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 singlet charge-transfer state (<sup>1</sup>CT), triplet charge-transfer state (<sup>3</sup>CT), and locally excited triplet state (<sup>3</sup>LE). 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 <sup>3</sup>CT 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 relation 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 ~ 30 s) of emission including prompt fluorescence, TADF, <sup>3</sup>CT phosphorescence, and <sup>3</sup>LE phosphorescence. We obtained the energy band of CT states where <sup>1</sup>CT and <sup>3</sup>CT states are distributed in the range of 2.85-3.00 eV and 2.64-2.96 eV, respectively. We tested various global hybrid and long-range corrected functionals for the TD-DFT calculation of <sup>3</sup>CT 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 robust dihedral angle scan of <sup>3</sup>CT 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 angle of donor-acceptor (θ<sub>D-A</sub>) and acceptor-linker (θ<sub>A</sub>) of TPSA in frozen toluene lie within the range of 70°≤θ<sub>D-A</sub>≤90° and 0°≤θ<sub>A</sub>≤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.
