Correlation Effects on ππ* Transition Energies in the Series of Linear Polyenes. II. σπ Correlation Effects in the Minimal Basis Set

The $\mathrm{\sigma \pi }$ interaction effect on the $\mathrm{\pi \pi *}$ transition energies is calculated in a second‐order perturbation expansion of transition energies, using $\pi$ delocalized and σ localized orbitals. The effect of the $\mathrm{\sigma \sigma *}$ monoexcited configurations decreases when the dimension increases, but the effect of higher excitations increases simultaneously, and the final $\mathrm{\sigma \pi }$ second‐order effect is almost constant for the first band of the series of linear polyenes. The $\mathrm{\sigma \pi }$ interaction changes the spacing between the $\mathrm{\pi \pi *}$ singlet excited states in small systems. Three $\pi$ parametrizations are compared: The $\mathrm{\sigma \pi }$ interaction is not sufficient to give a reasonable transition energy when one uses the classical atomic orbitals with $\text{ζ\hspace{0.17em}=\hspace{0.17em}1.625}$ , but when one starts from the atomic orbitals optimized by Silverstone and Joy, the total second‐order effect in the minimal basis set gives a final transition energy only 1 eV above the experimental one.