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 ($1^1{B}_u^{+}$/$S_2$) band edge generates triplets via singlet fission. This process is not thought to involve the $2^1{A}_g^{-}$/$S_1$ 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 $1^1{B}_u^{-}$, and $3^1{A}_g^{-}$ singlet states and $1^5{A}_g^{-}$ quintet state lie below the $S_2$ state. The $1^1{B}_u^{-}$, $3^1{A}_g^{-}$ and $1^5{A}_g^{-}$ 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., $2^1{A}_g^{-}$, $1^1{B}_u^{-}$, $3^1{A}_g^{-}$, $\cdots$), 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 $2^1{A}_g^{-}$ state, cannot undergo singlet fission. But higher energy members (e.g., the $3^1{A}_g^{-}$) state, owing to their increased kinetic energy and reduced electron-lattice relaxation, can undergo singlet fission for certain chain lengths.

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