Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 1 1 B u + and 2 1 A 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, 1 1 B u + and 2 1 A g − , and their ordering. The 1 1 B u + state is a singly excited state with an ionic nature originating from the HOMO→LUMO one‐electron transition while the covalent 2 1 A 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 1 1 B u + state is calculated to be slightly lower by 0.1 eV than the doubly excited 2 1 A 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 2 1 A g − state is the lowest excited singlet state at the ground‐state geometry. The present theory also indicates that the 2 1 A g − state lies clearly below the 1 1 B 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 2 h relaxed excited‐state geometries. The covalent 2 1 A g − state is much more sensitive to the geometry variation than is the ionic 1 1 B u + state, which places the 2 1 A g − state significantly below the 1 1 B u + state at the relaxed geometry. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 157–175, 1998