The A_g ⁺ state falls below 3A_g ^- at carotenoid-relevant conjugation lengths

Spectroscopy of all-trans linear polyenes is characterized by a one-photon electronic transition to a bright S₂ state and two-photon transition to a lower-lying dark S₁ state. We apply ab initio quantum chemistry to distinguish additional diffuse dark singlet states. Building on a systematic implementation of CASSCF and DMRGSCF coupled to strongly-contracted NEVPT2, we report the excitation energies for a series of polyenes from butadiene to C₁₆H₁₈ at optimized S₀, S₁ and S₂ geometries. Ionic/covalent state inversion within each manifold is identified at seven conjugated double bonds, making the B_u ^- a dark intermediate state at its optimized geometry and the A_g ⁺ the S₃ state at the S₀ optimized geometry. The relevance of these results to the function of carotenoids in photosynthetic light harvesting is discussed.