An optimization of the 2pz atomic orbitals is rederived for the ground-state energy of conjugated systems. Within some reasonable assumptions, this optimization (analogous to that proposed by Silverstone and Joy) allows the orthogonalized 3pz atomic orbitals to be considered as v rtual orbitals in the CI calculation when one starts from a SCF calculation performed in the minimal basis set of optimized n = 2 atomic orbitals. The reorganization of the π* MO in the ππ* excited state leads to a spatial expansion in the singlet state and a spatial contraction in the triplet state. But this effect is less and less important when the dimension n of the π system increases, and the corresponding energetic correction decreases as n−2. A less pronounced effect is obtained on the π singly occupied orbital; the doubly occupied MO's are not significantly modified in the singlet state. The role of the 3pz atomic orbitals in the correlation effects on the transition energies is much more important. It is not mainly due to the π→3pz monoexcited configurations (which only give a correction proportional to n−1) but to the doubly and triply excited states: Their correction tends towards a constant value which has been estimated.

Denis, A., & Malrieu, J. P. (1970). Correlation Effects on ππ* Transition Energies in the Series of Linear Polyenes. III Dynamical Correlation Effects. The Journal of Chemical Physics, 52(12), 6076–6089.