Modulating Efficiency and Color of Thermally Activated Delayed Fluorescence by Rationalizing the Substitution Effect

Thermally activated delayed fluorescence (TADF) constitutes the process by which third-generation organic light-emitting diodes (OLEDs) are being designed and produced. Despite several years of trial-and-error attempts, mainly driven by chemical intuition about how to improve a certain aspect of the process, few studies focused on the in-depth description of its two key properties: efficiency of the T1 → S1 intersystem crossing and further S1 → S0 emission. Here, by means of a newly developed theoretical formalism, we propose a systematic rationalization of the substituent effect in a paradigmatic class of OLED compounds, based on phenothiazine-dibenzothiophene-S,S-dioxide, known as PTZ-DBTO2. Our methodology allows to discern among geometrical and electronic effects induced by the substituent, deeply understanding the relationships existing between charge transfer, spin density, geometrical deformations, and energy modulations between electronic states. By our results, we can finally elucidate, depending on the substituent, the fate of the overall TADF process, quantitatively assessing its efficiency and predicting the color emission. Moreover, the general terms by which this methodology was developed allow its application to any chromophore of interest.


Benchmark calculations and solvent effect
A benchmark of DFT functionals and basis sets has been performed in order to select the most suitable level of theory for this study.Moreover, the effect of considering an implicit solvent has been evaluated, using the Polarizable Continuum Model (PCM). 1 Table S1.Benchmark of DFT functionals in gas phase using the SVP basis set.Energies are computed in the corresponding electronic state and shown in eV, relative to the S0 minimum of the axial conformation.

Functional
Axial  S3.Implicit solvent effects calculated by linear response PCM (LR-PCM, through Integral Equation Formalism) and state-specific corrected-linear response PCM (cLR-PCM).The values for toluene and dichloromethane (DCM) vs gas phase refer to the M062X/SVP level of theory.Energies are computed as gaps between the minimum energy of each potential energy surface and the S0 minimum of the axial conformation, hence resulting in an equilibrium approach.For LR-PCM calculations, it can be noted that, with respect to gas phase, the S0-S1 energy gap is slightly blue-shifted for the equatorial conformation, while it is slightly red-shifted for the axial conformation, when considering both toluene and DCM solvents.In any case, the S0-S1 shift is within |0.12| eV, almost within the error of the method.

Axial conformation
Concerning the axial conformation, cLR-PCM calculations confirm qualitatively the results obtained by LR-PCM, by slightly stabilizing T1 and S1 minima in both toluene and DCM.A higher effect is found for the equatorial conformation, where cLR-PCM calculations indicate a more pronounced stabilization of the S1 minimum coupled to a destabilization of the T1 minimum.

Substituent effect on the S1-S0 energy gap: theoretical formalism
An analogous theoretical development as the one presented in the main text for the S1-T1 energy gap can be performed for the S1-S0 energy gap.First, we define its variation due to substitution as: where  0  are the geometrical coordinates of the substituted derivative and  0  are the coordinates of the reference molecule.In this case,  0  refers to the minimum energy structure in the S1 state for the substituted system, while  0  refers to the equivalent point for the unsubstituted system.
The energy differences are defined as: In a similar way as presented in the main text for the T1 state, the energy change induced by the substituent can be expanded in terms of a function series up to first order.This expansion is made around the equilibrium geometry of the unsubstituted system Chr-H (i.e.,  0  ≡ ).In our case, this corresponds to the S1 minimum energy structure: where  (1) represents the constant shift (independent of the coordinates) that the -R substitution induces on the S1 state of the unsubstituted (Chr-H) system.Additionally, the  (1) term provides the first variation of the energy as a function of the coordinates.Similarly to what is done for the T1 state (see main text), taking the gradient of the previous equation, we obtain: This gradient equals zero when  =  0  , leading to: where  0  −  0  is the vector providing the structural displacement of the system after substitution in the S1 state.Therefore,  (1) is the force induced by the substituent as it has been defined elsewhere. 3This force is responsible for the change in the structure upon substitution (from  0  to  0  ) on S1.
Analogously to the case of the S1-T1 energy gap variation (see main text), it is possible to determine the variation of the S1-S0 energy gap due to substitution (-R), giving rise to: The variation of the S1-S0 energy gap due to substitution can be expressed as: The  (1) −  (0) term provides the differential stabilization of the two states due to the presence of the substituent, while the term ( 0  ) T ( (1) −  (0) ) provides the change of the differential structural effect within the chromophore due to the force induced by the substituent.
In the following, we limit our expansion in the energy difference the to zero th -order term.
Analogously to the S1-T1 treatment, it has been assumed that the substituent induced forces are basically the same in both states, and therefore  (1) −  (0) ≈ 0.
Finally, the variation on the S1-S0 energy gap due to substitution is: where the first two terms correspond to the geometrical effect that the substitution induced to the chromophore, while the third term corresponds to the zero th -order differential effect of the substituent on the electronic energy of both S1 and S0 states.For simplicity, this expression can be written as:

Discussion of the four-states model
In this section we aim to compare our findings -regarding the role of the electronic nature of S1 and T1 on the modulation of the S1-T1 energy gap, already discussed in the main text -with the published four-states model. 2 For this purpose, the Mulliken charges at the T1 minimum have been computed for S0, S1 and T1.Then, the charges of the donor and acceptor moieties have been calculated for each electronic state as the sum of the Mulliken charges of the atoms included in each part.Finally, the electronic nature of Locally Excited (LE) or Charge Transfer (CT) states is assigned to S1 and T1: an LE state has the same distribution of the charges as in S0, while for a CT state the charge is localized in a different part of the molecule compared to S0. Analyzing the results shown in Figure S6, a similar conclusion as the one already discussed in the main text and in agreement with the four-states model 2 can be drawn: both S1 and T1 have to be CT states to reach the S1-T1 degeneration region.

Spin-orbit coupling values
Table S4.Sin-Orbit Coupling (SOC) values computed at the T1 minimum geometries.The SOC value of the reference system is given in the first row.The following rows refer to the derivatives, including for each of them the SOC value and the SOC difference with respect to the reference (∆SOC).

Application of the Marcus theory
In this work we modulate S1-T1 and S1-S0 energy gaps through the indicated formalism.In the case of the S1-T1 energy gap, such magnitude () can be directly related to the required activation energy (Δ ≠ ) to populate the S1 state from the T1 minimum.Especially, applying the Marcus theory, it can be shown that: where λ is the reorganization energy and ΔG is the reaction energy.Since Δ ≠ depends quadratically from , both positive and negative values of  (left and right panel of Figure S12) result in a positive Δ ≠ , thus lowering the efficiency with respect to  = 0 (middle panel of Figure S12), corresponding to S1-T1 energy degeneracy at the T1 minimum.

3 .
Figure S1.Geometries corresponding to the T1 minima of the equatorial and axial conformations of the PTZ-DBTO2 reference compound, including the NTOs and the CT character involved in the S1→S0 transition.

Figure S2 .
Figure S2.NTOs and CT character involved in the emissive S1→S0 transition, at the S1 minimum of the PTZ-DBTO2 reference compound.

Figure S6 .
Figure S6.Representation of the S1 and T1 CT character, and classification of the compounds regarding the electronic nature of these two electronic states: CT/CT, CT/LE, LE/CT and LE/LE.The reference compound is shown with a red star.

Figure S8 .
Figure S8.Variation of the CT character in S1 for the derivatives under study, evaluated at the S1 minimum, due to the geometrical effect.

Figure S9 .
Figure S9.Upper panel: Energy stabilization (negative values) and destabilization (positive values) of S0 due to the geometrical effect.Lower panel: Energy destabilization of S1 due to the geometrical effect.

Figure S10 .
Figure S10.Natural transition orbitals involved in the S1→S0 transition computed for the S1 minimum geometry of each compound.

Figure S11 .
Figure S11.a) S1-S0 oscillator strength as a function of the S1 charge transfer character, and b) variation of the S1-S0 oscillator strength with respect to the reference system (5•10 -4 ), for all the derivatives under study.

Figure S12 .
Figure S12.Scheme of the Marcus theory applied to S1 and T1 potential energy surfaces, in the case of S1-T1 inversion.
Figure S13.Representation of the S1-S0 emission energy gap vs. the corresponding S1-T1 energy gap, computed for the 33 derivatives under study, as in Figure10of the main text, but using TD-DFT.Slightly higher S1-T1 energy gaps are found for all compounds.

Table S2 .
Benchmark of basis sets in gas phase using the M062X DFT functional.Energies are shown in eV, relative to the S0 minimum of the axial or equatorial conformation.