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 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.

Dihedral Angle Distribution of Thermally Activated Delayed Fluorescence Molecules in Solids Induces Dual Phosphorescence from Charge-Transfer and Local Triplet States

“…In addition, the rotation of the two peripheral phenyls linked to the triazine has a minor effect on the CT energy of the TADF molecules. 24 Hence, we considered the rotation of the dihedral angle between the acceptor (triazine) and the linker (θ A ) and the dihedral angle between the donor (acridine) and the linker (θ D ) as the major origin of the energy distribution of the CT states (Figure 6a). The geometries for the 1 CT/ 3 CT energy scan along the dihedral angles were obtained as follows: (1) The 1 CT geometries of the TADF molecules were optimized with the CAM-B3LYP functional, (2) The 3 CT geometries were optimized with the M06-2X functional using the optimized 1 CT geometries as the input geometries, (3) dihedral angles (θ A /θ D ) were manually modified for the CT energy scan.…”

“…61−63 The detailed procedure of the TD-DFT calculations is shown in our previous report. 24 The CT energy scans along the dihedral angles and their corresponding NTOs are shown in Figures 6a,b,d and S12− S15. At θ D = 90°, the NTOs for the 1 CT and 3 CT states of TPSA are almost the same, and the electron and hole orbitals are separated, resulting in a small ΔE ST of 0.02 eV.…”

“…We set the upper limit of potential energy as 5 kJ to set the range of the dihedral angle distribution to reproduce the energy band of 1 CT states of the TADF molecules. 24 The ground-state solution-phase energies differ among the TADF molecules due to the steric hindrance of methyls substituted at the phenyl linkers. The energy distribution of S 1 ( 1 CT) and T 1 ( 1 CT) energies of the TADF molecules induced by the distribution of θ A and θ D are shown in Figure 6f, and the combined distributions are shown in Figure 6g.…”

“…However, the energy distribution of 1 CT and 3 CT states stemming from the conformational distribution of TADF molecules in immobile organic solid films or frozen solutions are not considered in many reports that cover the RISC process of TADF molecules. 23,24 Especially, the energy distribution of 3 CT states is rarely considered, while the energy distribution of 1 CT states is often considered by timeresolved spectra and transient photoluminescence (PL) decays. 25−32 In addition, 3 CT and 1 CT states are often considered degenerate states, assuming the orthogonal D−A structure of the TADF molecules.…”

Photophysical Properties of Benzophenone-Based TADF Emitters in Relation to Their Molecular Structure

“…Tamm−Dancoff approximation (TDA) has been used, as this approach avoids unphysically stable triplet states in CT molecules while maintaining a good description of the singlet excited states, hence yielding more accurate and balanced results for ΔE ST calculations. 40,41 The absorption spectra as well as the energies of the lowest lying singlet and triplet excited states have been computed with different functionals (B3LYP, 42−45 BLYP, 42,45,46 PBE0, 43,45,47,48 M06-2X, 42,45,49 CAM-B3LYP, 42,45,50,51 and LC-ωPBE 52−54 ) and 6− 31 + G(d,p) basis set, and the performances of these functionals have been evaluated with respect to experimental data. Absorption spectra have been modeled, including the effects of vibrational and thermal motion via Wigner distribution sampling of the equilibrium region on the potential energy surface by generating 40 conformations via the Newton-X program 55 on the equilibrium region of the PES.…”