Coupled-cluster approach to electron correlation in one dimension. II. Cyclic polyene model in localized basis

The many-electron correlation problem for one-dimensional metalliclike systems with Born--von K\'arm\'an boundary conditions, represented by the Pariser-Parr-Pople and the Hubbard Hamiltonian cyclic polyene models, ${\mathrm{C}}_{\mathrm{N}}$${\mathrm{H}}_{\mathrm{N}}$, N=2n=4\ensuremath{\nu}+2, \ensuremath{\nu}=1,2,..., is studied using the coupled-cluster approach in the localized Wannier basis representation. Various truncation schemes for the pair clusters are examined. It is shown that already the intracell pair-cluster approximation, which can be handled analytically and yields the same expression for the correlation energy as the variational approach of Ukrainskii, provides a reasonable approximation in the entire range of the coupling constant. Using all doubly excited clusters composed of locally excited particle-hole pairs, one obtains the exact correlation energy in the fully correlated limit assuming that the coupled-pair equations are corrected for the connected quadruply excited cluster contributions. This is achieved by using the recently developed approximate coupled-pair approach with corrections for the quadruply excited clusters (ACPQ), which is almost identical, except for a numerical factor of certain diagrams, with the standard approximate coupled-pair approach. The ACPQ approach removes the singularities which otherwise plague the standard coupled-pair approach and yields very good correlation energies in the entire range of the coupling constant even when the ${n}^{3}$ doubly excited pair clusters are truncated to only n+10 locally and quasilocally excited pair clusters in the localized Wannier basis representation.