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  • 1
    Electronic Resource
    Electronic Resource
    The He isoelectronic series and the Hooke's law model: Correlation measures and modifications of Collins' conjecture (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 6135-6142 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The recently developed concept of a correlation entropy, S, as a quantitative measure of the correlation strength present in a correlated quantum many-body state is applied to the ground states of the He isoelectronic series He(Z) with varying nuclear charge Z and of the Hooke's law model HLM(ω) with varying oscillator frequency ω. S is constructed from the natural orbital occupation numbers. It vanishes for weak correlation (large coupling constants Z or ω), and increases monotonically with decreasing Z or ω (strengthening correlation). A reduced correlation energy per particle Δecorr and a dimensionless ratio ε=|Ecorr/E| are introduced which vanish asymptotically in the weak correlation limit in contrast to Ecorr and ecorr=Ecorr/N. These two intensive quantities, Δecorr and ε, are compared with s=S/N. For both model systems, dΔecorr/ds≥0 and dε/ds≥0 (which modifies Collins' conjecture that |Ecorr|∼S). © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478560
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  • 2
    Electronic Resource
    Electronic Resource
    Clusterentwicklung der Informationsgrößen im Besetzungszahl-Formalismus der klassischen Gleichgewichts-Statistik (1967)
    Springer
    Communications in mathematical physics 5 (1967), S. 191-204 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By means of quantum field theoretical methods (occupation number formalism, linked graph theorem, functional derivation) the cluster developments of classical equilibrium statistics are rederived. Thereby an information quantity comprehending all partial information about a system is introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646340
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  • 3
    Electronic Resource
    Electronic Resource
    Das allgemeine Exponential-Verbundgraphentheorem (1967)
    Springer
    Communications in mathematical physics 5 (1967), S. 301-316 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract General theorems concerning reordering of products of exponential functionals are formulated and proved. Their applicability in different fields of many particle theory is mentioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646481
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  • 4
    Electronic Resource
    Electronic Resource
    Correlation strength and information entropy (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 363-369 
    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 correlation present in the nondegenerate ground state of an interacting Fermi system is discussed in terms of reduced density matrices and their cumulant expansion. By generalizing a result obtained for the interacting uniform electron gas (correlation induced exchange-hole narrowing), possible measures of the correlation strength in terms of natural occupation numbers (the eigenvalues of the true one-particle density matrix) are introduced. These quantities-the v-order nonidempotency and the information entropy of the natural occupation numbers-result from the correlated many-body wave function and characterize the ground-state correlation in addition to the usual correlation energy. The uniform electron gas serves as a first illustrative example. © 1995 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560560422
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  • 5
    Electronic Resource
    Electronic Resource
    Correlation entropy of the H2 molecule (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 935-941 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Correlation of a quantum many-body state makes the one-particle density matrix nonidempotent. Therefore, the Shannon entropy of the natural occupation numbers measures the correlation strength on the one-particle level. Here, it is shown how this general idea of a correlation entropy must be adapted for two-electron systems in view of conservation laws which mix Slater determinants even in the noninteracting limit. Results are presented for the correlation entropy s of H2 as a function of the nucleus-nucleus separation R. In the ground state, the entropy of the spatial factor of the wave function maximizes 1.7 bohr beyond the Coulson-Fischer separation. The role of the correlation entropy in density functional theory is also discussed. © 1997 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Attempts toward a pair density functional theory (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1361-1374 
    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: A generalized density functional theory (DFT) is proposed based on a generalized Hohenberg-Kohn theorem with the pair density as the key quantity and the kinetic energy as a universal functional of the pair density. It is assumed that there exists an effective interaction potential which, via the corresponding two-particle (2P) Schrödinger equation, generates 2P orbitals (geminals) from which follows the pair density, just as in the conventional DFT the density follows from 1P orbitals (as the solutions of an effective 1P Schrödinger equation). According to three different representations (natural spectral resolutions) of the pair density or the cumulant pair densities in terms of geminals, three versions of a pair DFT (PDFT) are formally sketched. Also considered are the relation between electron correlation and particle-number fluctuations in fragments of the system and the use of the pair density for an estimation of such fluctuations. © 1996 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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