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

Abstract: Probing extended polyene systems with energy in excess of the bright state ($1<sup>1B_u<sup>+$/$S_2$) band edge generates triplets via singlet fission. This process is not thought to involve the $2<sup>1A_g<sup>-$/$S_1$ 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 $1<sup>1B_u<sup>-$, and $3<sup>1A_g<sup>-$ singlet states and $1<sup>5A_g<sup>-$ quintet state lie below the $S_2$ state. The $1<sup>1B_u<sup>-$, $3<sup>1A_g<sup>-$ and $1<sup>5A_g<sup>-$ 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., $2<sup>1A_g<sup>-$, $1<sup>1B_u<sup>-$, $3<sup>1A_g<sup>-$, $\cdots$), 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 $2<sup>1A_g<sup>-$ state, cannot undergo singlet fission. But higher energy members (e.g., the $3<sup>1A_g<sup>-$) state, owing to their increased kinetic energy and reduced electron-lattice relaxation, can undergo singlet fission for certain chain lengths.