TD-DFT and Experimental Methods for Unraveling the Energy Distribution of Charge-Transfer Triplet/Singlet States of a TADF Molecule in a Frozen Matrix

Reverse intersystem crossing (RISC) rate of a thermally activated delayed fluorescence (TADF) molecule is sensitive to the energy alignment of the singlet charge-transfer state (¹CT), triplet charge-transfer state (³CT), and locally excited triplet state (³LE). However, the energy distribution of the charge-transfer states originating from the conformational distribution of TADF molecules in a solid matrix inevitably generated during the preparation of a solid sample due to the rotatable donor-acceptor linkage is rarely considered. Moreover, the investigation of the energy distribution of the ³CT state is both theoretically and experimentally difficult due to the triplet instabilities of time-dependent density functional (TD-DFT) calculations and difficulties in phosphorescence measurements, respectively. As a result, the relationships between conformational distribution, configurations of excited state transition orbitals, and excited state energies/dynamics have not been clearly explained. In this work, we determined the energy distribution of CT states of the TADF emitter TPSA in frozen toluene at 77 K by the measurement of time-resolved spectra in the full time range (1 ns to 30 s) of emission including prompt fluorescence, TADF, ³CT phosphorescence, and ³LE phosphorescence. We obtained the energy band of CT states where ¹CT and ³CT states are distributed in the range of 2.85-3.00 and 2.64-2.96 eV, respectively. We tested various global hybrid and long-range corrected functionals for the TD-DFT calculation of ³CT energy of TPSA and found that only the M11 functional shows consistent results without triplet instability. We performed TD-DFT with the M11* functional optimized for a robust dihedral angle scan of ³CT states without triplet instability and reproduced the energy band structure obtained from the experiment. Through TD-DFT and experimental investigations, it is estimated that the dihedral angles of donor-acceptor (θ_D-A) and acceptor-linker (θ_A) of TPSA in frozen toluene lie within the range 70° ≤ θ_D-A ≤ 90° and 0° ≤ θ_A ≤ 30° respectively. Our results show that the dihedral angle distribution must be considered for further investigation of the photophysics of TADF molecules and the development of stable and efficient TADF emitters.