Structural and electronic properties of infinite cis and trans polyenes: Perturbation theory of electron correlation effects

The geometrical structure of five infinite polyene models ( equidistant and alternating trans, equidistant cis, cis ‐ transoid , and trans ‐ cisoid ) have been optimized using three different atomic basis sets at the Hartree–Fock level and by including electron correlation effects within the second order of Møller–Plesset perturbation theory. The single‐particle energy bands have also been corrected for correlation effects applying the electron polaron method. Bond alternation has always reduced the energy (both for trans and cis ) polyenes but this stabilization energy has decreased with an increasing basis set and has saturated about 3 mH for trans and trans ‐ cisoid and about 7.5 mH for the cis ‐ transoid model. On the absolute energy scale, however, the alternating trans structure has always turned out to be more stable than either the cis ‐ transoid or the trans ‐ cisoid one. The energetic order is in all cases trans < cis ‐ transoid < trans ‐ cisoid . Using the largest basis set with correlation, the corresponding energy differences are Δ E ( trans → cis ‐ transoid ) = 1.69 mH and Δ E ( trans → trans ‐ cisoid ) = 6.12 mH, respectively. The HF values of the valence‐band widths vary in the region of 4–6 eV for the cis models and about 7 eV for the trans one. Correlation reduced them by about 20%, and the centers of the bands were shifted upward by about 2 eV due to self‐energy renormalization. The best values for the electron polaron valence bandwidths are 6.4, 4.2, 3.3, and 5.2 eV for the alternating trans, trans‐cisoid, cis‐transoid, and equidistant cis models, respectively. The vertical ionization potentials of the above four structures are 4.80, 5.47, 5.71, and 4.18 eV, respectively. The conduction bands have a width of 6–8 eV at the HF level (except equidistant cis with 4.6 eV for the larger basis sets) that will be reduced by about 15–20% due to polaron formation. The bands are shifted in this case uniformly downward by about 2–3 eV due to correlation. The best values obtained for the conduction bandwidths are 4.7, 6.4, 5.6, and 3.7 eV, respectively. These band shifts reduce the HF value of the fundamental gap by several eV's for all models. For the largest basis set, the Δ E gap values change from 6.6, 6.9, 7.7, and 5.3 eV ( HF results for the alternating trans, trans‐cisoid, cis‐transoid, and equidistant cis models, respectively) to 2.7, 3.2, 4.5, and 2 eV, respectively, at the correlated level.