Bond length alternation in cyclic polyenes. IV. Finite‐order purturbation theory approach

The problem of bond length alternation in linear extended systems with conjugated double bonds is examined on a simple cyclic polyene model using finite‐order many‐body perturbation theory. Three different partitionings of the model Hamiltonian are employed, namely the Hückel, Møller–Plesset, and Epstein–Nesbet partitionings. The dependence of correlation energy on bond length alternation is examined in each case, showing an almost constant behavior of Møller–Plesset and Epstein–Nesbet perturbation energies in contrast to a strong dependence on distortion, favoring undistorted structures, for the Hückel perturbation and UHF correlation energies. The origin of an unphysical character of the Hückel perturbation theory and the inappropriateness of the UHF approach for the problem considered are pointed out. The second‐ and third‐order Møller–Plesset and also the second‐order Epstein–Nesbet perturbation theories yield results which are similar to those obtained with the RHF method and which clearly favor the bond length alternating structures, leading to the bond length distortion of about 0.045 Å and to the stabilization energy per site (relative to the equidistant geometry) of about 0.03 eV.