Theory of the dark state of polyenes and carotenoids

A theory is developed to describe the singlet dark state (usually labeled S1 or 2Ag) of polyenes and carotenoids. The properties of this state explain the nonemissive properties of linear polyenes, it is responsible for the photoprotection properties of carotenoids in light harvesting complexes, and because of its triplet-pair character, it is thought to be the cause of singlet fission in polyene-type systems. The theory described here assumes that in principle this state is a linear combination of singlet triplet-pairs and a singlet charge-transfer exciton. Crucially, these components only couple when the triplet pair occupies neighboring C-C dimers, such that an electron transfer between the triplets creates a nearest-neighbor singlet charge-transfer excitation. This local coupling stabilizes the 2Ag state and induces a nearest-neighbor attraction between the triplets. In addition, because of the electron-hole Coulomb attraction in the exciton, the increased probability that the electron-hole pair occupies neighboring dimers enhances the triplet-triplet attraction: the triplet pair is ???slaved??? to the singlet exciton. The theory also predicts that as the Coulomb interaction is increased, the 2Ag state evolves from a predominately charge-transfer exciton with a small component of triplet-pair character to a state predominately composed of a triplet pair with some exciton character. Above a critical Coulomb interaction there is a decoupling of the triplet-pair and exciton subspaces, such that the 2Ag state becomes entirely composed of unbound spin-correlated triplet pairs. The predictions of this theory of a triplet-pair binding energy in carotenoids of ca. 0.4 eV are consistent with density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model. It also predicts that the single-triplet component of the 2Ag state in carotenoids is ca. 50%.