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  • 1
    Electronic Resource
    Electronic Resource
    Fonctions autocohérentes et intégrales radiales pour les ions de la série du fer (1968)
    Springer
    Theoretical chemistry accounts 10 (1968), S. 367-371 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The radial integrals 〈3d¦r k ¦3d〉, k=−3, −1, 2, 4 and 〈4p¦r k ¦3d〉, k= 1, 3 for first-row transition-metal ions have been computed from analytical self-consistent field wave functions. The expressions 〈4p¦r k ¦3d〉 allow to compute the oscillator strengths of dipolar electric transitions for an trapped in a crystalline matrix iron group ion. Les intégrales 〈3d¦r k ¦3d〉, k=−3, −1, 2, 4 et 〈4p¦r k ¦3d〉, k=1, 3, relatives aux ions de la première série de transition, sont calculées à l'aide de fonctions radiales Φ 3d et Φ 4p , autocohérentes. Les expressions 〈4p¦r k ¦3d〉 permettent d'évaluer les forces d'oscillateur de transitions dipolaires électriques relatives à un ion du groupe du fer engagé dans une matrice cristalline.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00526504
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  • 2
    Electronic Resource
    Electronic Resource
    Coulombic and ring-shaped potentials treated in a unified way via a nonbijective canonical transformation (1984)
    Springer
    Theoretical chemistry accounts 66 (1984), S. 31-42 
    Details
    ISSN: 1432-2234
    Keywords: Coulomb, Kratzer, Sommerfeld, and Hartmann potentials ; canonical transformations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract This paper is concerned with the three-dimensional potentialV q =ησ2 (2a 0/r−q ηa 0 2/r 2 sin2 θ) ε0 which comprises as particular cases the ring-shaped potential (q = 1) and the Coulomb potential (q = 0). The Schrödinger equation for the potentialV q is transformed via a nonbijective canonical transformation, viz., the Kustaanheimo-Stiefel transformation, into a coupled pair of Schrödinger equations for two-dimensional harmonic oscillators with inverse-square potentials. As a consequence, the discrete spectrum for the potentialV q is obtained in a straightforward way. A special attention is paid to the caseq = 0. In particular, the coupled pair of Schrödinger equations for two-dimensional harmonic oscillators is tackled in the situations where the spectrum for the potentialV 0 is discrete, continuous, or reduced to the zero point. Finally, some group-theoretical questions about the potentialV q are mentioned as well as a connection, via the Kustaanheimo-Stiefel and the Levi-Civita transformations, between the quantum-mechanical problems for the potentialV q and the Sommerfeld and Kratzer potentials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00577137
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  • 3
    Electronic Resource
    Electronic Resource
    On quantum groups and their potential use in mathematical chemistry (1992)
    Springer
    Journal of mathematical chemistry 11 (1992), S. 13-25 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The quantum algebrasu q (2) is introduced as a deformation of the ordinary Lie algebrasu(2). This is achieved in a simple way by making use ofq-bosons. In connection with the quantum algebrasu q (2) we discuss theq-analogues of the harmonic oscillator and the angular momentum. We also introduceq-analogues of the hydrogen atom by means of aq-deformation of the Pauli equations and of the so-called Kustaanheimo Stiefel transformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164192
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  • 4
    Electronic Resource
    Electronic Resource
    Energy levels of paramagnetic ions: Algebra. V. Weak-field models (1986)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 29 (1986), S. 485-495 
    Details
    ISSN: 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 explore a generalized weak-field model for the description of the electronic properties of a partly filled shell(S) ion in a crystalline field. Such a model corresponds to the one developed, in parts III and IV of this series, for dN and fN ions in cubical symmetry except that the constraint relations are relaxed. This leads to a fourteen-parameter weak-field model for dN ions in octahedral symmetry and to a 33-parameter weak-field model for fN ions in octahedral symmetry. The latter two models are completely equivalent to the corresponding strong-field models as developed by Griffith and by Tanabe, Sugano, and Kamimura. The constraint relations of parts III and IV are further discussed. In particular, the role they play in fitting procedures is examined. As a conclusion, the weak-field model of III and IV appears as a phenomenological version of the generalized weak-field model introduced in this paper.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560290321
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  • 5
    Electronic Resource
    Electronic Resource
    Energy levels of paramagnetic ions: Algebra. II (1969)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 795-822 
    Details
    ISSN: 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 correspondence rules between the algebra of coupling coefficients of the special unitary group SU(2) and the associated algebra of a subgroup G of SU(2) are presented. The matrix elements of the irreducible representations of G are written in a convenient quantization scheme and different relations between these matrix elements and the Clebsch-Gordan coefficients of G are derived. Such a formalism is appropriate for numerous spectroscopic problems. As an example, it is applied to crystal field theory and electron paramagnetic resonance. General formulas from which a large number of results are rederived and generalized in a straightforward fashion are given. Numerical values of coupling coefficients for the tetragonal and cubic groups are listed in the Appendix.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560030606
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  • 6
    Electronic Resource
    Electronic Resource
    Comparison between the point-charge electrostatic model and the angular overlap model: The general case (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 403-420 
    Details
    ISSN: 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 aim of this paper is to explore in detail the mathematical connection between the point-charge electrostatic model and the angular overlap model. More precisely, for any configuration nlx in any symmetry, the matrix elements, and therefore the energy levels, as given by the angular overlap model restricted to the antibonding effects λ (for any of the possible λ's), are deduced from an effective potential constructed according to the point-charge electrostatic model. This allows us to give a mathematical proof of the equivalence between the point-charge electrostatic model and the angular overlap model taking into account all the antibonding effects λ. Finally, the sum rules for the angular overlap model are examined in the light of the formulae connecting the two models considered. Numerical tables for obtaining the results as given by the angular overlap model restricted to any of the antibonding effects from those as given by the point-charge electrostatic model are listed for the configurations nlx with l = p, d, f and g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090304
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  • 7
    Electronic Resource
    Electronic Resource
    Energy levels of paramagnetic ions: Algebra. III. The case of dN ions in cubical symmetry (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 28 (1985), S. 213-232 
    Details
    ISSN: 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 developed in the first two papers of this series is applied to the investigation of a new weak-field model. This crystal-field model lies on the use of a symmetry-adapted weak-field basis and an effective Hamiltonian involving in a symmetrical way both spin- and orbit-dependent contributions. Some general properties of this Hamiltonian are studied and complete calculation of its matrix elements is conducted in a symmetry-adapted weak-field basis in the case of an arbitrary configuration nlN in any symmetry. The case of a configuration ndN in octahedral symmetry is fully explored. In this case, the proposed weak-field model is restricted to a 12-parameter model which accounts for isotropic and anisotropic Coulomb interactions, isotropic and anisotropic spin-orbit interactions, and crystal-field interactions. A comparison between this 12-parameter weak-field model and the 14-parameter strong-field model is established. Equivalence between the latter two models requires two constraint relations to be satisfied for some strong-field parameters. These two relations are examined with various viewpoints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560280205
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  • 8
    Electronic Resource
    Electronic Resource
    Classical trajectories for two ring-shaped potentials (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 43 (1992), S. 625-645 
    Details
    ISSN: 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 present paper deals with the classical trajectories for two superintegrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to ring-shaped potentials. They admit two maximally superintegrable systems as limiting cases, viz., the isotropic harmonic oscillator system and the Coulomb-Kepler system in three dimensions. The planarity of the trajectories is studied in a systematic way. In general, the trajectories are quasi-periodic rather than periodic. A constraint condition allows to pass from quasi-periodic motions to periodic ones. When written in a quantum mechanical context, this constraint condition leads to new accidental degeneracies for the two systems studied. © 1992 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560430503
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  • 9
    Electronic Resource
    Electronic Resource
    An alternative parametrization for the theory of complex spectra (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 421-429 
    Details
    ISSN: 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 aim of this paper is to investigate a new parametrization for the matrix, set up on the states of an open (nuclear or atomic) shell, of any two-body interaction expandable in multipoles. Such a parametrization is particularly convenient for expressing the term energies in a simple form and for producing high degeneracies among the terms. Further, the parametrization considered allows the two-body interaction to be decomposed into a Dirac interaction and a remaining part.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090305
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  • 10
    Electronic Resource
    Electronic Resource
    Energy levels of paramagnetic ions: Algebra. IV. The case of fN ions in cubical symmetry (1986)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 29 (1986), S. 11-22 
    Details
    ISSN: 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 symmetry-adapted formalism and the weak-field model described in the first three papers of this series are applied to the case of a configuration nfN in octahedral symmetry. In this case, the latter weakfield model is restricted to a 30-parameter model which accounts for isotropic and anisotropic Coulomb (repulsion) interactions, isotropic and anisotropic spin-orbit interactions, and crystal-field interactions. A comparison between this 30-parameter weak-field model and a 33-parameter strong-field model is established. Equivalence between these two models requires three constraint relations to be satisfied for some strong-field parameters. The three relations are examined on various viewpoints.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560290103
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