Accurate Treatment of Charge-Transfer Excitations and Thermally Activated Delayed Fluorescence Using the Particle-Particle Random Phase Approximation.

Thermally activated delayed florescence (TADF) is a mechanism that increases the electroluminescence efficiency in organic light-emitting diodes by harnessing both singlet and triplet excitons. TADF is facilitated by a small energy difference between the first singlet (S1 ) and triplet (T1 ) excited states (Δ E(ST)), which is minimized by spatial separation of the donor and acceptor moieties. The resultant charge-transfer (CT) excited states are difficult to model using time-dependent density functional theory (TDDFT) because of the delocalization error present in standard density functional approximations to the exchange-correlation energy. In this work we explore the application of the particle-particle random phase approximation (pp-RPA) for the determination of both S1 and T1 excitation energies. We demonstrate that the accuracy of the pp-RPA is functional dependent and that, when combined with the hybrid functional B3LYP, the pp-RPA computed Δ E(ST) have a mean absolute deviation (MAD) of 0.12 eV for the set of examined molecules. A key advantage of the pp-RPA approach is that the S1 and T1 states are characterized as CT states for all of experimentally reported TADF molecules examined here, which allows for an estimate of the singlet-triplet CT excited state energy gap (Δ E(ST) = 1 CT - 3 CT). For experimentally known TADF molecules with a small (<0.2 eV) Δ E(ST) in this data set, a high accuracy is demonstrated for the prediction of both the S1 (MAD = 0.18 eV) and T1 (MAD = 0.20 eV) excitation energies as well as Δ E(ST) (MAD = 0.05 eV). This result is attributed to the consideration of correct antisymmetry in the particle-particle interaction leading to the use of full exchange kernel in addition to the Coulomb contribution, as well as a consistent treatment of both singlet and triplet excited states. The computational efficiency of this approach is similar to that of TDDFT, and the cost can be reduced significantly by using the active-space approach.