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 ($1{\phantom{\rule{0.16em}{0ex}}}^{1}{B}_{u}^{+}$/${S}_{2}$) band edge generates triplets via singlet fission. This process is not thought to involve the $2{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$/${S}_{1}$ 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 $1{\phantom{\rule{0.16em}{0ex}}}^{1}{B}_{u}^{\ensuremath{-}}$ and $3{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$ singlet states and $1{\phantom{\rule{0.16em}{0ex}}}^{5}{A}_{g}^{\ensuremath{-}}$ quintet state lie below the ${S}_{2}$ state. The $1{\phantom{\rule{0.16em}{0ex}}}^{1}{B}_{u}^{\ensuremath{-}}$, $3{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$, and $1{\phantom{\rule{0.16em}{0ex}}}^{5}{A}_{g}^{\ensuremath{-}}$ 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., $2{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$, $1{\phantom{\rule{0.16em}{0ex}}}^{1}{B}_{u}^{\ensuremath{-}}$, $3{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$, $\ensuremath{\cdots}$), 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 $2{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$ state, cannot undergo singlet fission. But higher-energy members (e.g., the $3{\phantom{\rule{0.16em}{0ex}}}^{1}{A}_{g}^{\ensuremath{-}}$) state, owing to their increased kinetic energy and reduced electron-lattice relaxation, can undergo singlet fission for certain chain lengths.