First-Principles Quantum Dynamics of Singlet Fission: Coherent versus Thermally Activated Mechanisms Governed by Molecular $\pi$ Stacking

Singlet excitons in $\pi$-stacked molecular crystals can split into two triplet excitons in a process called singlet fission that opens a route to carrier multiplication in photovoltaics. To resolve controversies about the mechanism of singlet fission, we have developed a first principles nonadiabatic quantum dynamical model that reveals the critical role of molecular stacking symmetry and provides a unified picture of coherent versus thermally activated singlet fission mechanisms in different acenes. The slip-stacked equilibrium packing structure of pentacene derivatives is found to enhance ultrafast singlet fission mediated by a coherent superexchange mechanism via higher-lying charge transfer states. By contrast, the electronic couplings for singlet fission strictly vanish at the $C_{2h}$ symmetric equilibrium $\pi$ stacking of rubrene. In this case, singlet fission is driven by excitations of symmetry-breaking intermolecular vibrations, rationalizing the experimentally observed temperature dependence. Design rules for optimal singlet fission materials therefore need to account for the interplay of molecular $\pi$-stacking symmetry and phonon-induced coherent or thermally activated mechanisms.

Figure 1

(a) Crystal structure of TIPS-pentacene and the dimer model constructed for MRMP2 calculations, where the side group is simplified as alkyne. (b) Crystal structure of rubrene and the dimer model for MRMP2 calculations, where the side group is neglected. (c) Energy diagram showing the vertical (solid lines) and relaxed (dashed lines) excitation energies to the Frenkel exciton, XT (blue), and triplet pair, TT (purple), in TIPS-pentacene (TIPS-PN) and rubrene (RB), together with those of the herringbone dimers of anthracene (AN), tetracene (TN), and pentacene (PN). (d) Diagram of electron configurations of XT, TT, and CT states in the three-site, nine-state model.

Figure 2

Cumulative populations of ${\mathrm{XT}}_n$ (blue), ${\mathrm{CT}}_n$ (red), and ${\mathrm{TT}}_n$ (purple) in the quantum dynamics calculations of singlet fission in TIPS-pentacene. (a) Initial exciton is localized on the center molecule (${\mathrm{XT}}_2$), and all electronic couplings are considered. Only one of (b) direct and (c) CT-mediated pathways are considered. Dynamics from (d) bright delocalized exciton with the initial amplitude $({\mathrm{XT}}_1,{\mathrm{XT}}_2,{\mathrm{XT}}_3)=(1/\sqrt{3},1/\sqrt{3},1/\sqrt{3})$, and from (e) dark exciton, $({\mathrm{XT}}_1,{\mathrm{XT}}_2,{\mathrm{XT}}_3)=(1/\sqrt{3},-1/\sqrt{3},1/\sqrt{3})$.

Figure 3

(a) Overlap integral $⟨{\mathrm{\Psi }}_{\mathrm{T}\mathrm{T}}|{\mathrm{\Psi }}_{\mathrm{X}\mathrm{T}}⟩$ of vibrational wave packets on the XT and TT states during singlet fission in TIPS-pentacene (black), and those considering only the direct (blue) and superexchange (red) pathways, where the initial exciton is localized on ${\mathrm{XT}}_2$. The overlap for rubrene (green) is negligibly small. (b) Potential energy surface of TT (color) and XT (gray scale) states of TIPS-pentacene in an effective-modes $(x_1^{\prime },x_2^{\prime })$ representation [19]. The solid and dashed red circles indicate the Frank-Condon region from the ground state and the spread of the wave packet, respectively.

Figure 4

(a) Potential curve with respect to displacement along the short molecular axis as obtained from DFT calculations of three rubrene molecules extracted from the crystal. To account for the steric hindrance from the other side of the molecular layer, the mirror image of the calculated potential curve is added. (b) TT-XT (black) and TT-CT (red) electronic couplings by MRMP2. (c) Schematic illustration of the conical intersection at the $C_{2h}$ $\pi$ stacking (red circle) and the avoided crossing due to symmetry breaking, where the black and blue parabolas illustrate the adiabatic potentials and the seam of diabatic potentials, respectively. (d) TT population during singlet fission in rubrene considering a bright initial exciton. Two intermolecular modes (connecting sites 1 and 2, and sites 2 and 3, respectively) are considered, where $⟨N_{\text{phonon}}⟩$ are zero (blue), three (black), and six (red). (e) The black line is identical to that in Fig. 4, which is compared with TT evolution considering only one of the direct (green) and superexchange (purple) pathways.