Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene π-electron models

Methods accounting for correlation effects in quasi-one-dimensional π-electron systems and based on the restricted Hartree–Fock (RHF ) single determinantal reference state are briefly reviewed as well as their role in the bond length alternation (or dimerization) problem in polyactylene-like systems, as described by the semiempirical Hamiltonians of the Pariser–Parr–Pople (PPP ) type. Particular attention is given to the π-electron model of cyclic polyene homologous series C_NH_N, N = 2n = 4v + 2, v = 1,2,…, which can be regarded as an idealized model of one-dimensional metallic-like systems with imposed Born–von Kármán boundary conditions when N ∞. These models provide a useful bridge between the typical aromatic systems, represented by benzene (N = 6) π-electron model, and long linear polyenic chains, since the properties of these systems hardly change once a sufficiently large N (?26 or 30) is reached. It is shown that due to the quasidegenerate character of the RHF reference employed, and the related prominence of connected quadruply excited cluster components in the exact wave function, most of the standard technieques suffer a singular behavior break down entirely for large enough systems, particularly in the strongly correlated regime. The approximate coupled pair theory that accounts for quadruply excited clusters (ACPQ method) is shown to be free of these shortcomings and is extended to include also approximately the effects of connected triexcited cluster components. These results are compared with other recently examined approximate methods accounting for the tri- and quadruply excited clusters and the proposed ACPQ +T (ACPQ ) procedure is shown to provide the best results in the whole range of the coupling constant.