Correlated vibrational frequencies of polymers: MBPT(2) for all-trans polymethineimine

Polymethineimine is a conjugated polymer, isovalent with polyacetylene, which was first synthesized in 1971. It has been found to be a semiconductor, though prior theory did not support that. Except for its vibrational frequencies which have been measured, little about the polymer is known. MBPT(2) is applied to calculate its equilibrium structure, band gap, and vibrational frequencies. The latter represents the first time an ab initio correlated method has been applied to this problem for an infinite system. The calculations for three basis sets, STO-3G, 6-31G, and 6-31G** demonstrate that both basis and electron correlation have a strong influence on its optimized geometry. The MBPT(2) band gap with a polarized basis set (6-31G** ) is 4.7826 eV, compared to 8.54 for Hartree-Fock. According to our MBPT(2) calculations, the band gap of all-trans polymethineimine would be estimated to be about 1 eV larger than that of polyacetylene, i.e. ∼2.75±0.5 eV. Electron correlation is demonstrated to have an important effect on the computed vibrational frequencies, which we find to be in good agreement with experiment.