  We develop a theory of singlet fission in carotenoid dimers. Following
photoexcitation of the 'bright' state (i.e., a singlet electron-hole pair) in a
single carotenoid, the first step in the singlet fission process is ultrafast
intramolecular conversion into the highly-correlated 'dark' (or 2Ag) state.
This state has both entangled singlet triplet-pair and charge-transfer
character. Our theory is predicated on the assumption that it is the singlet
triplet-pair component of the 'dark' state that undergoes bimolecular singlet
fission. We use valence bond theory to develop a minimal two-chain model of the
triplet-pair states. The single and double chain triplet-pair spectrum is
described, as this helps explain the dynamics and the equilibrated populations.
We simulate the dynamics of the initial entangled pair state using the quantum
Liouville equation, including both spin-conserving and spin-nonconserving
dephasing processes. By computing the intrachain and interchain singlet,
triplet and quintet triplet-pair populations, we show that singlet fission
depends critically on the interchain coupling and the driving potential (that
determines endothermic versus exothermic fission). We also show that the
Horodecki pair-entanglement provides a good metric for singlet fission.
