Higher energy triplet-pair states in polyenes and their role in intramolecular singlet fission

Probing extended polyene systems with energy in excess of the bright state (\(1^1B_u^+\)/\(S_2\)) band edge generates triplets via singlet fission. This process is not thought to involve the \(2^1A_g^-\)/\(S_1\) state, suggesting that other states play a role. Using density matrix renormalisation group (DMRG) calculations of the Pariser-Parr-Pople-Peierls Hamiltonian, we investigate candidate states that could be involved in singlet fission. We find that the relaxed \(1^1B_u^-\), and \(3^1A_g^-\) singlet states and \(1^5A_g^-\) quintet state lie below the \(S_2\) state. The \(1^1B_u^-\), \(3^1A_g^-\) and \(1^5A_g^-\) states are all thought to have triplet-triplet character, which is confirmed by our calculations of bond dimerization, spin-spin correlation and wavefunction overlap with products of triplet states. We thus show that there is a family of singlet excitations(i.e., \(2^1A_g^-\), \(1^1B_u^-\), \(3^1A_g^-\), \(\cdots\)), composed of both triplet-pair and electron-hole character, which are fundamentally the same excitation, but have different center-of-mass energies. The lowest energy member of this family, the \(2^1A_g^-\) state, cannot undergo singlet fission. But higher energy members (e.g., the \(3^1A_g^-\)) state, owing to their increased kinetic energy and reduced electron-lattice relaxation, can undergo singlet fission for certain chain lengths.