Enhancing Singlet Fission Coupling with Nonbonding Orbitals.

Singlet fission (SF) is a process where a singlet exciton is split into a pair of triplet excitons. The increase in the excitonic generation can be exploited to enhance the efficiency of solar cells. Molecules with conjugated π bonds are commonly developed for optoelectronic applications including SF, due to their low energy gaps. The electronic coupling for SF in such well-stacked π-conjugated molecule pairs can be rather limited due to the orthogonal π and π* orbital overlaps that are involved in the coupling elements, leading to a large cancellation in the coupling. In the present work, we show that such limits can be removed by involving triplet states of different origins, such as those with nonbonding n orbitals. We demonstrate such an effect for formaldehyde and methylenimine dimers, with a low-lying n-π* triplet state (T1) in addition to the π-π* triplet (T2). We show that the coupling can be enhanced by 40 times or more for the formaldehyde dimer, and 15 times or more for the methylenimine dimer, with the T1-T2 state as the end product of SF. With 1759 randomly oriented pairs of formaldehyde derived from a molecular dynamics simulation, the coupling from a singlet exciton to this T1-T2 state is, on an average, almost two times larger than that for a regular T1-T1 state. We investigated a few families that have been shown to be prospective candidates for SF, using our proposed strategy. However, our unfavorable results indicate that there are clear difficulties in fulfilling the ES1 ≳ ET1 + ET2 energy criterion. Nevertheless, our results provide a new molecular design concept for better SF (and triplet-triplet annihilation, TTA) materials that allows future development.

First Principle Prediction of Intramolecular Singlet Fission and Triplet Triplet Annihilation Rates.

Intramolecular singlet fission and triplet-triplet annihilation (TTA) has been experimentally observed and reported. However, problems remain in theoretically accounting for the corresponding intramolecular electronic couplings and their rates. We used the fragment excitation difference (FED) scheme to calculate the coupling with states from restricted active-space spin-flip configuration interaction. We investigated three covalently linked pentacene dimers via a phenyl group in an ortho-, meta-, and para-arrangement. The singlet fission and TTA couplings were enhanced when two chromophores were covalently linked. With the Fermi golden rule, both the estimated singlet fission and TTA rates were in line with the experimental results. For systems with significant singlet-fission coupling, charge-transfer components were observed in the excited states involved, and charge-transfer states were also seen within 1 eV above the singlet excited states. Our approach allows for an analysis of through-bond versus through-space singlet fission in the full electronic wave functions. The FED scheme is useful for calculating intramolecular singlet-fission and TTA couplings.

Hamiltonian-Independent Generalization of the Fragment Excitation Difference Scheme.

The fragment excitation difference (FED) scheme is a useful method for calculating the complete diabatic couplings of various energy transfer systems. The lack of a good definition for the transformation of the transition density matrix to the off-diagonal FED matrix elements limits FED to single-excitation methods. We have developed a generalized FED scheme called the θ-optimized FED (θ-FED) scheme which does not require transforming the transition density matrices. In θ-FED, two states of interest are linearly transformed by a mixing angle θ into two mixed states. The excitation difference of each mixed state is evaluated and optimized numerically to determine the mixing angle. This approach allows for finding diabatic states and the corresponding couplings for a general set of Hamiltonians.