy computed by the restricted open-shell method of Roothaan lending credibility to the application of variational argument to the scaled pseudoenergy functional (Eav) for deriving the SOEH model. The numerical stability of the converged SOEH energy with respect to changes in trial vectors indicates the reliability of the method. The SOEH model is shown to perform well in the calculation of geometries of radicals and ions. The convergence behavior of the SOEH model is compared with that of the restricted open-shell method of Roothaan.
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  • 5
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    International Journal of Quantum Chemistry 21 (1982), S. 943-943 
    ISSN: 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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  • 6
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    International Journal of Quantum Chemistry 22 (1982), S. 183-190 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Operator Ω and reaction operator T of Löwdin are studied with a slightly different approach, which leads to a clearer understanding of their nature and brings out the relevance of the conditions for the invertibility of K studied in the preceding work in this series.
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  • 7
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    International Journal of Quantum Chemistry 22 (1982) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 8
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    International Journal of Quantum Chemistry 22 (1982), S. 241-251 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The roles of kinetic and potential energy operators in the formation of a chemical bond are investigated using the virial and electrostatic theorems. It is shown that an integrated form of the virial theorem throws a new light on a paradox involving changes in the mean kinetic energy on bond formation. Detailed calculations on the ground state of H2+ lead to a surprisingly simple electrostatic approximation to the bond. The entire potential curve is given to good accuracy (ca. 80% bond energy) by the electrostatic forces between the two protons and a single, nodeless, spherically symmetric charge cloud representing the electron, provided that, if the bond is stretched beyond about 3.6 a.u. the charge cloud switches suddenly from a central location to a position near one proton.
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  • 9
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    International Journal of Quantum Chemistry 22 (1982), S. 289-292 
    ISSN: 0020-7608
    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 the utilization of an average occupation number for open shell orbitals, having different occupation numbers in a degenerate wave function, tantamounts to disregard first order contributions in a CI-type expansion of the wave function. These contributions are taken into account in a SCF process that derives the differently occupied open shell orbitals as eigenfunctions of different Fock-type operators and accounts for the total symmetry.
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  • 10
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    International Journal of Quantum Chemistry 22 (1982), S. 351-365 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The singlet instabilities of the RHF ground state in infinite polyenes have been studied in the framework of a semiempirical PPP Hamiltonian, accounting for long-range Coulomb interactions until convergence of the ground-state energy per electron value. The symmetry-adapted RHF solution (SAS) has been shown to be unstable to the formation of bond-order alternation waves (BAW's) and charge-density waves (CDW's). The CDW solutions have been shown to be higher in energy than the corresponding BAW solutions and to represent saddle points of the energy hypersurface, unstable to the formation of BAW's for physically realistic range of variation of the semiempirical parameters. Analytical formulas for the SAS ground-state energy per electron have been derived in case of a Coulomb law and a Mataga-Nishimoto formula for the two-center Coulomb integrals.
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  • 11
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    International Journal of Quantum Chemistry 22 (1982), S. 415-420 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Calculations with pseudopotentials of double-zeta quality have been performed on ethylene, acetylene, and water molecules. A description of the carbon-carbon double and triple bonds is presented in the framework of the pseudo-FSGO method. A possible model of the oxygen lone pairs has been established and its functioning has been proved by calculations on the water molecule.
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  • 12
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    International Journal of Quantum Chemistry 22 (1982), S. 435-440 
    ISSN: 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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  • 13
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    International Journal of Quantum Chemistry 22 (1982), S. 441-441 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 14
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    International Journal of Quantum Chemistry 22 (1982), S. 459-484 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A generalization of the Hartree-Fock molecular orbital (MO) theory for treating diradical intermediates was explained pictorially by drawing molecular orbitals of diradical species such as ring-opened trimethylene. The generalized MO theory applied to elucidate electronic mechanisms of concerted, ionic, radical, and ion-radical reactions of organic reactants in the ground state. Generalized MO computations revealed the most essential characteristics of these reactions and mutal relationships between the worlds of Woodward-Hoffmann and Hughes-Ingold. Generalized MO studies supported our orbital symmetry, stability and pairing rules for concerted, ionic and radical reactions in the ground state, respectively. An extension of MO treatments to excited states reactions was briefly pointed out in relation to the density and spin correlation functions by the multireference CI wave functions.
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  • 15
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    International Journal of Quantum Chemistry 22 (1982), S. 547-556 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The nonplanarity of a peptide unit has been studied by the ab initio method (GAUSSIAN 76) considering both the pyramidal structure of nitrogen and the variation of the ω angle for the N-methyl-acetamide and N-ethyl-acetamide in their cis and trans conformations. Several semiempirical methods have also been used for the sake of completeness of this work. All methods except CNDO and PCILO support a nonpyramidal structure for the nitrogen. The distortions of the planarity of the peptide unit show for both cis and trans conformations of the model compounds a significant asymmetric shift of the minimum on the energy curve for the ω rotation.
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  • 16
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    International Journal of Quantum Chemistry 22 (1982), S. 293-298 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The calculations of long-range interaction energy are often based on multipole expansion. The truncated multipole expansion and interaction energy calculated with it are noninvariant with respect to an arbitrary choice of local coordinate systems. In this paper we show that truncated multipole expansion of form Σk = 1n CkR-k is “numerically” independent on a choice of local coordinate systems, if convergence conditions are satisfied.
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  • 17
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    International Journal of Quantum Chemistry 22 (1982), S. 307-330 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Euler transformation for accelerating convergence of a series is considered in the context of handling divergent (asymptotically convergent) perturbation series. A generalized (parametrized) version of this transformation is developed, based on the conjecture of Dalgarno and Stewart, which works better. Viewed from this standpoint, the Padé approximants follow as a special case of the parametrized Euler transformation (PET), as is the case with the μ transformation procedure of Feenberg in a perturbative context. The PET is shown to serve as a more general method of handling a divergent series and is able to appreciate the construction and convergence behavior of specific sequences of Padé approximants. The role of parametrization in the context of the Z-1 perturbation theory of atoms is also noted and the workability of the adopted strategy is demonstrated by choosing some specific test cases.
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  • 18
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    International Journal of Quantum Chemistry 22 (1982), S. 385-395 
    ISSN: 0020-7608
    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 formulated for enumerating and constructing isomerization reactions of molecules exhibiting large amplitude nonrigid motions. This method not only enumerates the isomers of nonrigid molecules and the corresponding rigid molecules but also the symmetry species spanned by the equivalent structures whose representative is an isomer. Consequently, using the method of correlating the symmetry species of a group to the symmetry species of its subgroup the splitting patterns of isomers of nonrigid molecule to those of rigid molecule are obtained. This provides an elegant method for both enumerating and constructing reaction graphs. The method is illustrated with examples.
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  • 19
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    International Journal of Quantum Chemistry 22 (1982), S. 429-431 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 20
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    International Journal of Quantum Chemistry 22 (1982), S. 443-443 
    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
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  • 21
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    International Journal of Quantum Chemistry 22 (1982), S. 537-545 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Enzymes are large aperiodic structures and this hinders both ab initio molecular orbital and Bloch-type band theory of calculations. A frontier orbital perturbation theory of catalysis is applied to enzymes. Reasons are given for proposing that the induced-fit conformational changes, essential to enzymatic catalysis, leads to an increase in the electronic eigenvalue density at the active site, enhancing the necessary catalytic orbital perturbation.
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  • 22
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    International Journal of Quantum Chemistry 22 (1982), S. 575-582 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The hypothesis that an electrostatic effect of the buried aspartate side chain may contribute considerably to the extreme catalytic power of serine proteinases is presented. This statement is based on an analysis of environmental effects, due to amino acid residues in the vicinity of the Ser-221…His-64 couple and to hydration in subtilisin BPN'.
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  • 23
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    International Journal of Quantum Chemistry 22 (1982), S. 661-662 
    ISSN: 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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  • 24
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    International Journal of Quantum Chemistry 22 (1982), S. 681-690 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The influence of a small deformation of CĈO angle in phenol (tilt), into the rotational far-infrared (FIR) spectrum is analyzed using several approaches. In all of them, the CNDO/2 method is used to determine the potential energy functions. In a first step, the C—O bond and the rotation axis are both supposed to coincide with the C2 symmetry axis of the phenyl group. With this assumption the torsional frequencies are calculated in both the symmetric and asymmetric rotor approximations. In a second step, the tilt of the C—OH bond is determined theoretically and found to be -3°, measured from the C2 symmetry axis, the C—OH bond crossing this axis, Using this second geometry, and taking as the rotation axis the C2 axis, the torsional frequencies are again determined in both approximations. An improvement of the calculated transition energies is encountered at each stage of the calculation, when compared with experimental data. Finally the importance of the introduction of a tilt into the FIR torsional frequency calculations is discussed.
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  • 25
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    International Journal of Quantum Chemistry 22 (1982), S. 775-782 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The considerations of Walsh rules are extended to rationalize the loss of planarity in the 1,3nπ* states of simple carbonyl and thiocarbonyl molecules. The role of Fermi correlation in shaping the differences between conformations in the singlet and the triplet state is emphasized. The role played by the π* orbital is also considered.
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  • 26
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    International Journal of Quantum Chemistry 22 (1982) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 27
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    International Journal of Quantum Chemistry 22 (1982), S. 871-888 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In presence of external electric and magnetic fields, the Schrödinger equation for many-electron systems is transformed into a continuity equation and an Euler-type equation of motion in configuration space. Then, using the natural-orbital Hamiltonian, as defined by Adams, the two fluid-dynamical equations are derived in the three-dimensional space. This generates a “classical” view of such quantum systems, corresponding to an MCSCF wave function: The many-electron Schrödinger fluid consists of individual fluid components, each corresponding to a natural orbital and having its own charge density and current density. The local observables, viz., the net charge density and net current density, are obtained by merely summing over the natural orbitals, with the occupation numbers as weight factors; but, the net velocity field cannot be so obtained. Further, although each fluid component moves irrotationally in the absence of a magnetic field, the net velocity field is not irrotaional. The irrotational character of each velocity component is destroyed by rotation of the nuclear framework of the system while electron spin introduces an additional term, the spin magnetization moment, into each component current density. The physical significance of the fluid-dynamical equations as well as their advantages and disadvantages are discussed.
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  • 28
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    International Journal of Quantum Chemistry 22 (1982), S. 971-988 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A diabatic representation is introduced to describe electronic states around adiabatic pseudocrossings, as an alternative to presently available representations. A transformation from the adiabatic to the new diabatic representation is chosen to assure well behaved diabatic potentials for arbitrary momentum coupling strengths. Parameters of the transformation are determined by minimizing momentum couplings in the pseudocrossing region. The problem of two electronic states in one relative position variable is treated in detail and is studied with a numerical model. A comparison of results of our procedure and of other available ones is given. The present developments also provide a criterion for neglecting momentum couplings based on their strength and on the range of collision energies.
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  • 29
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    International Journal of Quantum Chemistry 22 (1982), S. 939-970 
    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: The magnitude of reorganization energies in the photoelectron (PE) spectra of various transition metal compounds with Mn, Fe, and Ni as 3d center is studied by means of a variable INDO Hamiltonian. The Koopmans defects are analyzed as a function of the one-electron resonance integral βμνAB and as function of the one- and two-center electron-electron interaction integrals. βμνAB has the property of an inverse coupling constant; reorganization effects are enlarged with reduced βμνAB values. In the limit of very small resonance integrals a reduction of the calculated Koopmans defects due to modified localization properties of the orbital wave function is encountered. The two-center electron-electron interaction integrals γμνAB have been calculated via an exponential formula with a variable range parameter. In the limit of long-range potentials with flattened γ;μνAB gradients a significant reduction of relaxation and correlation is diagnozed; large defects are predicted in the short-range limit with steep gradients in the repulsion potential. The one-center Coulomb and exchange integrals (γμνAA, KμνAA) have been modified by a multiplicative factor. With enlarged one-center integrals enhanced Koopmans defects are encountered. The reorganization energies are determined by means of a Green's function approach with a renormalized approximation for the self-energy part.
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    International Journal of Quantum Chemistry 22 (1982), S. 1153-1175 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using the optimal wave functions obtained by means of the superposition of correlated configurations method, elaborated previously, static and dynamic polarizabilities and rigorous lower bounds to them have been calculated for the ground states of three-electron atoms in the lithium isoelectronic sequence (Li I-C IV). The results can be treated with considerable confidence, especially for higher members of the sequence. Furthermore, the calculated rigorous lower bounds for static polarizabilities enable us to rule out several theoretical and experimental values obtained previously. The results obtained by us are then employed to evaluate the leading unknown terms in the Z-1-type expansion for the polarizability, extending thereby our treatment to much higher members of the isoelectronic sequence.
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    International Journal of Quantum Chemistry 22 (1982), S. 1209-1220 
    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: Two small groups (E, σν) and (E, C2) are proposed to describe the orbital symmmetry of the whole reaction paths with respect to suprafacial and antarafacial sigmatropic rearrangements. Furthermore, the symmetries of the two small groups are extended to the systems as a many body treatment performed by Matsen.
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  • 32
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    International Journal of Quantum Chemistry 22 (1982), S. 1271-1279 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: There is considerable evidence indicating that the carcinogenic action of vinyl chloride involves metabolic conversion to the epoxide (chlorooxirane) as the initial step. In order to learn more about its subsequent behavior, we have computed structures, energies and other properties for two different protonated forms of the epoxide, and also for two possible rearrangement products, chloroacetaldehyde and acetyl chloride. An ab initio SCF-MO procedure (GAUSSIAN 70) was used. Oxygen protonation is found to weaken both C—O bonds, the effect being greater for the bond involving the carbon bearing the chlorine. Chlorine protonation leads to a marked weakening of the C—Cl bond; this suggests a possible loss of HCl, leaving behind a carbonium ion (and possible alkylating agent or rearrangement precursor). Thus, while C—O bond breaking is doubtless an important reaction pathway for chlorooxirane, our results indicate that attention should also be focused upon the C—Cl bond; its rupture may conceivably be a key step in the biological action of vinyl chloride.
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  • 33
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    International Journal of Quantum Chemistry 39 (1991), S. 19-29 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A procedure for identifying redundancy in the Cartesian force constant matrix is described, and a prescription is given for generating the entire matrix of second derivatives from the minimal set of information. A proof is supplied which demonstrates that the number of nonredundant rows corresponding to a symmetry unique atom is necessarily less than three if the atom is invariant with respect to a symmetry operation of the point group other than the identity or inversion. Furthermore, only one row is required if the atom lies on a threefold or higher-order rotation axis. An application of the procedure to the evaluation of harmonic force constants by numerical differentiation of gradient vectors is briefly described.
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  • 34
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    International Journal of Quantum Chemistry 39 (1991), S. 31-45 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An intermediate neglect of differential overlap (INDO) model for elements of the second transition series is described. Values of exponents for the radial portion of the Slater basis atomic orbitals, the orbital ionization energies, and the beta (or bonding) parameters for these elements are reported. Use of the model to investigate equilibrium geometries, relative energy ordering of geometric isomers, spectroscopic transition energies, energy ordering of state wave functions of different symmetry, trends in dipole moments, and equilibrium stretching frequencies is reported. The results indicate that the INDO method is capable of yielding quality results for species containing atoms of the second transition series.
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  • 35
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    International Journal of Quantum Chemistry 39 (1991), S. 625-645 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The numerical properties of a two-dimensional integral representation [J. Grotendorst and E.O. Steinborn, Phys. Rev. A 38, 3857 (1988)] of the three-center nuclear attraction integral with a special class of exponential-type orbitals (ETO'S), the B functions [E. Filter and E.O. Steinborn, Phys. Rev. A 18, 1 (1978)] are examined. B functions span the space of ETO'S. The commonly occurring ETO'S can be expressed in terms of simple finite sums of B functions. Hence, molecular integrals for other ETO'S, like the more common Slater-type orbitals, may be found as finite linear combinations of integrals with B functions. The main advantage of B functions is the simplicity of their Fourier transform that makes the derivation of relatively simple general formulas for molecular integrals with the Fourier transform method possible. The integrand of the integral representation mentioned above shows sharp peaks causing, in the case of highly asymmetric charge distributions, slow convergence of the quadrature method used by Grotendorst and Steinborn. New quadrature schemes are presented that use quadrature rules based on Möbius transformations. These rules are well suited for the numerical quadrature of functions that possess a sharp peak at or near a single boundary of integration [H.H.H. Homeier and E.O. Steinborn, J. Comput. Phys., 87, 61 (1990)]. Numerical results are presented that illustrate the fact that convergence of the new quadrature schemes is about a factor two faster in case of highly asymmetric charge distributions.
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  • 36
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    International Journal of Quantum Chemistry 39 (1991), S. 681-688 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An orbital transformation that minimizes the sum of the squares of the off-diagonal Hamiltonian elements between the singly excited configurations is described. The resulting single-excitations-adapted molecular orbitals (SEAMOS) are found to be very suitable for the description of electronic excited states. The test calculations on the singlet and triplet excited states of the N2, CO, and H2CO molecules are presented.
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  • 37
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    International Journal of Quantum Chemistry 39 (1991), S. 709-727 
    ISSN: 0020-7608
    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 model based on physical, chemical, and biochemical mechanisms has been presented to evaluate the yields of DNA strand breaks (single and double) as a function of linear energy transfer (LET) or -dE/dx. Energetic heavy charged particles are considered explicitly to provide a general theory for low- as well as for high-LET radiation. There are three main features of the calculation: (a) track structure considerations for the energy deposition pattern, (b) three-dimensional structure of DNA molecules to provide information on the exact location of damage, and (c) a Monte-Carlo scheme to simulate the diffusion processes of water radicals. To avoid the complexities of a cellular medium, an aqueous solution of DNA is considered in the calculation. When the results of the calculations are compared with experimental measurements of the yields of strand breaks in mammalian DNA (exposed in a cellular complex), reasonable agreement is obtained. However, only those experimental data have been compared where there were no enzyme repair processes. The method of calculation has also been extended to study breaks in higher-order structures of DNA molecules such as chromatin. Specific limitations of the present model have been pointed out for making further improvements.
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  • 38
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    International Journal of Quantum Chemistry 39 (1991), S. 767-786 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Electronic aspects of the catalytic mechanism of liver alcohol dehydrogenase (LADH) are studied with the help of ab initio analytical gradient SCF MO methods. Three points are considered: (i) role of the catalytic zinc; (ii) geometry and electronic structure of the transition state for the hydride transfer reactions; and (iii) factors affecting the energy gap for the hydride transfer step, namely, substrate binding to zinc, reaction field, and serine 48 effects on the potential energy profile. The coordination sphere of the catalytic zinc has been modeled with an ammonia molecule and two SH- groups; complexes with CH3O-, CH3OH, and CH2O have been studied; a (6, 2, 2, 2, 1/6, 2, 1/3, 2) basis set has been used for Zn++; a (5, 2, 1, 1/3, 2) was used for oxygen, carbon, and sulfur; and a (3, 1) was used for hydrogen atoms. The hydride step was studied with two model systems: pyridinium cation/1,4-dihydropyridine coupled to the CH3O-/CH2O reaction, and cyclopropenyl cation/cyclopropene coupled to the CH3O-/CH2O system. For the latter, the role of Ser48 has been studied at the supermolecule level. The calculation on the hydride transfer step has been done at a 4-31G basis set level. The results obtained shed new light on the sources of catalytic activity of liver alcohol dehydrogenases.
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  • 39
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    International Journal of Quantum Chemistry 39 (1991), S. 839-849 
    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 treatment of chemisorption that uses the Green matrix of the surface and the admolecule, as well as a cluster calculation of a small surface cluster. Since full HF-SCF-band structures with nonlocal exchange are available now for larger systems for a couple of years, it is possible to treat the substrate surface and the admolecule on equal footing. This offers a natural way to solve the embedding problem. We have applied the formalism to the adsorption of H2 on beryllium and show that in contrast to cluster calculations there appears a binding, which is experimentally verified.
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  • 40
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    International Journal of Quantum Chemistry 39 (1991), S. 211-226 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The electronic absorption spectra of 2-, 3-, and 4-vinylpyridines and 1,2-(2,3-dipyridyl), 1,2-(2,4-dipyridyl), 1,2-(3,4-dipyridyl), and 1,2-(4,4-dipyridyl) ethylenes have been investigated in polar and nonpolar solvents. A correlation has been made between the geometry of the molecule and the observed spectrum. Molecular orbital calculations have been carried out using the INDO/S—CI procedure and a limited geometry optimization. The solvent effect at the MO level has been calculated. MO calculations predicted the existence of nπ* transitions that were not observed experimentally. The wave functions of the different CI states were calculated. The experimental transition energy as well as oscillator strength corresponded satisfactorily with the calculated ones. The observed transitions were assigned according to the results of MO calculations.
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    International Journal of Quantum Chemistry 39 (1991) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 42
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    International Journal of Quantum Chemistry 39 (1991), S. 251-267 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: From the speculations of G. N. Lewis in 1916, [J. Am. Chem. Soc. 38, 762 (1916)], the spectral predictions of R.S. Mulliken [Nature 122, 505 (1928)], and the quantum mechanical treatment by E. Hückel [Z. Phys. 60, 423 (1930)], the three lowest states of molecular oxygen (3Σg-, 1Δg, and 1Σg+) remained spectroscopic elusives until Gerhard and Lisa Herzberg [G. Herzberg, Nature 133, 759 (1934); L. Herzberg and G. Herzberg, Astrophys. J. 105, 353 (1947); G. Herzberg and L. Herzberg, Astrophys. J. 108, 167 (1948)], precisely defined them by observed infared transitions. The excited singlets remained of interest mainly to atmospheric spectroscopists and astrophysicists, and research on these species was scarce. The discovery in 1963 by A.U. Khan and M. Kasha [J. Chem. Phys. 39, 2105 (1963)] of the simple chemical production of singlet molecular oxygens by the aqueous reaction of hydrogen peroxide and hypochlorite released an explosion of research on the neglected species. Fifteen research symposia and research treatises confirm the broad range of chemical activities of singlet oxygen. The extension to biological systems is now proceeding, with surprising evidence of involvement of natural processes, including the action of singlet oxygen in white blood cell phagocytosis.
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    International Journal of Quantum Chemistry 39 (1991), S. 371-386 
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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 propose 10 desirable features or criteria for general purpose methods to be applied to the calculation of a range of spectroscopic properties. We discuss the second-order polarization propagator approximation (SOPPA) in light of these criteria by giving the actual computational expression used as well as a few numerical examples taken from the theory of NMR spectra (magnetic shieldings and spin-spin coupling constants). We demonstrate that SOPPA comes close to fulfilling these criteria.
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    International Journal of Quantum Chemistry 39 (1991), S. 423-436 
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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 analyzing asymmetric top rovibrational bands displaying both blended and resolved features is described. The two-phase computational procedure uses a modified version of the asymmetric rotor-band contour program FASTPLOT to generate a preliminary set of upperstate spectroscopic constants. The parameters are subsequently refined by employing the assigned line-fitting formalism of the ASYROT program using both resolved and blended features. The technique is detailed in a comprehensive analysis of the ν17 band of pyridine. Inclusion of quartic centrifugal distortion constants was found to satisfactorily model a high-resolution (0.004 cm-1) spectrum of this band, yielding a standard deviation of 0.00137 cm-1. The variation in the rotational parameters with vibrational quantum number is examined in terms of possible weak rovibrational perturbations to the ν17 state. An ab initio calculation of the ν17/ν27 Coriolis coupling constant indicates the observed results are consistent with the interaction of these two vibrational states.
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  • 45
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    International Journal of Quantum Chemistry 39 (1991), S. 521-521 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 46
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    International Journal of Quantum Chemistry 21 (1982) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 47
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    International Journal of Quantum Chemistry 21 (1982), S. 3-25 
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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 study of large orders of perturbation theory in various problems is reviewed: the anharmonic oscillator, the Zeeman and Stark problems, double wells, and the like. Padé and Borel summability and path integral ideas are discussed. The rigorous results on the subject are summarized.
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    International Journal of Quantum Chemistry 21 (1982), S. 105-118 
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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 original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least in the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams.
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    International Journal of Quantum Chemistry 21 (1982), S. 147-151 
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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 estimate radii of convergence of the Rayleigh-Schrödinger perturbation expansions for various energy levels of the π-electron model of the benzene molecule, described by the Hubbard Hamiltonian in both weakly and strongly correlated limits. They are determined using a “generalized” Cauchy criterion applied to the numerically determined coefficients of the pertinent expansions.
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    International Journal of Quantum Chemistry 21 (1982), S. 199-207 
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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 tunneling phenomena are surveyed. A unified, rigorous treatment of them can be based on a simple technique of integration by parts coupled with growth estimates of eigenfunctions, using, for example, WKB approximations. In particular, the analysis of Harrell and Simon of the resonance widths in the hydrogen Stark effect can be simplified.
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    International Journal of Quantum Chemistry 21 (1982), S. 195-197 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: It is proved that the Borel sum of the Rayleigh-Schrödinger perturbation expansion eigenvalue of the triple well anharmonic oscillators p2 + x2 - 2g2nx2n+2 + g4nx4n+2, g 〉 0, n = 2.3,… is a complex eigenvalue of a different problem. Its relation with the eigenvalues of the original Hamiltonian is discussed.
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    International Journal of Quantum Chemistry 21 (1982), S. 217-229 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 259-267 
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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 size consistency error formula, correcting for the erratic dependence on the number of particles in a doubly substituted (or otherwise restricted) configurational interaction (CI) treatment, is derived. The formula is expressed in terms of the particle pair eneriges ∊k and the normalization integrals Δk of the corrections to the unperturbed normalized wave function. The theory as well as the results for the 1A1 ground state of H2O and the 2B1 state of H2O+ show close agreement with the coupled electron pair approach (CEPA).
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    International Journal of Quantum Chemistry 21 (1982), S. 411-418 
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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 symmetry groups of all trees are shown to be expressible as generalized wreath products by a tree pruning algorithm. The symmetry groups of certain cyclic graphs which can be expresssed as generalized compositions are also shown to be generalized wreath products. The symmetry groups of complete multipartite graphs can be obtained in a similar manner. Character tables of symmetry groups of certain chemical graphs are also obtained.
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    International Journal of Quantum Chemistry 21 (1982), S. 851-855 
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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 comparative analysis is carried out on the strengths of binding of a series of transition metal ions to a water molecule using CNDO type MO theory developed earlier. Comparative features of the energetics of metal-ligand bonds in aquo and amine complexes are also analyzed.
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    International Journal of Quantum Chemistry 21 (1982), S. 885-897 
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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 reduced local energy EL of Rothstein and co-workers is discussed as a criterion for the local accuracy of approximate wave functions. The behavior of EL for different approximation levels is discussed. It is shown that, for particular classes of wave functions, fluctuations of EL reflect local inaccuracies of the wave function as compared to certain convergence limits. The applicability of this criterion is illustrated with approximate Hartree-Fock wave functions for water and methane.
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    International Journal of Quantum Chemistry 21 (1982), S. 927-935 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Starting from the Hohenberg-Kohn functional we show that when the energy density is given as a function of ρ and ∇ρ, i.e., ξ = ξ(ρ, ∇ρ), the condition ∇ρ · n = 0 (which was found by Bader et al. to define virial fragments), appears as a natural boundary condition for the variation of this functional. We also show that when the energy density includes second order derivatives (∇2ρ) this condition is necessary but not sufficient to guarantee the vanishing of the variation. The implications of these results are discussed in the context of a density functional theory for virial fragments.
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    International Journal of Quantum Chemistry 21 (1982) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 611-616 
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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 variation-perturbation method for solving a first-order equation of Rayleigh-Schrödinger perturbation theory is presented. The method consists of the combination of variational procedures and successive approximations. The recurrence formulas generate successively the higher-order approximations of the variational solutions. It is possible to obtain the almost exact solution within a few steps. The method is applied to the calculations of the polarizabilities of a one-dimensional harmonic oscillator and of the hydrogen atom, and the dipole-dipole interaction energy of two hydrogen atoms.
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    International Journal of Quantum Chemistry 21 (1982), S. 671-672 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 699-710 
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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: Energy optimization (Eo) and property optimization (PO) were performed on the H2O molecule. A definition of the “optimality” κ, a dimensionless quantity of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm optimality} \equiv \kappa = \left({\sum\limits_i {\left[{\omega _i \left\langle {\hat o} \right\rangle _i - O_i } \right]^2 } } \right) $$\end{document}has been proposed where ωi is a weighting factor, 〈ǒ〉i is the computed observable, and Oi is the corresponding property measured experimentally. The minimization of κ leads to property optimization methods (POM) which is a useful alternative to energy optimization methods (EOM).
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    International Journal of Quantum Chemistry 21 (1982), S. 727-739 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown how branching ratios can be obtained from complex coordinate rotation calculations. The procedure is applied to a rotational Feshbach resonance in a model atom-diatom van der Waals complex which has two open channels present, and to a simple two-channel model potential problem which has been treated by other workers.
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    International Journal of Quantum Chemistry 21 (1982) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 179-190 
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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 present summary results of a bound-state perturbation theory for a one-space and one-time dimension nonrelativistic spinless (Schrödinger) particle, a relativistic spinless (Klein-Gordon) particle, and a relativistic spin-half (Dirac) particle in central fields due to scalar or fourth-component vector-type interactions for an arbitrary bound state. This is accomplished by the reduction of the wave equations to Ricatti form. This enables a decoupling between the pair of coupled first order differential equations on the large and small component Dirac wave functions or a decoupling of the second order differential equation in the Schrödinger or Klein-Gordon equations. All corrections to the energies and wave functions, including corrections to the positions of the nodes in excited states, are expressed in quadratures in a hierarchial scheme, without the use of either the Green's function or the sum over intermediate states. For the ground states of a Schrödinger particle, it is possible to extend this technique to multidimension in the case where the perturbation is due to noncentral fields, for example, in the problem of a nonrelativistic hydrogen atom in a linear combination of multiple fields.
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    International Journal of Quantum Chemistry 21 (1982), S. 209-211 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 67
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    International Journal of Quantum Chemistry 21 (1982), S. 239-250 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A molecular theory of phase transitions in fatty acid monolayers at the air/water interface is proposed based on rotational ordering of molecules about their longitudinal axes. The first order statistical mechanical lattice model of Bell, Mingins, and Taylor (BMT) which is an equilibrium diluted Ising model is used to describe the monolayer behavior of some simple aliphatic carboxylic acids. The interaction energy parameters in the BMT model are adjusted to give reasonable agreement with the experimentally observed chain length dependence, and the energies thus obtained are compared with those calculated for interacting aliphatic carboxylic acid dimers by the technique of perturbative configuration interaction using localized orbitals (PCILO). It is concluded that intermolecular rotational ordering due to the anisotropy of the intermolecular potential plays a significant role in simple fatty acid monolayer phase behavior. A possible experimental test of the model is briefly described.
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    International Journal of Quantum Chemistry 21 (1982) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 69
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    International Journal of Quantum Chemistry 21 (1982), S. 369-398 
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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 superoperator formalism for matrix propagators is reviewed, with special attention to the validity of superoperator resolution of the identity. The equation of motion for the particle-hole propagator is discussed. Decoupling procedures based on inner projections and partitioning are examined showing the desirability of self-consistent approximations. The conditions under which a state can be a vacuum for a given linear manifold of operators are analyzed.
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    International Journal of Quantum Chemistry 21 (1982), S. 475-485 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The total (elastic and inelastic) intensity of electrons scattered by CO2 was measured in the s range of 1 to 12 Å-1 and compared with the theoretical intensity calculated from the Hartree-Fock molecular wave function and those calculated for the independent-atom-model (IAM) molecule. In the range of s ≲ 4 Å-1 the electron correlation effect on the total scattered intensity was found to be represented by that for the IAM molecule.
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    International Journal of Quantum Chemistry 21 (1982), S. 557-563 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electronic structures of TTF, TTF1+, and TTF2+ are described by means of an ab initio Hartree-Fock-Slater procedure with a double-zeta STO basis. Electronic and photoemission spectra, bonding, and charge distributions are discussed and compared to experiments and previous calculations.
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  • 72
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    International Journal of Quantum Chemistry 21 (1982), S. 591-610 
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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 bivariational scheme based on the general linear group of spin orbital space is presented, with the aim of obtaining approximations to the spectra of complex rotated Hamiltonians.
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    International Journal of Quantum Chemistry 21 (1982), S. 1079-1089 
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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 strategy for the evaluation of two-center overlap and Coulomb integrals is illustrated by using computer-generated formulas produced from 1s orbitals. There is no loss in generality as these formulas have the same structure for higher quantum numbers. For small parameter values, singularities may be removed from the formulas by expanding exponential functions and collecting coefficients of like powers by machine. Suitable terminated expansions, along with exact formulas, permit high accuracy throughout the entire possible range of parameter values.
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    International Journal of Quantum Chemistry 22 (1982) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 771-778 
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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 novel graph-theoretical approach for ordering Kekulé valence structures of benzenoid hydrocarbons is presented. The approach involves the transformation of the Kekulé structures into the subspaces of their individual double bonds. The submolecules generated in this way [H. Joela, Theor. Chim. Acta 39, 241 (1975)] are ordered according to suitable connectivity indices. The resulting orders parallel those predicted from the so called Kekulé indices [A. Graocvac, I. Gutman, M. Randić, and N. Trinajstć, J. Am. Chem. Soc. 95, 6267 (1973)]. A relation is thus illustrated between VB and MO theories. The method is new and allows the prediction of the relative stabilities of structures from purely combinatorial vent without resort to computer.
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    International Journal of Quantum Chemistry 21 (1982), S. 823-831 
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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: Class sum theory, the duality with IRREP methods and tensor operators in the group algebra are discussed by generalizing the diagrammatic approach of conventional IRREP theory to include group label manipulation. Concepts such as invariant nodes and Jucys-Levinson-Vanagas reduction theorems generalize straightforwardly. The results are capable of unique simplification for certain nodes, when the group rearrangement theorem is useable or when a class sum is performed. A duality transformation (between IRREP-partner and class-element labels) emerges as an important concept.
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    International Journal of Quantum Chemistry 21 (1982), S. 857-860 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the determination of a unique scaling parameter, based on scale-invariant forms for energy in the scaled zero-order Hamiltonian approach of Feenberg, is not possible because the higher-order invariants themselves are nonunique.
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    International Journal of Quantum Chemistry 21 (1982), S. 937-938 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 945-965 
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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: Relationships are formulated in an attempt to explain the variation in the antitumour activity and toxicity of a series of diacridines. Three types of conformation are considered, these being relevant to the three types of double intercalation of DNA. The CNDO/2 method, with the incorporation of symmetry adapted orbitals, is used to obtain electron reactivity indices. Significant correlations are presented between the biological activities and the electronic and steric indices employed.
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    International Journal of Quantum Chemistry 21 (1982), S. 1019-1028 
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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 α-helical protein molecule is modeled by a one-dimensional crystal chain with three peptide groups in the lattice cell and with the nearest and third neighbor interactions. Three types of solitonlike solutions describing excitation motion along the model have been obtained. The first one is three modulated waves which are in phase. The other two are modulated waves with phase shifts equal to ⅔π and \documentclass{article}\pagestyle{empty}\begin{document}$ {\textstyle{4 \over 3}} $\end{document}π, respectively.
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    International Journal of Quantum Chemistry 21 (1982), S. 1057-1060 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper gives a proof that spin projected Slater determinants provide a basis for Young's natural representation of the symmetric groups under permutation of the orbitals. The general reduction of sums of spin projected Slater determinants to give functions of pure spatial symmetry type requires this transformation.
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    International Journal of Quantum Chemistry 21 (1982), S. 1097-1103 
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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 tensor virial theorem is discussed in relation to different transformation matrices which are compatible with it.
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    International Journal of Quantum Chemistry 21 (1982), S. 1117-1121 
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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: Using the new expression for the dynamic multipole polarizabilities in terms of effective oscillator strengths and effective transition energies derived from the variational procedure based on the total energy expansion in terms of induced multipole moments, we have calculated the long-range dispersion force coefficients and the leading relativistic correction to the long-range potential between H, He+, He, and Li+. We have in addition calculated the oscillator strength sum rules for the above systems. Our results are comparable with those obtained using both a hydrodynamic model to quantum mechanics and double perturbation theory.
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    International Journal of Quantum Chemistry 22 (1982), S. 31-36 
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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 model of vibronic coupling of crude Born-Oppenheimer (CBO) potentials within the scope of the linear variational procedure is presented. First numerical results testing the model are discussed.
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    Notes: An asymptotic expansion method has been used to calculate the Morse matrix elements for the vibration-rotation transition. A general expression has been derived for the quartic matrix elements, which can be reduced to the expressions for the cubic, quadratic, and linear matrix elements. The results agree extremely well with those given by the factorization method outlined by Badawi et al., and are similar to those given by Coquant et al., who used quite complicated and lengthy equations based on the Dunham potential. Earlier works to calculate the electronic transition probability parameters utilizing the above mentioned asymptotic expansion technique have also been extended and modified.
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    International Journal of Quantum Chemistry 22 (1982), S. 115-125 
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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: We have investigated the conformational dependences of the torsional potential and dipole moment of double-rotor molecules related to acetone, using semiempirical and ab initio calculations and expressing the results in terms of limited Fourier-series expansions. The use of the isodynamic operations of nonrigid molecules to obtain symmetry-adapted quasianalytic forms for the various properties helps compute the representative surfaces with a minimum number of points. Potential surfaces have been calculated for planar ground-state acetone (CNDO/2, STO/3G, and STO/4-31G) and both pyramidal excited-triplet acetone and ground-state dimethylamine (CNDO/2). For groundstate acetone STO/4-31G brings the results obtained with STO/3G closer to those from CNDO/2 and from experiment. The potential surface of excited-triplet acetone appears intermediate between those of ground-state acetone and dimethylamine. For dipole moments the convergence of the harmonic expansions of the vector components is slower than that of the torsional potential whereas that of the vector magnitude is faster.
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    International Journal of Quantum Chemistry 22 (1982), S. 1177-1188 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some compositions of the addition and subtraction operators and recurrence relations for the Sanibel-type coefficients cu, v (n, s, M) generated by these compositions are studied. A local representation of the fermion creation-annihilation operators via the addition and subtraction operators is obtained. Operators of single excitations, coupling, and decoupling operators, in terms of which the unitary group generators can be expressed are defined. The resulting representation of the nonelementary unitary group generators is much more simple than in the Gelfand-Tzetlin basis and in the most general case contains only six logically different terms, each of them possessing quite transparent physical significance.
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    International Journal of Quantum Chemistry 22 (1982), S. 1263-1270 
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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 behavior of a rigid rotor perturbed by an electric field is studied. An hypervirial calculation, to obtain the perturbation series without calculation of the perturbed wavefunctions, is used to determine the Stark-shifted eigenvalues. A numerical estimation of the m equals; 0 → m = 1 transition for the lowest vibrational state (v = 0) and the first rotational state (J = 1) for the HF and DF molecules using Padé approximants is made.
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    International Journal of Quantum Chemistry 22 (1982), S. 1307-1307 
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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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    International Journal of Quantum Chemistry 21 (1982), S. 69-92 
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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: Instead of the Schródinger equation HΨ = EΨ subject to the boundary condition 〈ϕ|Ψ〉 = 1, where ϕ is a normalized reference function in the Hilbert space, one studies the inhomogeneous equation (H - E)ΨE = aϕ, where E is a complex variable, with the same boundary condition, which gives a = 〈ϕ|H|ΨE〉 - E = E1 - E. Introducing the projector P = 1 - |ϕ〉〈ϕ| for the complement to O = |ϕ〉〈ϕ|, one finds easily the explicit solution ΨE = (1 - PH/E)-1ϕ = (1 + TEH)ϕ, where TE = (E - PH)-1P = P(E - PHP)-1P is the reduced resolvent associated with the auxiliary Hamiltonian H̄ = PHP. The existence of these operators is discussed. It is shown that, if the parameter E is real in the “discrete part” of the spectrum to H, then E and E1 = 〈ϕ|H|ΨE〉 = 〈ϕ|H + HTEH|Φ〉 ≡f(E) bracket a true eigenvalue E satisfying the relation E = f(E). The Newton-Raphson solution to the equation F(E) = E - f(E) = 0 is related to the variation principle. Putting H = H0 + V and expanding the inverse (E - PH0 - PV)-1 in terms of powers of V or (V - α), one gets various expansions relating to finite-order perturbation theory. Exact expressions for the ordinary wave and reaction operators are obtained. If A is an arbitrary nonsingular operator and h = {h1,h2,…,hn} is a linearly independent set, the inner projection Án = |h〉 〈h|A-1|h〉-1〈h| is a “rational approximation” to the operator A which converges toward A when n→∞ and the set h becomes complete. If A is positive (or has a finite negative part) the convergence is from below. Applying this principle to the partitioning technique, one gets rational perturbation approximations instead of the standard power series, similar to the Padé approximants but derived in a different way with the remainder term under control. The method has been used to calculate lower bounds to eigenvalues.
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    International Journal of Quantum Chemistry 21 (1982), S. 125-131 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The wave function for hydrogen in the Stark effect (or for the negatively anharmonic oscillator) with an outgoing-wave boundary condition, constructed in Langer-Cherry fJWKB form, is continued back to the origin. The asymptotic expansions for ReE and ImE are determined by the requirement that the wave function be regular at the origin to zeroth and first order in the exponentially small parameter that characterizes ImE. One fJWKB function turns out to be the Rayleigh-Schrödinger perturbation theory wave function.
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    International Journal of Quantum Chemistry 21 (1982), S. 173-177 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the renormalization group imposes severe restrictions on analytic continuation in coupling constant in the case of field theories in four dimensions.
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    International Journal of Quantum Chemistry 21 (1982), S. 215-215 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 251-258 
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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 practical scheme for the calculation of excited states of the same symmetry as a given reference state is outlined in the context of the Hartree-Fock method. In order to prevent the excited state from “collapsing” into a lower-lying state, the prediagonalized Fock matrix is diagonalized in a restricted subspace, deleting the component associated with the orbital which participates in the excitation. Computationally, the deletion is accomplished by means of a “big shift” of the associated diagonal element of the prediagonalized Fock matrix. The resulting wave function will not be fully relaxed, but can be shown to be orthogonal to the reference state. The method has been implemented in a molecular UHF program. Applications to the 4σg-1 hole state of CO and to an excited state of the CuCl42- ion are reported.
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    International Journal of Quantum Chemistry 21 (1982), S. 357-357 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 21 (1982), S. 399-410 
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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: Using the variational principle, equations have been obtained for density matrix of molecules with the external perturbation of the common type present. The perturbed wave function was taken as a superposition of the ground and single-excited configurations made of the Hartree-Fock molecular spin orbitals. On the basis of these equations a series of variants of static perturbation theory have been worked out for the ground and excited states of closed-shell molecules.
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    International Journal of Quantum Chemistry 21 (1982), S. 465-473 
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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: CI calculations were performed on the energies and relative intensities of the outer and inner valence levels of the CS molecule. Breakdown of the one-particle model is discussed in terms of CI, and the results are compared with the analogous investigations using the Green's function technique.
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    International Journal of Quantum Chemistry 21 (1982), S. 565-579 
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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 employed an effective potential and a single-zeta basis in SCF-MO computations to estimate the relative stability of linear disilyne HSiSiH and five isomeric structures defined in earlier all-electron ab initio SCF-MO computations. The effect of electron correlation has been estimated by generalized valence-bond (GVB) computations for the five valence electron pairs of these structures. All our computations indicate that linear disilyne is the least stable structure and that H2SiSi, the silicon analog of vinylidene carbene, is the most stable structure. In these structures silicon occurs in divalent and tetravalent states. The nature of silicon bonding in these valence states is illustrated by contour diagrams of the GVB orbital pairs.
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    International Journal of Quantum Chemistry 21 (1982), S. 581-590 
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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 developed for obtaining the spectra of trees of NMR and chemical interests. The characteristic polynomials of branched trees can be obtained in terms of the characteristic polynomials of unbranched trees and branches by pruning the tree at the joints. The unbranched trees can also be broken down further till we obtain a tree containing just two vertices. This effectively reduces the order of the secular determinant of the tree we started with to determinants of orders atmost equal to the number of vertices in the branch containing the largest number of vertices. An illustrative example of a NMR graph is given for which the 22 × 22 secular determinant is reduced to determinants of orders atmost 4 × 4 in just the second step of the algorithm. The tree pruning algorithm can be applied even to trees with no symmetry elements and such a factoring can be achieved. Methods developed here can be elegantly used to find if two trees are cospectral and to construct cospectral trees.
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    International Journal of Quantum Chemistry 21 (1982), S. 633-645 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An effective Hamiltonian for open-shell molecular systems is constructed. The unrestricted Hartree-Fock orbitals are applied as a basis set of one-particle functions. This effective Hamiltonian is determined as a simple product of the original total Hamiltonian and the spin annihilator. The second-quantization formalism and the Feynman-Goldstone diagrammatic technique are used. The resulting effective hamiltonian is composed of zero- to four-particle terms. A possibility of applying the nondegenerate diagrammatic perturbation theory constructed over this effective Hamiltonian is discussed.
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