Mechanism of Enhanced Triplet-Triplet Upconversion in Organic Molecules

We use time-dependent density functional theory (TDDFT) to investigate the mechanism of efficient triplet-triplet upconversion (TTU) in certain organic materials. In particular, we focus on materials where some singlets are generated in a two-step spin-nonconserving process (T₁ + T₁ → T₂ → S₁). For this mechanism to contribute significantly, the intersystem crossing (ISC) from the high-lying triplet to the singlet (T₂ → S₁) must outcompete the internal conversion (IC) to the low-lying triplet (T₂ → T₁). By considering multiple families of materials, we show that the T₂ → S₁ ISC can be enhanced in a number of ways: the substitution of electron-donating (ED) and electron-withdrawing (EW) groups at appropriate positions; the substitution of bulky groups that distort the molecular geometry; and the substitution of heavy atoms that enhance the spin-orbit coupling (SOC). In the first two cases, the enhancements are consistent with El-Sayed's rule in that rapid T₂ → S₁ ISC requires significant differences in the characters of the S₁ and the T₂ wavefunctions. Together, these effects enable a wide tunability of T₂ → S₁ ISC rates over at least 5 orders of magnitude. Meanwhile, the T₂ → T₁ IC is inhibited in these systems due to the large T₂ - T₁ energy gap >0.5 eV, which entails a high energy barrier to the T₂ → T₁ IC and the prediction of a slow rate regardless of the substituents or the presence of heavy atoms. In this way, tuning the T₂ → S₁ ISC appears to provide an effective strategy to achieve systematic improvement of TTU materials.