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  • American Institute of Physics (AIP)  (4)
  • 1
    Electronic Resource
    Electronic Resource
    Cluster expansion of the Hubbard model energy of acyclic conjugated hydrocarbons (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 1191-1195 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Regularities in the ground state energy of acyclic conjugated hydrocarbons have frequently been noted at the level of Hückel molecular orbital calculations. In this paper it is shown that the Hubbard model, which includes electron correlation, shows the same types of regularities even in the highly correlated limit. These regularities are rationalized by showing that the Hubbard energy can be fit to a (rapidly convergent) cluster expansion which embodies the physically appealing notion that a molecule consists principally of localized bonds which interact progressively more weakly with more distant parts of the molecule. Relations to previous expressions for the energy, derived within the Hückel approximation, are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460026
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Real-space renormalization for Heisenberg models on two-dimensional lattices (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 5841-5846 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Real-space renormalization methods which simply shift and rescale the interaction parameters in the nearest-neighbor Heisenberg model are investigated for two-dimensional lattices of equivalent sites. Results are presented for the hexagonal, square-planar, triangular, and Kagome lattices via three different renormalization techniques. The first, which has been studied for some time, uses perturbation theory to evaluate the renormalized interactions. The second uses the variational method to improve on the perturbative results. The third method is based on a cluster expansion and is found to give much improved agreement with numerical results form Monte Carlo calculations, but it does not provide a variational bound to the exact solution. The dependence of all three methods on the size and shape of the renormalized block of sites is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467299
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  • 3
    Electronic Resource
    Electronic Resource
    Ground and excited Hubbard states for buckminsterfullerene with uniform and alternating bond strengths (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 8233-8240 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A detailed investigation on the π-electronic ground and lowest excited g- and u-symmetrical singlet and triplet states of icosahedral C60 is performed in the framework of the semiempirical Hubbard model using single and double excited configuration interaction (SDCI) upon an appropriately chosen reference space constructed out of Hartree–Fock-type molecular orbitals. We present SDCI results for energies, wave-function symmetries, bond orders and spin–spin correlations for these states. For the ground state, second order Møller–Plesset (MP2) and size-consistency corrected energies are presented and compared with Monte Carlo results. We also examine the influence of bond length alternation on the calculated properties. It is shown that within the Hubbard model the lowest excited g and u singlet and triplet states of C60 give very similar overall bond orders and spin–spin correlations. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481477
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  • 4
    Electronic Resource
    Electronic Resource
    Variational resonance valence bond study on the ground state of C60 using the Heisenberg model (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 873-880 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A detailed variational resonance valence bond (RVB) study is performed for the S=0 ground state of the C60 molecule in the framework of the Heisenberg model. It is shown that the 12 500-dimensional Kekulé space can be divided into two subspaces of respective dimensions 5828 and 6672, of which the first one recovers 99.82% of the energy of the full Kekulé space. This 5828-dimensional subspace is derived from the main Kekulé function, which is formed from spin pairs on hexagon–hexagon bonds only, by simple rotations of the three spin pairs in disjoint sets of hexagonal rings of C60 in all possible ways. This indicates that the concept of the stability of the aromatic sextet still plays an important role even in this nonalternant system. Further, the inclusion of some longer range RVB functions like Dewar-type functions and functions involving Claus structures is investigated, and the effect on the ground-state energy as well as on the nearest neighbor correlation functions is examined. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476627
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