Thermally activated delayed fluorescence: A critical assessment of environmental effects on the singlet–triplet energy gap

Abstract

The effective design of dyes optimized for thermally activated delayed fluorescence (TADF) requires the precise control of two tiny energies: the singlet-triplet gap, which has to be maintained within thermal energy, and the strength of spin-orbit coupling. A subtle interplay among low-energy excited states having dominant charge-transfer and local character then governs TADF efficiency, making models for environmental effects both crucial and challenging. The main message of this paper is a warning to the community of chemists, physicists, and material scientists working in the field: the adiabatic approximation implicitly imposed to the treatment of fast environmental degrees of freedom in quantum-classical and continuum solvation models leads to uncontrolled results. Several approximation schemes were proposed to mitigate the issue, but we underline that the adiabatic approximation to fast solvation is inadequate and cannot be improved; rather, it must be abandoned in favor of an antiadiabatic approach.

Effective models for TADF: the role of the medium polarizability

“…The importance of properly accounting for spin-vibronic terms, well beyond the Marcus or MLJ models, has been very clearly expressed by Penfold et al 14 In their approach, using a diabatic basis, with Q independent SOC among basis states, they regain the Q -dependence of the adiabatic SOC matrix elements accounting for the non-adiabatic mixing of different diabatic states, getting closed formulas thanks to a perturbative treatment. In our essential state model 34 the mixing between the CT and the LE triplets, is parametrized to reproduce the adiabatic Q -dependent SOC interaction and singlet–triplet gap, as obtained from TD-DFT. Then RISC and ISC rates are obtained via a direct non-adiabatic diagonalization of the adopted effective Hamiltonian in an approach that fully accounts for non-adiabatic phenomena and the anharmonicity of the system, without the need to rely on perturbative expansions for the spin-vibronic matrix elements.…”

“…The effective model developed for DMAC–TRZ in ref. 34 opens the way to a nominally exact calculation of RISC, ISC and radiative rates fully accounting for anharmonicity and non-adiabaticity. It also allows to investigate the effects of a fine-tuning of model parameters, showing, e.g.…”

“…Since the electronic degrees of freedom of the matrix are faster than the molecular degrees of freedom of interest, the antiadiabatic approximation can be adopted to renormalize out the medium degrees of freedom, leading to a very simple and inspiring effective molecular Hamiltonian that has precisely the same expression as in eqn (2), but with a renormalized z value: 32,34 …”

“…In any case, we feel that the overall agreement is very good considering that we are exploiting the same model that was previously defined and parametrized against TD-DFT results and validated against experiment. 34…”

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

“…Among those environmental effects, we mention thermal fluctuations of molecular conformations or microscopic electronic polarization effects in amorphous films of carbazole derivatives [8], thus, opening a whole world of future studies and applications around this unexpected issue. However, for solvation effects, current implementations of continuum solvation models should be employed with caution since it could lead to spurious excitedstate energy inversion [9].…”