UNDERSTANDING THE INTERNAL HEAVY-ATOM EFFECT ON THERMALLY ACTIVATED DELAYED FLUORESCENCE: APPLICATION OF ARRHENIUS AND MARCUS THEORIES FOR SPIN-ORBIT COUPLING ANALYSIS

The mechanism of heavy-atom effect on organic blue TADF emitters is investigated using a combined Arrhenius and Marcus theories approach. Basic molecular design principles of such hybrid organic TADF materials are formulated.


Section S2. Detailed discussion on spectral properties
Analysis of the nature of lowest excited electronic states on the basis of steady-state measurements. In nonpolar ZNX films at room temperature (RT), all three emitters (H, diCl, diBr) show vibronically-structured emission band with a maximum localized at 465-467 nm ( Figure 1C).
The onsets of fluorescence spectra (λonset, Figures S6A-C) were determined to be around 423, 418 and 421 nm for H, diCl, and diBr, respectively, which gives the S1-state energies of 2.93, 2.97 and 2.95 eV, respectively ( Table S1). In more polar PMMA, the emission becomes broad and structureless, and shifts to 492-499 nm range. The onsets of fluorescence in PMMA were estimated to be around λonset = 430, 427 and 428 nm for H, diCl, and diBr respectively (Figures S6D-F), which gives the energy levels of 1 CT states at 2.88, 2.90 and 2.89 eV. Such positive solvatofluorochromism typical for most of TADF emitters arises from the charge transfer (CT) character of the S1-state [S1].
To reveal the nature and the energy of the lowest triplet excited states the phosphorescence measurements at low temperature were performed. As shown in Figures S6A-C, the phosphorescence spectrum of H in ZNX is red-shifted and has different shape as compared to that of fluorescence, with onset around λonset = 437 nm, which gives the energy level at 2.84 eV. The presented phosphorescence spectrum profile perfectly matches the shape of emission of the isolated acceptor fragment that was measured separately, as depicted in Figure S6G. Taking into account the previous studies of similar compound DMAC-TRZ [S2] our results indicate that the lowest triplet excited state of H in ZNX is of the localized nature ( 3 LEA) originating from the acceptor fragment.
The same conclusion was made for the diCl and diBr derivatives, as no significant differences in the phosphorescence spectra of diCl and diBr in ZNX were observed. In fact, as the halogens were introduced into donor fragment, they were not expected to affect the acceptor-localized 3 LEA state.
With respect to this, the energy gap ΔE1CT-3LE between lowest excited singlet ( 1 CT) and triplet ( 3 LEA) states in ZNX was estimated to be of 94, 133 and 114 meV for H, diCl and diBr, respectively ( Table   S1).
In more polar PMMA films, the phosphorescence spectrum of H broadens, becomes structureless and red-shifted as compared to the one measured in ZNX ( Figure S6D). It should be noted, that in PMMA at 10K, to distinguish phosphorescence from the 1 CT-fluorescence, careful S5 analysis of TRES was conducted. As mentioned above, the specific feature of the 1 CT-fluorescence in DF region is its gradual blue-shift with the delay time. In PMMA films at 10K, the emission does not shift after the 50µs delay time ( Figure S8). Its onset value in H falls around 443 nm, which is 0.04 eV below the 3 LEA state. Such observation indicates, that in PMMA phosphorescence occurs from the triplet charge-transfer ( 3 CT) state, energy of which is estimated around 2.80 eV. Similar observations for diCl and diBr gave the 3 CT levels of 2.81 eV (onset at 441 nm, Figures S6E and   S1F). Taking into account these energies, the values of energy gap between lowest 1 CT and 3 CT states (ΔE1CT-3CT) were estimated as 85, 95 and 86 meV, as summarized in Table 1  Phosphorescence spectra of isolated fragments: acceptor (G) and donors of H, diCl and diBr (H) were measured at 10 K with 30ms time delay under excitation λexc=320 nm. Table S1. Photophysical parameters.

Time-resolved emission spectra and emission decays
As can be seen in Figure S7, the PL decay for each of studied emitters contains two well-separated areas in nano-and microsecond regimes corresponding to the prompt and delayed emission. The PL intensity decay profiles measured in the presence of oxygen differ from those recorded in the vacuum due to quenching by molecular oxygen, which confirms that TADF is mediated by triplet state(s). To verify whether the delayed emission originates from the 1 CT-state, detailed time-dependent analysis of PL spectra was carried out (Figures S8A and S9A). Through the entire timescale of PL spectra of each emitter, all the collected spectra have roughly similar shape and maximum (Figures S8B-D, S9B-D). Therefore, the fast component can be identified as prompt fluorescence (PF), occurring from the directly excited 1 CT-state, whilst the slow one is due to the delayed fluorescence (DF), where emission from the 1 CT-state is preceded by ISC and rISC.
For time-resolved emission spectra (TRES) in PF region over the first 100 ns, the emission maximum red-shifts from 452 to 463 nm in ZNX and 473 to 497 nm in PMMA (Figures S8-S11). In S9 the DF regime starting from 1 µs, TRES undergo the red shift from 455 nm to 481 nm. Such spectral behavior can be explained by the distribution of 1 CT states due to the coexistence of different emitter conformations. As suggested in previous reports [S2, S3], the most crucial conformers differ by the dihedral angle between donor and acceptor units (θ, Figures 1B and 1D, main text). At the very early stages of PF, the blue-shifted fluorescence spectrum originates from the conformers with the most deviated θ-value from the optimal 90 o . The deviation from orthogonality leads to the increased overlap of molecular orbitals (MOs) involved in the CT transition, and thus better conjugation of donor and acceptor fragments. For this reason, such conformers have higher energies of 1 CT states and higher value of S1-S0 oscillator strength, which enables relatively fast emission. As θ approaches to orthogonal, the 1 CT state becomes more stabilized due to decreased conjugation between D and A, which leads to red-shift of emission and lower S1-S0 oscillator strengths. Such conformers emit at the late PF. The opposite behavior is observed for the DF region. The red-shifted emission is responsible for the early-DF, whilst in the late-DF blue shift is observed. As the most orthogonal conformers have the smallest energy gap between singlet and triplet state ΔEST, which according to Marcus-Hush equation (eq. 2 in main text) leads to the highest rISC rates, their red-shifted DF appears first.
Consequently, as the θ-deviation increases, ΔEST increases too, rISC becomes slower and the DF spectrum gradually shifts to shorter wavelengths.
The distribution of 1 CT-state energy and relatively constant energy of the 3 CT-state ( Figure   S12A-C), explains relatively high values of ΔE1CT-3CT mentioned above.    Figure S12. PL intensity decay profiles of H, diCl, and diBr in PMMA with PL spectra taken at different time delays measured at 10 K. Excitation wavelength λexc=370 nm.
. S17 Section S3: Determination of photophysical parameters PL decay curves (presented in Figures S8A, S9A and S13) were fitted with the multiexponential equation: where is the pre-exponential factor, τ is the decay time and ( ) is emission intensity. Average lifetimes of prompt (τ ) and delayed fluorescence (τ ) were determined using the following formula: where is fractional contribution of -th component expressed as: The ratio of DF and PF quantum yields ⁄ was determined as follows [S4]: where ( ) and ( ) is the pre-exponential factor of delayed and prompt fluorescence component, respectively; τ ( ) and τ ( ) is the lifetime of delayed and prompt fluorescence component, respectively. The rate constants of radiative ( ) and nonradiative ( ) decay and intersystem crossing ( ) are given by equations: here φ is PLQY ( + ). Further, the quantum yields for ISC and rISC were calculated as Finally, the rate constant of rISC ( ) was calculated as Photophysical parameters are presented in Tables 1 (main text) and S4. Time-resolved PL measurements were conducted within the temperature range of 298-10 K ( Figure   S13). The PL decays in the 298 -150 K range contained only prompt and delayed fluorescence, thus phosphorescence did not interfered. The latter temperature range was thus used for further investigations. The PL decay analysis as described in section S3 enabled kISC and krISC constant rates at various temperatures (Tables S5, S6). To determine the energy barriers Ea for ISC and rISC, the Arrhenius law equation was applied: where k B stands for Boltzmann constant, and A is pre-exponential constant ( Table 2, main text).   Figure S14. Arrhenius plots for emitters dispersed in ZNX.  Figure S15. Arrhenius plots for emitters dispersed in PMMA.

S22
More detailed information can be derived using the Marcus-Hush equation: where V is SOC constant, ħ is reduced Planck's constant, λ is sum of internal and external (λsolv) reorganization energies for respective transition, ΔEST is the energy gap between singlet 1 CT and respective triplet state. This semiclassical expression, commonly used to predict constant rates for nonradiative transitions in D-A structure of TADF compounds can be connected with the Arrhenius equation (S11) by the following relations: Consequently, by matching the ΔEST and λ parameters to satisfy both relations, where Ea and are derived from Arrhenius plot, it is possible to estimate empirical SOC values V for each transition, as it is presented in Table 2 (main text).
As discussed in main text, because ISC transition does not require thermal activation under all conditions investigated (Ea = 0), the relation (S14) predicts the same values of ΔEST and λ: Assuming equal values of ΔEST for both ISC and rISC (S6): the ΔEST and λ values can be obtained from eq. (S14) and Ea ( Table 2). The VISC and VrISC parameters are then available from eq. (S14) and A ( Table 2): The assumption (S16) seems to be valid because regardless of the ISC and rISC mechanism, the ΔE1CT-3CT and ΔE1CT-3LE(A) values were determined to be similar (Table 1). On the other hand, the changes in the obtained VISC and VrISC values are much greater than those in ΔEST. Therefore, the assumption (S16) introduces minor uncertainty and does not affect the most important conclusions made for ISC and rISC mechanisms.
By performing single-point TD-DFT calculations for H, diCl and diBr, we determined the values of inner reorganization energies λin for each ISC transition, namely: using the following formulas: where:

3LE(A) 1CT
-TD-DFT energy of 3 LE(A) excited state at the 1 CT optimized geometry The λout value of 0.05 eV was used for all calculations.

S28
Calculations for rISC rate constants. rISC constant rates were calculated using Marcus-Hush formula (S12), computationally predicted λ values and experimentally determined ΔEST values.
Due to the coexistence of excited molecules in various triplet states, their contribution to the rISC transition was considered as proportional to the population of respective triplet states ( Table S10). Figure S16. Alignment of the excited triplet states of investigated emitters.

Determination of population of lowest triplet excited states
Relative population χ of lowest triplet excited states was determinated using Boltzmann distribution law: where Δ denotes the energy difference between lowest triplet state (T1) and respective triplet state (Ti): = exp (− (T − T 1 ) ).

Reorganization energy λ 3CT→1CT [ ] consists of two terms (inner λ 3CT→1CT
in [ ] and outer λ 3CT→1CT out ): The first term λ 3CT→1CT in [ ] refers to the energy that is dissipated by molecule during relaxation to the equilibrium geometry in a given state.
It can be calculated using the formula: where: 1CT [ ] -TD-DFT energy of 1 CT state at 3 CT-state geometry calculated for i-th rotamer with dihedral angle, 1CT − TD-DFT energy of 1 CT state at optimized 1 CT-state geometry.
The second term λ 3CT→1CT out is a measure of solvatation effects, and in case of interaction between excited states with the same nature (CT) it can be approximated as follows: Boltzmann distribution law was used to estimate relative population of rotamers [ ]: where: • [ ]energy calculated for i-th rotamer with dihedral angle, 1CT -energy at optimized 1 CT-state geometry.
Below, complete set of computed parameters for prediction of k 3CT→1CT in H, diCl and diBr within developed rotational model is presented (Tables S12 -S14 and Figures S17 -S19).  Figure S17. Computational parameters for the prediction of k 3CT→1CT in H calculated within rotational model.  Figure S18. Computational parameters for prediction k 3CT→1CT in diCl calculated within rotational model.

Table S14
Computational parameters for k 3CT→1CT prediction in diBr using rotational model.  Figure S19. Computational parameters for the prediction of k 3CT→1CT in diBr calculated within rotational model.

S35
The statistically weighted oscillator strengths (f) values for all rotamers were calculated according to the procedure reported previously. [S3] Thus obtained f value slightly increases with the introduction of halogen from 0.016 (H) to 0.020 (diCl and diBr). One can thus suggest that the value of oscillator strength reversely correlates with the CT strength.

S36
Section S7: Computational details for the prediction of rISC rate constant within the vibrational model via direct 3 CT-1 CT transition Within the vibrationally-assisted direct SOC model presented below, total k 3CT→1CT consists of fractional constant rates k 3CT→1CT , originating from one θ-rotamer (θ =90°) at various deviations from optimal geometry induced by low-frequency vibrations (<100 cm -1 ): where is -th vibrational mode, is the number of considered modes (here = 8, see Figure   S19). shown.

S37
Single point TD-DFT calculations of energetic and SOC parameters were performed for various modifications of the S0-state 90-rotamer structure, in which each vibration was "scanned" by changing its amplitude in a -2 -+2 range. Such structures were generated using Chemchraft software, version 1.8. For the i vibrational mode, fractional constant rate k 3CT→1CT was performed taking into account contribution of each vibrational isomer as follows: where: • [ ] -Boltzmann distribution function, molar fraction of -th isomer with amplitude in the vibration, • -number of calculated isomers, usually m = 29 unless mentioned differently.
Reorganization energy consists of two terms (inner and outer): The first term λ 3CT→1CT in [ ] refers to the energy that is dissipated by the molecule relaxing to the equilibrium geometry at given state. It can be calculated using the formula: where: 1CT [ ] − TD-DFT energy of 1 CT state at 3 CT-state geometry calculated for j-th isomer within vibration, • 1CT, 1CT [ 0 ] − TD-DFT energy of 1 CT state at optimized ( 0 refers to amplitude = 0) 1 CTstate geometry calculated within vibration.
The second term λ 3CT→1CT out is a measure of solvatation effects, and in case of interaction between excited states with the same nature (CT) can be approximated as follows: Boltzmann distribution law was used to estimate relative population of isomers ( [ ]), which was calculated for the ground S0-state: [ ]energy calculated for j-th isomer within the vibration at S0 state, [ 0 ] -energy at the S0-state optimized geometry.
At the end, contribution of the 3 CT-1 CT transition rate constant from each vibrational mode µ 3CT→1CT to the total k 3CT→1CT was calculated (see Table S18) using: As an example, below we present a complete set of computed parameters for the prediction of the 3 CT-1 CT transition rate constant within the first vibrational mode (k 3CT→1CT 1 ) in H, diCl and diBr (Tables S15 -S17 and Figures S20 -S24).   Figure S22. Computational parameters for the prediction of k 3CT→1CT 1 in diCl.  Figure S23. Computational parameters for the prediction of k 3CT→1CT 1 in diBr.  Figure S24. Computed fractional rates k 3CT→1CT for various vibrational modes.

Figure S25
Computed SOC dependences on amplitudes of various vibrational modes.

S44
Section S8: The assumptions towards rotational-vibronic model of direct 3 CT-1 CT transition Analysis of the results obtained by rotational and vibronic models can lead to the following conclusions. The rotational model describes SOC enhancement of the 3 CT-1 CT transition thanks to the specific molecular rotationsdeviations of the θ dihedral angle. Such a model thus reflects the structural diversity of emitter in macroscopic condenced medium and takes into account only most important conformations -θ-rotamers. The rotational model seems to be optimal solution for the description of photophysics of light-atom emitters with orthogonal structure.
The presented vibronic model describes further SOC enhancement of the 3 CT-1 CT transition in selected emitter molecule (θ-rotamer) thanks to the low-energy molecular vibrations. Analysis of the effect of relatively low-amplitude atomic movements on the electronic structure provides fine prediction of SOC, energy gaps and finally spin-flip rate constants.
Obviously, complete TADF model should combine such rotational and vibronic models. For all θ-rotamers existing at room temperature, the effect of molecular vibrations on the electronic structure should be analyzed quantitatively. This task is, however, extremely time-consuming and computationally expensive.
To approximate such a rotational-vibronic model, we assumed that vibrational SOC enhancement in the 90°-rotamer is similar to that in other θ-rotamers. To estimate the value of such enhancement, relative contribution of transition via the ω1 rotational channel versus all vibrational channels was used: µ 3CT→1CT , calculated for the 90°-rotamers of H, diCl, and diBr (Table S18). The statistical sum of k 3CT→1CT obtained from rotational model (Tables S15-S17) was divided by the µ 3CT→1CT 1 giving rotational-vibronic values of k 3CT→1CT presented in Table S19. Such values showed the best correlation with the experimental rISC rate constants confirming the correctness of the above mentioned assumptions. 1.09 1.10 5.05 a -experimental determination of rate constant described in Section S3: Determination of photophysical parameters; b -prediction of rate constant within "rotational" model described in Section S6: Computational details for prediction rISC rate constant within rotational model via direct 3 CT-1 CT transition; c -prediction of rate constant within "vibrational" model described in Section S7: Computational details for the prediction of rISC rate constant within rotational model via direct 3 CT-1 CT transition.

S46
Section S9: Molecular electronic orbitals Molecular orbitals involved in the formation of key excited electronic states are presented below.

Figure S26. Computed MOs
As can be seen from the respective MO, the 1CT and 3CT states are formed via electron density transfer from DMAC donor to aryl-s-triazine acceptor. The 3 LEA state is formed due to redistribution of electronic density within the acceptor fragment. The 3 LED state is formed due to redistribution of electronic density within the donor fragment. These data support the conclusions made on the basis of spectral analysis in main text and page S4-S5.