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  • 1
    Electronic Resource
    Electronic Resource
    A new iterative method for solving the time-independent Schrödinger equation based on the generalized Bloch equation. I. Boson systems: The quartic anharmonic oscillator (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 777-795 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The eigenvalue problem of the time-independent Schrödinger equation is solved as usual by expanding the eigenfunctions in terms of a basis set. However, the wave-function expansion coefficient (WECs), which are certain matrix elements of the wave operator, are determined by an iterative method. For these WECs, we deduced new nonlinear equations utilizing the concept of a reference space and the generalized Bloch equation for the wave operator. To test these equations, the method is used to calculate with great accuracy the energy eigenvalues of the ground state and first few excited states of the quartic anharmonic oscillator, whose Rayleigh-Schrödinger perturbation series diverges strongly for every nonzero coupling constant. © 1997 John Wiley & Sons, Inc.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Iterative determination of eigenvalues of the time-independent Schrödinger equation by the use of the generalized Bloch equation (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 257-268 
    Details
    ISSN: 0020-7608
    Keywords: reference space ; effective Hamiltonian ; generalized bloch equation ; quartic anharmonic oscillator ; H2O molecule ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Recently, we proposed an iteration method for solving the eigenvalue problem of the time-independent Schrödinger equation [H. Meißner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997)]. The eigenfunctions are expanded in terms of a basis set. The wave-function expansion coefficients (WECs) are matrix elements of the wave operator. They are determined iteratively by utilizing a reference space, the concept of an effective Hamiltonian, and the generalized Bloch equation. In this article, the WEC iteration method is applied to the calculation of the ground state and of some excited states of a quartic anharmonic oscillator, i.e., a Boson system, using a large reference space, as well as of the H2O molecule, i.e., a Fermion system. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 257-268 1997
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Improved quadrature methods for the Fourier transform of a two-center product of exponential-type basis functionsDedicated to Professor K. Ruedenberg on the occasion of his 70th Birthday. (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 399-411 
    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 numerical properties of a one-dimensional integral representation [H. P. Trivedi and E. O. Steinborn, Phys. Rev. A 27, 670 (1983)] for the Fourier transform of a two-center product of certain exponential-type orbitals (ETOs), the B functions [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)], are examined. These functions span the space of ETOs. Hence, molecular integrals for other ETOs, 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, making, in the cases of highly asymmetric charge distributions and/or large momentum vectors, usual quadrature methods rather slow. New quadrature schemes are presented that utilize Möbius-transformation-based quadrature rules. These rules are well suited for the numerical quadrature of functions possessing a sharp peak at or near one 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 the new quadrature schemes are much more efficient than are automatic quadrature routines.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560410303
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  • 4
    Electronic Resource
    Electronic Resource
    On the evaluation of overlap integrals with exponential-type basis functions (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 42 (1992), S. 761-778 
    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 numerical properties of a one-dimensional integral representation [H.P. Trivedi and E. O. Steinborn, Phys. Rev. A 27, 670 (1983)] for the overlap integral of a two-center product of certain exponential-type orbitals (ETOs) the B functions [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)], are examined. B functions possess a very simple Fourier transform that results in relatively simple general formulas for molecular integrals derivable using the Fourier transform method. In addition, molecular integrals for other ETOs, like the more common Slater-type orbitals, can be written as finite linear combinations of integrals with B functions because these functions span the space of ETOs. The integrand of the integral representation mentioned above shows peculiarities requiring special quadrature methods, especially in the case of highly asymmetric charge distributions. It is shown that good results can be obtained using Möbiustransformation-based quadrature rules well suited for the numerical integration of functions possessing a sharp peak at or near one boundary of integration [H. H. H. Homeier and E. O. Steinborn, J. Comput. Phys. 87, 61 (1990)]. The method based on Möbius-type quadrature is compared to several other methods  -  based on other quadrature rules, finite sums, and infinite series representations together with convergence acceleration  -  to evaluate overlap integrals with B functions. The numerical results indicate that the new quadrature schemes are more efficient than are the other methods.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560420416
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  • 5
    Electronic Resource
    Electronic Resource
    Möbius-Type quadrature of electron repulsion integrals with B functions (1990)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990), S. 349-363 
    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 numerical properties of a three-dimensional integral representation [J. Grotendorst and E. O. Steinborn, Phys. Rev. A 38, 3857 (1988)] of the electron repulsion 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', 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 which 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. Quadrature schemes are presented which utilize quadrature rules based upon Möbius transformations. These rules are well suited for the numerical quadrature of functions which 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 which illustrate the fact that the new quadrature schemes are also applicable in case of highly asymmetric charge distributions.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560382435
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  • 6
    Electronic Resource
    Electronic Resource
    Molecular one-electron integrals over slater-type atomic orbitals and irregular solid spherical harmonics (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 413-438 
    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 one-electron integral over Slater-type atomic orbitals centered at A and B and irregular solid spherical harmonics as operator centered at C is evaluated analytically by using elliptical coordinates and translation of the solid spherical harmonics from center C to either focus A or B. A special case is the three-center nuclear attraction integral which is also evaluated by means of the Neumann expansion and expressed without associate Legendre functions of the second kind. The strict observation of the charge distribution concept leads to compact expressions for the integral. It has the further advantage that the charge density distributions which have been developed for the two-center cases and used in calculations for diatomic molecules can be utilized.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060304
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  • 7
    Electronic Resource
    Electronic Resource
    Evaluation of multicenter integrals over Slater-type atomic orbitals by expansion in terms of complete sets (1980)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 18 (1980), S. 219-226 
    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: Multicenter integrals over Slater-type orbitals can be expanded in series with known coefficients if they are considered as elements of appropriate Hilbert spaces. Some test calculations for the three-center nuclear attraction integrals are given.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560180131
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