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  • 1
    Electronic Resource
    Electronic Resource
    Some results for symmetric-group-adapted reduced density operators (1992)
    Springer
    Theoretical chemistry accounts 82 (1992), S. 239-248 
    Details
    ISSN: 1432-2234
    Keywords: Reduced density operators ; Spin-adaptation ; Creation and annihilation operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Reduced density operators of thep-th order adapted to irreducible representations of the permutation group are expressed in terms of spin-adaptedp-electron creation and annihilation operators. Simple rules for expressing products of two density operators as linear combinations of the symmetry-adapted density operators and formulas for calculating matrix elements of these operators are derived. The results may be useful in many-body perturbation theory, in coupled cluster methods, in theory of spin-adapted reduced Hamiltonians, and in statistical theories of spectra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113256
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Matrix elements of one- and two-electron operators (1973)
    Springer
    Theoretical chemistry accounts 29 (1973), S. 151-166 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Mit Hilfe einer graphischen Darstellung wird ein einfacher Algorithmus zur Bestimmung der Werte der Matrix-Elemente von spinfreien Ein- und Zweielektronenoperatoren abgeleitet. Durch diese Methode werden alle Fälle erfaßt, die auftreten, wenn die Wellenfunktionen wechselweise orthogonale, antisymmetrisierte Produkte von Spinorbitalen (von denen angenommen wird, daß sie einen orthogonalen Satz bilden) darstellen und Eigenfunktion der L 2 und L z Operatoren sind. Die erhaltenen Formeln eignen sich für Rechnungen mit und ohne Verwendung eines Computers.
    Notes: Abstract A graphical representation of matrix elements of spin-free one- and two-electron operators is used for deriving a simple algorithm for the evaluation of their values. The method covers all the cases which may occur when wave functions are taken as mutually orthogonal antisymmetrized products of spinorbitals (which are assumed to form an orthonormal set) and are eigenfunctions of L 2 and L z operators. The resulting formulas are suitable as well for computer programming as for hand calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00529438
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  • 3
    Electronic Resource
    Electronic Resource
    Relativistic treatments for bound-state atomic energies (1974)
    Springer
    Theoretical chemistry accounts 35 (1974), S. 183-187 
    Details
    ISSN: 1432-2234
    Keywords: Relativistic bound state atomic energies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The merits of the various methods, used for the determination of relativistic energies, are discussed on the basis of numerical results. It is concluded that, at present, the perturbation approach, based on the Pauli approximation of the Dirac-Breit equation, is more accurate (up to Z 〈 48) than the variational approach. Furthermore it is expected that, in any case, the prediction of ionization potentials and energy levels will be equally satisfactory by either method. Consequently, and taking into account the importance of the correlation effects (not only because of the contribution of the correlation energy but also because of their influence on the prediction of the hyperfine structure), it is suggested that it may be worthwhile to direct more efforts towards multiconfigurational Dirac-Breit-Pauli calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00546903
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  • 4
    Electronic Resource
    Electronic Resource
    Coupling constants in the direct configuration interaction method (1979)
    Springer
    Theoretical chemistry accounts 51 (1979), S. 175-188 
    Details
    ISSN: 1432-2234
    Keywords: Configuration interaction method, coupling constants in the direct ∼
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00572926
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  • 5
    Electronic Resource
    Electronic Resource
    A multireference direct CI program based on the symmetric group graphical approach (1987)
    Springer
    Theoretical chemistry accounts 71 (1987), S. 187-199 
    Details
    ISSN: 1432-2234
    Keywords: Configuration interaction method ; Symmetric group graphical approach ; Electron correlation problem ; Multi-reference CI program
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Specific features of an SGGA-based multireference direct CI program working in large internal spaces are discussed. In particular, advantages resulting from the explicit separation of the orbital and the spin spaces are explored. Concepts allowing for the efficient creation of a flexible and symmetry-adapted CI basis, for the high-speed generation of the coupling coefficients and for structuring a simple permutation driven algorithm to handle the orbital space are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00526416
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  • 6
    Electronic Resource
    Electronic Resource
    Relativistic and correlation corrections to electron affinities of alkali and halogen atoms (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 313-316 
    Details
    ISSN: 1432-2234
    Keywords: Electron affinities ; relativistic corrections ; correlation corrections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Electron affinities (EAs) of alkali and halogen atoms have been calculated using Hartree-Fock and Dirac-Hartree-Fock methods. Comparing the results with the experimental values, relativistic and correlation corrections to EAs have been estimated. In the case of alkalines correlation correction constitute 110%–120% of the experimental EA values. In the case of halogens the corresponding numbers are 30%–60%. Relativistic effects are negligibly small for alkalines but significant for halogens (40% of the experimental value for At).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01151608
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Symmetric‐group‐based methods in quantum chemistry (1998)
    Springer
    Journal of mathematical chemistry 23 (1998), S. 127-149 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The eigenvalue problem of a Hamiltonian represented in a finite-dimensional model space being the N-electron subspace of the 2K-spinorbital Fock space is analyzed. It is pointed out that the permutation group S N is a very convenient framework for this analysis. The resulting approach is known as the symmetric group approach to the N-electron problem. Its applications to construction of a basis in the model space, to the evaluation of matrix elements of spin‐independent and of spin‐dependent operators and, finally, to solution of the eigenvalue problem of the Hamiltonian are briefly reviewed. Recently developed applications of the symmetric group to studies of the Heisenberg Hamiltonian spectra and to evaluation of spectral density distribution moments are also dicussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019196502971
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  • 8
    Electronic Resource
    Electronic Resource
    Characters of two-row representations of the symmetric group (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 261-264 
    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: Characters of irreducible representations (irreps) of the symmetric group corresponding to the two-row Young diagrams, i.e., describing transformation properties of N-electron eigenfunctions of the total spin operators, have been expressed as explicit functions of the number of electrons N and of the total spin quantum number S. The formulas are useful in various areas of theory of many-electron systems, particularly in designing algorithms for evaluation of spectral density moments. © 1997 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Statistical theory of spectra (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 51 (1994), S. 425-437 
    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 rapidly developing field of statistical theory of spectra of many-electron systems is briefly reviewed. In particular, new formal developments, their implementations in studying general properties of the model spaces, and links to the reduction problem are addressed. Applications in molecular and atomic spectroscopy are also discussed. © 1994 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560510610
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  • 10
    Electronic Resource
    Electronic Resource
    Symmetric group graphical approach to the direct configuration interaction method (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 783-824 
    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: An approach to the configuration interaction method based on symmetric groups (SGA) is developed. The formalism is an alternative of the unitary group approach (UGA). In many aspects the present formulation seems to be superior to UGA. In particular, in SGA the orbital and the spin parts of the configuration state functions may be processed separately. In consequence its graphical formulation is much simpler and the coupling constant expressions are more compact than the UGA analogs. A special emphasis is put on direct CI implementations. In addition to formulas for coupling constants, explicit expressions allowing for separation of external and internal space contributions are also presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560220411
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