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  • 1
    Electronic Resource
    Electronic Resource
    Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in α2Presented at the 10th Seminar on Computational Methods of Quantum Chemistry, Strasbourg, September 3-6, 1996 (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 225-239 
    Details
    ISSN: 0020-7608
    Keywords: relativistic Hamiltonians ; two-component methods in relativity ; perturbation methods in relativity ; Douglas-Kroll approximation ; regular approximations in relativity ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of nonsingular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy-Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in α, leading to transformed Hamiltonians with the two-component block accurate through α2k, k=1, 2, 3,… . These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than α2k. Their relation to other nonsingular methods of relativistic quantum chemistry (the Douglas-Kroll method, the regular Hamiltonian schemes) is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas-Kroll scheme and amounts to relatively easy modification of the core Hamiltonian.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 225-239, 1997
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Picture change and calculations of expectation values in approximate relativistic theories (1998)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 68 (1998), S. 159-174 
    Details
    ISSN: 0020-7608
    Keywords: relativistic quantum chemistry ; relativistic connections to expectation valves ; two/one-component methods in relativity ; perturbation methods in relativity ; Douglas-Kroll approximation ; mass-velocity+Darwin approximation ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The effect of the so-called picture change on expectation values of one-electron operators in approximate two(one)-component relativistic theories is discussed. This effect is expected to be particularly large for operators which assume large values in the vicinity of heavy nuclei. The numerical results illustrating the picture change effect on electric field gradients at nuclei have been obtained in the spin-free Pauli and Douglas-Kroll approximations. It has been found that the picture change effect lowers the electric field gradient at I in HI by about 1 a.u. Very large picture change effect (-8 a.u.) has been calculated for HAt. It is concluded that in accurate calculations of expectation values of operators involving high inverse powers of the electron-nucleus distance the picture change, which accompanies the transformation of the Dirac (Dirac-Coulomb) equation to approximate two(one)-component relativistic Hamiltonians, must be taken into account.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 159-174, 1998
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Constrained solutions of the eigenvalue problem in truncated basis setsThis article is dedicated to the memory of the late Professor Jean-Louis Calais. (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 35-38 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that simple orthogonality constraints between some set of known approximate eigenfunctions and another set of functions which are to be determined as approximate eigensolutions need to be modified. The proposed modification introduces a measure of the approximate character of the known functions and leads to the reduction of the dimensionality of the eigenvalue problem for other solutions. The discussed method is fully variational and leads directly to a Hermitian eigenvalue problem. This approach is also independent of the choice of truncated basis sets for different classes of approximate solutions of the eigenvalue problem. © 1997 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Ionization potentials and electron affinities of Cu, Ag, and Au: Electron correlation and relativistic effects (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 557-565 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The electron correlation and relativistic effects on ionization potentials and electron affinities of Cu, Ag, and Au are investigated in the framework of the coupled cluster method and different 1-component approximations to the relativistic Dirac-Coulomb Hamiltonian. The first-order perturbation approach based on the massvelocity and Darwin terms is found to be sufficiently accurate for Cu and Ag while it fails for Au. The spin-averaged Douglas-Kroll no-pair method gives excellent results for the studied atomic properties. The ionization potentials obtained within this method and the coupled cluster scheme for the electron correlation effects are 7.733(7.735) eV for Cu, 7.461(7.575) eV for Ag, and 9.123(9.225) eV for Au (experimental values given in parentheses). The calculated (experimental) electron affinity results for Cu, Ag, and Au are 1.236(1.226), 1.254(1.303), and 2.229(2.309) eV, respectively. There is a marked relativistic effect on both the ionization potential and electron affinity of Ag which sharply increases for Au while Cu exhibits only a little relativistic character. A similar pattern of relativistic effects is also observed for electric dipole polarizabilities of the coinage metal atoms and their ions. The coupled cluster dipole polarizabilities of the coinage metal atoms calculated in this article in the Douglas-Kroll no-pair formalism (Cu: 46.50 au; Ag: 52.46 au; Au: 36.06 au) are compared with our earlier data for their singly positive and singly negative ions. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 557-565, 1997
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
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