Theory of the Dark State of Polyenes and Carotenoids

TL;DR

This paper develops a theoretical model describing the dark singlet state in polyenes and carotenoids, emphasizing the coupling between triplet pairs and charge-transfer excitons and how Coulomb interactions influence this state.

Contribution

The theory introduces a new framework linking triplet-pair states and charge-transfer excitons, explaining the evolution of the dark state with Coulomb interaction strength.

Findings

The 2Ag state is stabilized by local coupling between triplet pairs and charge-transfer excitons.

Increasing Coulomb interaction causes the 2Ag state to transition from exciton-dominant to triplet-pair dominant.

The theory aligns qualitatively with high-level density matrix renormalization group calculations.

Abstract

A theory is developed to describe the singlet dark state (usually labeled S1 or 2Ag) of polyenes and carotenoids. The theory assumes that in principle this state is a linear combination of a singlet triplet-pair and an odd-parity charge-transfer exciton. Crucially, these components only couple when the triplet-pair occupies neighboring dimers, such that an electron transfer between the triplets creates a nearest-neighbor charge-transfer excitation. This local coupling stabilises the 2Ag state and induces a nearest neighbor attraction between the triplets. In addition, because of the electron-hole 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 charge-transfer exciton. The theory also predicts that as the Coulomb interaction is increased, the 2Ag state evolves from a predominately odd-parity charge-transfer exciton state 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 charge-transfer exciton subspaces, such that the 2Ag state becomes entirely composed of an unbound spin-correlated triplet pair. The predictions of this theory are qualitatively consistent with high-level density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model.