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/S2) band edge generates triplets via singlet fission. This process is not thought to involve the 2^1A−g/S1 state, suggesting that other states play a role. Using density matrix renormalization 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 S2 state. The 1^1B−u, 3^1Ag, and 1^5A−g states are all thought to have triplet-pair character, which is confirmed by our calculations of bond dimerization, spin-spin correlation, and wave function 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,⋯), 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