Bond length alternation in cyclic polyenes. V. Local finite-order perturbation theory approach

The finite-order many-body perturbation theory using the localized Wannier orbital basis is applied to the problem of bond length alternation in the Pariser–Parr–Pople model of cyclic polyenes C_N H_N, N = 4v + 2, which may be regarded as a simplified model of polyacetylene. Both the Møller–Plesset and the Epstein–Nesbet-type partitionings of the model Hamiltonian are employed. The localized orbital basis enables an efficient truncation of the perturbation theory summations over the intermediate states as well as an elimination of energetically unimportant diagrams, thus enabling one to obtain the fourth-order Møller–Plesset-perturbation energies with a relatively small computational effort even for large polyenes. The results obtained with the second-, third-, and fourth-order Møller–Plesset and with the third-order Epstein–Nesbet perturbation theories yield very similar bond length distortions (about 0.05 Å) and stabilization energies per site (about 0.04 eV) as obtained earlier with the RHF , one-parameter AMO , and delocalized orbital perturbation theories. The effects of truncation and diagram elimination in the fourth-order Møller–Plesset perturbation theory and the abnormal behavior of the second-order Epstein–Nesbet perturbation theory results in the localized Wannier basis near the instability threshold of the RHF solutions are discussed.