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

Abstract

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 (θD-A) and acceptor-linker (θA) of TPSA in frozen toluene lie within the range 70° ≤ θD-A ≤ 90° and 0° ≤ θA ≤ 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.