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  • 1
    Electronic Resource
    Electronic Resource
    Gauge transformations of electron group functions (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 9461-9472 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Within the scope of the electron group functions (EGF) theory, the concept of gauge transformations (GT) of EGFs is introduced as such transformations that leave the state of the entire system invariant. The variational equations for EGFs should contain additional terms representing the Pauli repulsion part of the pseudopotential and being consistent with the choice of EGFs (the requirement of gauge consistency). The GTs present a natural way of ab initio defining the generalized many-electron pseudopotentials produced by an internally correlated subsystem. Some specific, but rather general forms of GTs are proposed. One of the form is defined using properties of group functions with odd number of electrons. The GTs belonging to another class are defined using properties of antisymmetrically annulling (ASA) functions introduced in our earlier work and studied further in the present work. In particular, we introduce the ASA kernel basis set for a given group function and show that any function ASA the given group function can be expanded in terms of this set. The algebraic properties of GTs and of their sets are studied, both general ones and specific for the mentioned forms. In general case, the proposed GTs depend on a set of parameters which are functions rather than numbers, that can provide improved transferability of pseudopotentials. The linear transformations of one-electron functions of a determinant as well as the procedures of strong orthogonalization of a group function to a determinant (by Fock, Veselov, and Petrashen', and by Szasz) are shown to be special cases of the GTs considered. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471689
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  • 2
    Electronic Resource
    Electronic Resource
    Localization of electron group functions (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 581-590 
    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 requirements of variational freedom of electron group functions and their spatial separation are basic statements of the group functions method as they are necessary for taking into account the intragroup electron correlation while neglecting the intergroup one. But these requirements seem to be inconsistent with one another. This contradiction can be removed using the notion of antisymmetrical annulment of many-electron functions introduced in the present work. The transformation of group functions (GF) by means of functions antisymmetrically annulling (ASA) other GF's is proposed that does not affect the whole system's wave function but can be used for localizing GF's. The problem of construction of a function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Phi $\end{document} ASA a given Φ can be reduced to solving a system of linear algebraic equations. A sufficient condition of existing of nontrivial \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Phi $\end{document} is obtained.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560410404
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  • 3
    Electronic Resource
    Electronic Resource
    Integral-geometrical consideration of density matrices (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 535-545 
    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 ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators Θλk are represented using particular values (at specially chosen ) of the Radon transform of the N-DM spatial parts (or their sums) DNλ(x′ | x″) (here, is a d-plane in the n-space ∝n of x = (x′, x″)), with n = 6N, d = 3 (N - k), x′ ≡ (r′1,⃛, r′N), x′ ≡ (r1″,⃛, r″N ()). In this way, the problem is reduced to investigation of the properties of the functions . For a normalizable N - DM, it is proved that are bounded functions. The properties of implied by the N-DM permutational symmetry, Hermiticity, and positive definiteness are found. A formal procedure of reconstruction of all N-DM corresponding to a given k-RDM is proposed. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560560511
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