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  • 1
    ISSN: 1432-2234
    Keywords: Electronic circular dichroism ; Trans-cyclooctene ; London atomic orbitals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 789-809 
    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: Effective solutions for two difficulties which may be present in MCSCF calculation are discussed: (i) We show how the large configuration state function state expansion case may be handled simply and effectively without the introduction of extraneous projection operators or Lagrange multipliers; (ii) we present a simplified two-electron integral transformation procedure which significantly reduces the operation count (and hence computational efficiency is increased) for second order and particularly for third order MCSCF procedures. The procedures we introduce use some freedom available in the orthogonal complement Cl space and the virtual orbital space to simplify MCSCF calculations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 959-971 
    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 linear, quadratic, and cubic response of a multiconfigurational Hartree-Fock state to a time independent one-electron perturbation has been derived. A comparison between the exact response functions as obtained from Rayleigh-Schrödinger perturbation theory and the multiconfigurational Hartree-Fock response functions allows a identification of matrix elements of the perturbation operator between the ground and excited states and between excited states. We discuss some ambiguities which result from such an identification.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 25-60 
    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 discuss how the local convergence of Newton-Raphson and fixed Hessian MCSCF iterative models may be rationalized in terms of a total order of convergence in an error vector and a corresponding error term. We demonstrate that a sequence of N Newton-Raphson iterations has a total order of convergence of 2N and that a sequence of N fixed Hessian iterations has a total order of convergence of N + 1. We derive the error terms of a Newton-Raphson and a fixed Hessian sequence of iterations. We discuss the implementation of the fixed Hessian and the Newton-Raphson approaches both when linear and nonlinear transformations of the variables are carried out. Sample calculations show that insight into the structure of the local convergence of Newton-Raphson and fixed Hessian models can be based on an order of convergence and an error term analysis.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 0040-5744
    Keywords: Key words: Electronic circular dichroism ; Trans-cyclooctene ; London atomic orbitals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary.  The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the ex act operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations on trans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The r otatory strength calculated for trans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that of trans-cyclooctene.
    Type of Medium: Electronic Resource
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