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Probing extended polyene systems with energy in excess of the bright state($1^1B_u^+$/$S_2$) band edge generates triplets via singlet fission. Thisprocess is not thought to involve the $2^1A_g^-$/$S_1$ state, suggesting thatother states play a role. Using density matrix renormalisation group (DMRG)calculations of the Pariser-Parr-Pople-Peierls Hamiltonian, we investigatecandidate states that could be involved in singlet fission. We find that therelaxed $1^1B_u^-$, and $3^1A_g^-$ singlet states and $1^5A_g^-$ quintet statelie below the $S_2$ state. The $1^1B_u^-$, $3^1A_g^-$ and $1^5A_g^-$ states areall thought to have triplet-triplet character, which is confirmed by ourcalculations of bond dimerization, spin-spin correlation and wavefunctionoverlap with products of triplet states. We thus show that there is a family ofsinglet excitations(i.e., $2^1A_g^-$, $1^1B_u^-$, $3^1A_g^-$, $\cdots$),composed of both triplet-pair and electron-hole character, which arefundamentally the same excitation, but have different center-of-mass energies.The lowest energy member of this family, the $2^1A_g^-$ state, cannot undergosinglet fission. But higher energy members (e.g., the $3^1A_g^-$) state, owingto their increased kinetic energy and reduced electron-lattice relaxation, canundergo singlet fission for certain chain lengths.

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