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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 1485-1486 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3392-3404 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Renormalization is a method often used to approximate the eigenvalues of a Hamiltonian that cannot be solved exactly. It consists of splitting the Hamiltonian into a solvable part and a remainder which is then minimized. The inner projection technique, first introduced by Löwdin in the sixties, was developed to bracket the eigenvalues between lower and upper bounds. Combining renormalization and Löwdin's inner projection yielded the so-called "renormalized inner projection technique.'' In this study, this method will be applied to the quartic, sextic, and octic anharmonic oscillators. Lower and upper energy bounds are obtained for finite values of the coupling constant as well as for the infinite case. The relation between the renormalized inner projection and perturbation theory will also be discussed. Another feature of this study is the importance of symbolic computation in allowing us to manipulate expressions with unevaluated parameters and to perform calculations in rational arithmetics or high decimal precision. Thus Löwdin's rational approximants can be expressed explicitly as rational fractions in terms of the coupling constant and values for the limit constant can be obtained with amazing high accuracy, namely, 62, 33, and 21 decimal places for the quartic, sextic, and octic oscillator, respectively.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 10717-10729 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: By considering chains of hydrogen and helium atoms with one Gaussian function centered on each atomic sites, i.e., the simplest possible metallic and insulating model systems retaining all the characteristics of the restricted Hartree–Fock–Roothaan method for extended chains, a scheme is proposed to carry out accurately and efficiently both Coulomb and exchange lattice sums which occur in a Gaussian basis set environment. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 209-223 
    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 goal of this article is to illustrate the use of symbolic computation in solving problems in physics and chemistry. For instance, the application of the inner projection technique combined with renormalization is shown to give very tight bounds for the ground-state energy of anharmonic oscillators. Some typical results are presented. Further, it has been observed that inner projection is directly applicable to the PPP and Hubbard Hamiltonians. The results for the model of benzene are briefly presented. A new method for summing divergent series, which we call the Weniger summation method, is proposed. This method is used, with excellent results, for the summation of divergent perturbation series for the energy of anharmonic oscillators. This method is also applied for the summation of the divergent series corresponding to the ground-state energy of the Hubbard Hamiltonian of the infinite chain. Other applications of the Weniger summation method to diffusion and heat conduction problems are summarized.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 50 (1994), S. 207-231 
    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: In this article, we demonstrate a complementarity between the quasi-spin SU(2) algebra of the Hubbard model and the pseudo-orthogonal group O(m,m), where n = 2m is the number of lattice sites. It is shown that all N-electron states for the one-dimensional Hubbard model, corresponding to given values of spin and quasi-spin, give rise to an irreducible representation of O(m,m). Moreover, the cyclic group Cn symmetry of the Hamiltonian is investigated and the O(m,m) ↓ Cn branching rules are determined with the use of the U(n) q-dimension formula. © 1994 John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990), S. 831-851 
    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 important role of model Hamiltonians for quantum mechanical description of the molecular electronic structure is discussed, and the effectiveness of the Pariser-Parr-Pople (PPP) model in calculations of molecular properties, in building of other models, and in various theoretical exploits is emphasized. The striking simplicity and transparence, yet remarkable reality and credibility, of this model is illustrated by applying the basic coupled cluster approach (CCD), as well as its extension approximating triexcited clusters (CCSDT-1), to the PPP model of benzene. The explicit final equations are obtained using the symbolic computation language MAPLE for both the orthogonal and nonorthogonal versions of the CC formalism. These equations are presented using the interface between MAPLE and the typesetting language TROFF. In this way, the explicit CC equations are obtained in terms of basic parameters of the model, starting from the CI description and showing their equivalence with those obtained via diagrammatic techniques. A new insight into the structure of CC equations at various levels of approximation is thus achieved and a useful model for electron correlation is provided.
    Additional Material: 9 Tab.
    Type of Medium: Electronic Resource
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