Singularity-free internal conversion golden-rule rate with application to correlated triplet pair recombination in bipentacenes

We introduce a singularity-free golden-rule rate expression for internal conversion (IC), a spin-conserved radiationless relaxation process, expressed as the product of a nonadiabatic coupling term and the time integral of a vibration correlation function. For a set of small polyatomic molecules (acenes and azulene), we show that our calculated rates are in near quantitative agreement with the rates derived from experiments. Interestingly, we find that our rates do not agree with previous golden-rule-based theoretical efforts; detailed analysis shows that while the level of electronic structure theory can play a role, the more significant error is from not fully converging the numerical time integral over the oscillatory vibration correlation function. We then use our singularity-free IC rate expression to compute the rate of recombination of the correlated triplet pair state generated by intramolecular singlet fission in a trio of bipentacenes. We show that the recombination rates are in good agreement with experimentally observed trends-specifically, the rates are robust to temperature changes and decrease rapidly with increasing inter-monomer dihedral angle. Finally, we use a pair-wise breakdown of normal mode contributions to the rate to identify the key vibrational modes that drive recombination in bipentacenes.