Theoretical study of the π → π* excited states of linear polyenes: The energy gap between 1¹B_u⁺ and 2¹A_g^- states and their character

Multireference perturbation theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the valence π → π* excited states of 1,3-butadiene, 1,3,5-hexatriene, 1,3,5,7-octatetraene, and 1,3,5,7,9-decapentaene. Our focus was put on determining the nature of the two lowest-lying singlet excited states, 1¹B_u⁺ and 2¹A_g^-, and their ordering. The 1¹B_u⁺ state is a singly excited state with an ionic nature originating from the HOMO → LUMO one-electron transition while the covalent 2¹A_g^- state is the doubly excited state which comes mainly from the (HOMO)² → (LUMO)² transition. The active-space and basis-set effects are taken into account to estimate the excitation energies of larger polyenes. For butadiene, the 1¹B_u⁺ state is calculated to be slightly lower by 0.1 eV than the doubly excited 2¹A_g^- state at the ground-state equilibrium geometry. For hexatriene, our calculations predict the two states to be virtually degenerate. Octatetraene is the first polyene for which we predict that the 2¹A_g^- state is the lowest excited singlet state at the ground-state geometry. The present theory also indicates that the 2¹A_G^- state lies clearly below the 1¹B_u⁺ state in decapentaene with the energy gap of 0.4 eV. The 0-0 transition and the emission energies are also calculated using the planar C_2h relaxed excited-state geometries. The covalent 2¹A_g^- state is much more sensitive to the geometry variation than is the ionic 1¹B_u⁺ state, which places the 2¹A_g^- state significantly below the 1¹B_u⁺ state at the relaxed geometry.