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  • 1
    ISSN: 1432-2234
    Keywords: Bivariational procedures ; Method of moments, reliability and convergence characterization of
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A convergence characterization of the Galerkin-Petrov method by means of quantities characterizing pairs of subspaces is presented. The usefulness of our approach for setting up reliable computational schemes is demonstrated for the He atom ground state. Several methods of constructing pairs of subspaces for use in quantum chemistry are suggested.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2234
    Keywords: Bivariational procedures ; Method of moments, reliability of ∼
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 21 S and 31 S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.
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  • 3
    ISSN: 1432-2234
    Keywords: Bivariational procedures ; Method of moments, reliability of ∼ ; Electron correlation ; Beryllium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.
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  • 4
    ISSN: 1432-2234
    Keywords: Bivariational procedures ; Method of moments, reliability of ∼
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 21 S and 31 S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 1969-1972 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The two usual definitions of energy increments that characterize convergence of electronic energy calculations are shown to be numerically significantly different. In two special cases, helium and neon, their ratios are approximately 1.4. Care must be exercised when comparing calculations from separate sources lest differences of definition be interpreted physically.
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  • 6
    ISSN: 1432-2234
    Keywords: Coupled cluster approach ; Method of moments approach ; Many-electron correlation problem ; Intruder states ; Quasi-degeneracy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The single reference coupled cluster (CC) approach to the many-electron correlation problem is examined from the viewpoint of the method of moments (MM). This yields generally an inconsistent (overcomplete) set of equations for cluster amplitudes, which can be solved either in the least squares sense or by selective projection process restricting the number of equations to that of the unknowns. These resulting generalized MM-CC equations always contain the standard CC equations as a special case. Since, in the MM-CC formalism, the Schrödinger equation will be approximately satisfied on a subspace spanned by non-canonical configurations, this procedure may be helpful in extending the standard single reference CC theory to quasi-degenerate situations. To examine the potential usefulness of this idea, we explore the linear version of the CC approach for systems with a quasi-degenerate reference, in which case the standard linear theory is plagued with singularities due to the intruder states. Implications of this analysis for the structure of the wavefunction are also briefly discussed.
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  • 7
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The F2 ground state potential curve has been computed near re by means of the MCSCF, CI(SD), MR-CI(SD) and the recently proposed CPF method. Extensive sets of polarization functions including up to five d sets, three f sets, and one g set have been used to study the convergence of the total energy of De, and re for these methods on basis set extension. SCF and MCSCF show a similar behavior and are practically converged on the 2d1f level. Convergence is much slower for methods which include external correlation, such as CI(SD), MR-CI(SD), CPF. The largest calculation performed—MR-CI(SD) for a [6 4 2 1] basis—included 280 076 configuration state functions, and yields De and re with an accuracy of 0.07 eV and 0.015 a.u. These remaining errors are attributed mainly to the neglect of g functions. The present results provide detailed information concerning the relative importance of polarization functions which can be ordered as: d(1)〉d(2)(approximately-greater-than)f(1)〉d(3) for SCF and MCSCF and d(1)〉f(1)(approximately-greater-than)d(2)〉g(1)(approximately-greater-than)f(2)(approximately-greater-than)d(3) for methods including external correlation.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 7617-7622 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Third-order pair energies and the total third-order energy are obtained for the first time for an atomic system containing 3d electrons. The variational–perturbation method is applied within the framework of the Rayleigh–Schrödinger perturbation theory with H0=HHF. The N-electron first-order wave function is defined in terms of orbital configurations of one-electron functions and symmetry-adapted pair functions in the form of partial-wave (PW) expansions. Extensive basis sets including all PW up to l,l'≤9 are used. For Zn2+ the total third-order energy amounts to about 9% of the second-order energy obtained in the same basis set, which is considerably more than for closed-shell ten-electron systems. Values of the energy functional for the function ψ0+λψ1 are also reported. The latter represent the most accurate variational results obtained so far for atomic systems containing 3d electrons.
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