Coupled-cluster approach to electron correlation in one dimension: Cyclic polyene model in delocalized basis

Abstract

The many-electron correlation problem for metalliclike systems with Born—von Kármán boundary conditions, as modeled by the cyclic polyene Pariser-Parr-Pople and Hubbard Hamiltonians, is examined over the entire range of the coupling constant using the coupled-pair (CP) many-electron theory based on the exponential-cluster ansatz for the exact wave function. It is shown that the standard CP theory breaks down not only in the highly correlated, but even in the intermediately correlated, regions, and the nature of its singular behavior in these regions is examined. This breakdown is linked with the increasingly important role played by the connected quadruply excited clusters, which invalidate the basic assumption of the CP theory, as the highly correlated limit and/or the extended character of the model are approached. The contribution from the quadruply excited clusters is then taken into account using the new version of the approximate coupled-pair theory corrected for connected quadruply excited clusters, called ACPQ. This approximation is almost identical with the standard approximate coupled-pair (ACP) -theory approach, in which only factorizable (with respect to hole pairs) nonlinear terms are retained, and differs from it only by a numerical factor associated with one of the nonlinear diagrams. It is shown that the ACPQ not only removes the singularities and associated convergency problems of the standard CP approaches, but, in fact, provides excellent quantitative results over the entire range of the coupling constant, yielding the exact correlation energy in the strongly correlated limit.