Understanding the internal heavy-atom effect on thermally activated delayed fluorescence: application of Arrhenius and Marcus theories for spin–orbit coupling analysis

Abstract

Hybrid organic emitters containing abundant heavy atoms (HAs) are of rapidly growing interest for organic light emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF). As substitutes of expensive and toxic heavy-metals, HAs can accelerate reverse intersystem crossing (rISC), whose low rate is specifically troublesome in blue all-organic TADF materials. Unfortunately, due to complex photophysics even qualitative predictions of the HA effect on organic emitters and hence molecular design are currently very challenging. Here, we report a photoluminescence data analysis approach for investigations of the TADF mechanism based on empirical spin–orbit coupling constants. Using this approach, heavy-halogen derivatives of a popular blue TADF emitter are investigated to understand the mechanism of the HA effect and molecular design fundamentals of high-efficiency TADF materials bearing HAs. Different HA effects on direct and reverse ISC were revealed. We thus conclude that to improve TADF in organic emitters (i) HA should participate in low-energy molecular vibrations which activate rISC between the lowest excited triplet and singlet states of the charge-transfer (CT) character and (ii) ISC should be minimized through a large energy gap between the ¹CT-state and HA-affected locally-excited (³LE) triplet state.

---

Introduction

Pure organic materials with thermally activated delayed fluorescence (TADF) have been extensively investigated recently with an aim to replace heavy-metal complexes in organic light emitting diodes (OLEDs). The tempting prospect of minimization of the use of expensive and toxic rare-earth metals stimulates numerous efforts to develop highly efficient all-organic TADF materials which meet the specific demands of OLED technology. The most demanded here remains the efficient transformation of triplet excitons dominating under electric excitation to the light emission. Since the emission from the triplet state is conditioned by the change of spin, a spin-forbidden process, the rate and efficiency of such emission are usually low, which makes triplet harvesting a challenging task for organic materials.^1,2 Thanks to stable emission color, TADF is regarded as one of the best triplet harvesting approaches. Triplet excitons are converted to the singlet ones via reverse intersystem crossing (rISC) and thus light emission always occurs from the S₁ state of the emitter (Fig. 1A). Due to the spin-forbidden nature of the T₁–S₁ transition, the main limitation of TADF is the rISC rate, which depends on the strength of the spin–orbit coupling (SOC). After almost a decade of successful implementation of the first general molecular design strategy of TADF materials for OLEDs,³ achieving fast rISC in the nanosecond domain as demanded by the OLED technology remains the most challenging issue, especially for the deep-blue emitters. Obviously, our scarce knowledge about the origin, mechanisms and ways of manipulation of SOC in TADF emitters is a serious barrier for further progress in this field.

Fig. 1 (A) General diagram of triplet exciton utilization via rISC, (B) structures of the investigated TADF emitters, (C) steady-state PL of the investigated compounds in ZNX and PMMA, (D) PL decays of investigated compounds, excitation wavelength λ_exc = 370 nm, (E) PL intensity decay of H with evolution of PL onset indicated, and (F) calculated dependence of the ¹CT-state energy on the dihedral angle θ.

In light-atom organic materials, SOC is too low to enable fast rISC.⁴ The introduction of cheap and abundant heavy atoms (HAs) into organic TADF emitters seems to be the most obvious and promising way to increase SOC,^5–8 and accelerate rISC, generally referred to as a “heavy-atom effect”.⁹ Undoubtedly, modification of organic emitters with the heavy atoms of groups 14–17 opens new prospects in the engineering of heavy-metal-free materials for optoelectronics. Unfortunately, at the current state of knowledge, even qualitative prediction of the HA effect on organic TADF emitters is extremely challenging. The attachment of HA at different positions of the emitter can have a different effect on intersystem crossing (ISC), rISC, and other processes, intermolecular interactions and eventually TADF efficiency.

From the point of view of the molecular design of TADF emitters, the idea of introducing HA into organic emitters can be controversial. On the one hand, HA can accelerate rISC and thus help to convert triplet states into excited singlet ones, which is favorable for TADF emitters. On the other hand, HA can accelerate ISC thus leading to the conversion of the emissive S₁ state to triplet ones. This is highly undesired for a TADF emitter, as it decreases the amount of singlet excitons in an OLED device which could be deactivated radiatively. The rapidly growing number of publications focusing on such hybrid organic emitters with nonmetallic HAs indicates their complex and non-intuitive effect on TADF.^10–17 On the one hand, the reports on the increase in rISC rate constant (k_rISC)¹⁰ and even achievement of its record high value of 6 × 10⁷ s⁻¹,¹¹ shortened lifetimes of delayed fluorescence (DF)¹² and excellent OLED performance with suppressed efficiency roll-off¹³ indicate the beneficial role of the HA effect. Some other articles however, indicate its complex nature. For example, several articles report on a strong ISC enhancement and a weaker one for rISC¹⁴ or vice versa;¹⁵ some reports conclude negligible HA effect on rISC.¹⁶ Even more surprising is the observation that a TADF emitter with a silicon atom can show an rISC twice as fast as its germanium analogue.¹⁷ Such investigations indicate that HA presence itself does not necessarily warrant rISC acceleration, whilst the demanded selective enhancement of rISC instead of ISC is very challenging.¹⁸ Obviously, none of the literature reports confirm the HA effect in organic emitters to a quantum physical relation derived for atoms: V ∼ Z⁴, where V is a spin–orbit coupling constant and Z is the atomic number.

Taking the above mentioned into account, in this study we aimed to reveal the ways of selective rISC acceleration and define the main principles of molecular design to enable them. To shed light on the complex processes covered by the term “heavy-atom effect”, we performed thorough analysis of the electronic properties and spin–flip mechanisms in a series of (deep)-blue TADF emitters. Chlorine and bromine derivatives of a widely studied emitter 9,10-dihydro-9,9-dimethyl-10-(4-(4,6-diphenyl-1,3,5-triazin-2-yl)phenyl)-acridine (DMAC-TRZ, Fig. 1B) were selected after explanation of its photophysics.¹⁹ To focus on the internal HA effect and distinguish it from the external one, methyl groups were introduced to the side rings of an acceptor fragment which minimized the emitter-emitter intermolecular interactions.²⁰ Temperature and polarity dependent photophysical investigations analyzed within Arrhenius and Marcus theories enabled estimation of SOC, energy gaps and reorganization energies using experimental data. It was found that due to different mechanisms of ISC and rISC, the HA effect manifests in different ways. Whilst ISC is accelerated up to 8 times due to the enhanced SOC between the states of different nature, rISC can be accelerated less than 3 times via vibronic activation of SOC between the states of the same nature. The presented results reveal that introduction of HA can improve TADF in the case of (i) effective activation of specific molecular vibrations involved in rISC and (ii) lack of ISC acceleration to localized triplet states.

Experimental section

Materials

Zeonex® (ZNX, Zeonex480R, density = 1.01 g cm⁻³) or poly-methyl methacrylate (PMMA, 120000 Mw, density = 1.18 g cm⁻³) were purchased from Zeon Europe GmbH and Sigma-Aldrich, respectively. Solvents for the synthesis and spectroscopic measurements were of corresponding grades and were used as supplied.

Synthesis of emitters, isolated donor, and acceptor molecules

10-(4-(4,6-Bis(2-methylphenyl)-1,3,5-triazin-2-yl)phenyl)-9,9-dimethyl-9,10-dihydroacridine (H) was synthesized as described previously.²⁰

Typical halogenation procedure

0.1 mmol of H or 9,9-dimethyl-10-phenyl-9,10-dihydroacridine and 0.22 mmol N-chlorosuccinimide (for diCl and diCl-DMAC) or N-bromosuccinimide (for diBr and diBr-DMAC) were dissolved in 0.5 mL of chloroform and stirred at 55 °C for 12 h in the dark. ¾ of the solvent was evaporated and the residue was treated with methanol. The resulting precipitate was collected and purified using column chromatography on SiO₂ with appropriate hexane-chloroform mixtures as eluents.

10-(4-(4,6-Bis(2-methylphenyl)-1,3,5-triazin-2-yl)phenyl)-2,7-dichloro-9,9-dimethyl-9,10-dihydro-acridine (diCl)

Pale yellow powder, yield 87%. ¹H NMR (500 MHz, CDCl₃, δ): 1.67 (s, 6H) 2.87 (s, 6H), 6.28 (d, J = 8.80 Hz, 2H), 6.94 (d, J = 8.07 Hz, 2H), 7.34–7.64 (m, 10H), 8.31–8.34 (m, 2H), 8.94 (d, J = 7.70 Hz, 2H). ¹³C NMR (250 MHz, CDCl₃, δ): 174.47, 170.01, 139.09, 139.05, 135.87, 131.98, 131.79, 131.38, 131.33, 131.26, 131.20, 126.49, 126.20, 126.18, 125.32, 115.45, 36.43, 30.86, 22.48. MALDI-TOF m/z: calcd for C₃₈H₃₀Cl₂N₄, 613.2 [M + H]⁺; found, 613.4. For ¹H and ¹³C NMR spectra see the ESI† (Fig. S1 and S2).

10-(4-(4,6-Bis(2-methylphenyl)-1,3,5-triazin-2-yl)phenyl)-2,7-dibromo-9,9-dimethyl-9,10-dihydro-acridine (diBr)

Pale yellow powder, yield 91%. ¹H NMR (500 MHz, CDCl₃, δ): 1.67 (s, 6H), 2.87 (s, 6H), 6.22 (d, J = 8.69 Hz, 2H), 7.08 (dd, J = 8.69, 2.27 Hz, 2H), 7.40 (t, J = 7.55 Hz, 4H), 7.44–7.51 (m, 4H), 7.53 (d, J = 2.27 Hz, 2H), 8.29–8.35 (m, 2H), 8.94 (d, J = 8.69 Hz, 2H). ¹³C NMR (250 MHz, CDCl₃, δ): 174.47, 169.99, 144.35, 139.44, 139.09, 136.73, 135.86, 131.97, 131.85, 131.80, 131.33, 131.23, 131.20, 129.41, 128.19, 126.18, 115.91, 113.67, 36.35, 30.94, 22.47. MALDI-TOF m/z: calcd for C₃₈H₃₀Br₂N₄, 701.1 [M + H]⁺; found, 701.2. For ¹H and ¹³C NMR spectra see the ESI† (Fig. S3 and S4).

2,7-Dichloro-9,9-dimethyl-10-phenyl-9,10-dihydroacridine (diCl-DMAC)

White powder, yield 69%. ¹H NMR (500 MHz, CDCl₃, δ): 1.67 (s, 6H) 6.21 (d, J = 8.79 Hz, 2H) 6.94 (dd, J = 8.92, 2.06 Hz, 2H) 7.31 (d, J = 7.14 Hz, 2H) 7.40 (d, J = 2.20 Hz, 2H) 7.53–7.58 (m, 1H) 7.64–7.68 (m, 2H) MALDI-TOF m/z: calcd for C₂₁H₁₇Cl₂N, 338.0 [M-CH₃]⁺; found, 338.2.

2,7-Dibromo-9,9-dimethyl-10-(4-methylphenyl)-9,10-dihydroacridine (diBr-DMAC)

White powder, yield 78%. ¹H NMR (500 MHz, CDCl₃, δ): 1.66 (s, 6H) 2.50 (s, 3H) 6.18 (d, J = 8.79 Hz, 2H) 7.07 (dd, J = 8.92, 2.33 Hz, 2H) 7.17 (d, J = 8.24 Hz, 2H) 7.44 (d, J = 7.96 Hz, 2H) 7.51 (d, J = 2.20 Hz, 2H) MALDI-TOF m/z: calcd for C₂₂H₁₉Br₂N, 442.2 [M-CH₃]⁺; found, 442.0.

9,9-Dimethyl-10-phenyl-9,10-dihydroacridine

A mixture of 9,9-dimethyl-9,10-dihydroacridine (1 mmol, 209 mg), iodobenzene (1 mmol, 204 mg), tris(dibenzylideneacetone)dipalladium(0) (0.05 mmol, 46 mg) and tri-tert-butylphosphonium tetrafluoroborate (0.1 mmol, 29 mg) was dissolved in 15 ml of dry toluene under an argon atmosphere. Potassium tert-butoxide (1.5 mmol, 168 mg) was added and the mixture was stirred at 100 °C overnight. The solvent was removed under vacuum, and the dry residue was dissolved in dichloromethane and washed with water. Crude compound was purified by column chromatography using a mixture of dichloromethane and hexane (1 : 9). White powder, yield 72%. ¹H NMR (500 MHz, CDCl₃, δ): 1.72 (s, 6H), 6.28 (d, J = 7.96 Hz, 2H), 6.93–7.01 (m, 4H), 7.36 (d, J = 7.41 Hz, 2H), 7.48 (d, J = 7.41 Hz, 2H), 7.51–7.55 (m, 1H), 7.62–7.67 (m, 2H). MALDI-TOF m/z: calcd for C₂₁H₁₉N, 270.3 [M-CH₃]⁺; found, 270.1.

9,9-Dimethyl-10-(4-methylphenyl)-9,10-dihydroacridine

Was synthesized using 4-iodotoluene using the same protocol as for 9,9-dimethyl-10-phenyl-9,10-dihydroacridine. White crystalline powder, yield 88%. ¹H NMR (500 MHz, CDCl₃, δ): 1.68 (s, 6H), 2.48 (s, 3H), 6.28 (d, J = 8.24 Hz, 2H), 6.87–6.93 (m, 2H), 6.95 (dt, J = 8.39, 1.45 Hz, 2H), 7.20 (dd, J = 8.09, 1.37 Hz, 2H), 7.39–7.46 (m, 4H). MALDI-TOF m/z: calcd for C₂₂H₂₁N, 300.4 [M + H]⁺; found, 300.2.

2,4-Bis(2-methylphenyl)-6-phenyl-1,3,5-triazine

2-Methylbenzamidine hydrochloride (11 mmol) and potassium tert-butoxide (10.8 mmol) were mixed in DMSO and stirred at RT for 30 min. Benzaldehyde (5 mmol) was added and the mixture was stirred at 100 °C for 12h. After cooling to RT, 2,3-dichloro-5,6-dicyano-p-benzoquinone (5 mmol) was added and the mixture was stirred at 50 °C for another hour. 50% aqueous methanol was added and the precipitate was collected by filtration. Column chromatography using 50% CHCl₃ in hexane afforded the pure title compound. White powder, yield 75%. ¹H-NMR (300 MHz, CDCl₃, δ): 2.84 (s, 6H), 7.35–7.41 (m, 4H), 7.42–7.47 (m, 2H), 7.53–7.57 (m, 2H), 7.58–7.61 (m, 1H), 8.28 (d, J = 7.63 Hz, 2H), 8.68 (s, 2H). MALDI-TOF m/z: calcd for C₃₈H₃₀Cl₂N₄, 338.2 [M + H]⁺; found, 338.2.

Sample preparation for photophysical measurements

Stock solutions of H, diCl and diBr in dichloromethane were added to Zeonex or PMMA solutions in toluene and dichloromethane solutions to obtain homogeneous mixtures, which were used for film preparation. The films were prepared by drop cast deposition on warm quartz plates, and left in the dark for 5h to enable evaporation of solvents. The final mass fraction of emitters dispersed in polymers was ca. 1%.

Photoluminescence measurements

UV-Vis absorption spectra were recorded using a Shimadzu UV-1900 spectrophotometer. Steady-state photoluminescence spectra were recorded using a Varian Cary Eclipse spectrofluorometer using front-face excitation geometry. The PL quantum yield (PLQY) was measured using an integrating sphere (Quantaurus C11347-11, Hamamatsu). Time-resolved measurements were performed at different temperatures using a customized system²¹ consisting of a pulsed YAG:Nd laser (PL2251A, EKSPLA) coupled with an optical parametric generator (PG 401/SH) as an excitation light source and 2501S grating spectrometer (Bruker Optics) combined with the streak camera system (C4334-01 Hamamatsu) as a detection unit. The system was equipped with a double-stage high vacuum pump (T-Station 85 Edwards) coupled with a closed-cycle helium cryostat (APD DE-202) and a temperature controller (LakeShore 336). To reduce scattering, reflections and secondary order artifacts, a set of various high performance optical bandpass (BP) and longpass (LP) filters were used: in the excitation path 325/50BP or 375/50BP (CWL/FWHM), depending on the selected excitation wavelength, together with LP filters: 375LP or 350LP (Edmund Optics). In order to build PL intensity decay profiles, streak camera images were integrated over a constant wavelength interval (460–490 nm for ZNX and 475–515 nm for PMMA samples).

Quantum chemical calculations

Quantum chemical calculations were conducted at the DFT/TD-DFT level of theory using the Gaussian 16 program package.²² The B3LYP functional²³ was used with the LAN2LDZ basis set. Firstly, for each compound, unconstrained geometry optimizations were performed for the ground (S₀), excited singlet (S₁) and excited triplet electronic states (T₁, T₂, T₃). Convergance of all geometry optimizations was verified by the vibrational analysis: no negative frequencies were observed, therefore calculated minima correspond to the “true” stationary points. The nature of the electronic excited states was determined by the analysis of molecular orbitals. Spin–orbit coupling constants were computed using the ORCA 4.2 software²⁴ package with the B3LYP functional, and the DEF2-TZVP basis set with included relativistic zero-order regular approximaion (ZORA).

Results and discussion

Synthesis

diCl and diBr were synthesized via efficient and simple halogenation of H using N-chlorosuccinimide and N-bromosuccinimide, respectively, as shown in Scheme 1. The isolation yields were close to 90%.

Scheme 1 Synthesis of diCl and diBr emitters.

Photoluminescence and excited-state alignment

The investigations of the TADF mechanism start with the analysis of the spectral features of the compounds and alignment of their lowest excited-states. The absorption spectra of the investigated compounds measured in solutions are very similar (Fig. S5, ESI†). Minor changes can be noticed at the long-wavelength band corresponding to the CT transition. The blue shift of the absorption maximum from 379 nm (H) to 373 nm is observed for diCl and to 375 nm for diBr. All compounds show deep-blue and sky-blue photoluminescence (PL) in nonpolar Zeonex® (ZNX) and more polar PMMA films, respectively (Table 1, Fig. 1C and Fig. S6, ESI†). Positive solvatochromism evidences a large change in the dipole moment during the S₁–S₀ transition and charge-transfer (CT) character of the S₁-state, like in DMAC-TRZ and other TADF emitters of D–A structure. The blue-shifted emission of diCl relative to H is the result of the negative inductive effect of chlorine atoms which decreases the donor strength and thus increases the ¹CT energy. Interestingly, in diBr this effect is almost negligible. Taking into account a similar trend in the absorption spectra, one can conclude that in such large π-systems, the electronic effect of bromine on the S₀–¹CT transition is lower than that of chlorine. The PL quantum yields (PLQYs) are the highest for H (99%) and diCl (85%) in PMMA, whereas the respective value for diBr is lower (Table 1).

Table 1 Steady-state and kinetic PL parameters of the investigated TADF compounds

Cmpd	Medium	PLQY^a [%]	PL^bλmax [nm]	ΔE1CT–3LE(A)^c [meV]	ΔE1CT–3CT^c [meV]	ΔE1CT–3LE(D)^c [meV]	τ PF [ns]	τ DF [μs]	k ISC [s^−1 10^7]	k rISC [s^−1 10^4]
a Values measured using integrating sphere and corrected for vacuum conditions (for the details see the ESI – Table S1). b Determined from steady-state photoluminescence measurement at 298 K (Fig. S6 and Table S1, ESI). c Determined from the difference of respective onsets of PL spectra, according to the general equation: ΔE1–2 = (1240/λonset1–1240/λonset2), onset values presented in Table S1 (ESI). d All of presented photophysical parameters (τPF, τDF, kISC and krISC) were calculated from the PL intensity decay profiles (Fig. S8A and S9A, ESI) measured at 298 K under a vacuum. A detailed procedure of the calculations of photophysical parameters is included in the ESI – Section S3).
H	ZNX	60	465	94	—	−230	15.3	171	5.1	1.03
diCl		75	462	133	—	−55	13.1	333	6.1	0.87
diBr		12	467	114	—	−55	2.2	104	38.5	1.74
H	PMMA	99	498	46	85	−278	17.1	96	3.8	2.92
diCl		85	492	72	95	−116	16.0	139	4.1	1.85
diBr		21	499	60	86	−109	2.8	38	30.8	8.23

---

Time-resolved emission spectra (TRES) reveal that the “¹CT-state” is a continuous energy band rather than a single-energy level (Fig. 1D and Fig. S7–S11, ESI†). In PMMA films, broadened steady-state emission spectra are the result of spectral shifts at different time delays due to coexistence of various rotameric species with different dihedral angles between donor and acceptor units (θ, Fig. 1B). Such rotamers play a key role in the TADF photophysics,^19,25–28 as the ¹CT-state energy and ³CT–¹CT energy gap (ΔE_1CT–3CT) are dependent on the θ value. Such θ-rotamers with high deviation from the optimal 90° value and high ¹CT-energy emit in the blue region in the very early prompt fluorescence (PF) region and late DF, whereas θ-rotamers close to 90° correspond to low ¹CT-energy, late-PF and early-DF emissions (Fig. 1E). The ¹CT energy thus deviates from 2.96 to 2.81 eV (H) (Fig. 1F and Table S1, ESI†) and 2.98 to 2.82 eV (diCl, diBr). Similar, but less pronounced dependences are observed for ZNX films (discussed in the ESI† – Section S2).

Thorough analysis of TRES at low temperatures reveals that different triplet states are responsible for the phosphorescence in different media. In ZNX, the vibronic structure of the phosphorescence spectrum differs from that of fluorescence, but matches perfectly the phosphorescence of an isolated acceptor (Fig. S6G, ESI†).²⁹ This suggests that the T₁ state is localized on the acceptor fragment, the ³LE(A)-state. Its estimated energy is 2.84 eV, similar to that in DMAC-TRZ.²⁷ In PMMA, the phosphorescence is different from the ³LE(A) one, but similar to fluorescence, and thus ³CT becomes the lowest triplet state (Fig. S6D–F, ESI†). In contrast to ¹CT, the ³CT-emission onset is relatively constant, thus ³CT is a single-energy level of 2.80 eV (H) and 2.81 eV (diCl, diBr, see the phosphorescence spectra depicted in Fig. S6D–F and S11A–C, ESI†). The energy of the third triplet state localized on the donor fragment (³LE(D)) was estimated from the phosphorescence of free donor molecules (Fig. S6H, ESI†). Thus the estimated ³LE(D)-energy is affected by halogen atoms, decreasing from 3.16 eV (H) to 3.02 and 3.01 eV in diCl and diBr, respectively.

The alignment of the excited states presented in Fig. 2A summarizes the discussion of spectral properties. In view of the TADF mechanism and HA effect, singlet–triplet energy gaps (ΔE_1CT–Ti) are discussed further. Minimal, maximal, and statistical mean energy gaps (Tables S2, S3 and Fig. S10, S11, ESI†) reveal the macroscopic diversity of molecular electronic systems due to the distribution of ¹CT-state energies. As the ³LE(A)-state is negligibly affected by the halogens, ΔE_1CT–3LE(A) varies similarly for all the emitters: in ZNX, from +0.06 to +0.15 eV with a mean value of ca. +0.10 eV; and in PMMA, from slightly negative to +0.14 eV with a mean value of ca. +0.05 eV (Table 1). The ¹CT–³CT energy difference estimated for the PMMA medium is also very similar for H and diBr, varying from 6.3 meV to 0.16 eV with the mean value of 85 meV; in diCl bearing the weakest donor fragment, the CT states are slightly more distanced (Table 1 and Table S1, ESI†). Therefore, the alignment of S₁, T₁, and T₂ states is generally similar for studied compounds. The distinguished electronic feature of halogenated emitters is the ³LE(D)-state being closer to ¹CT. The lowest mean ΔE_1CT–3LE(D) values are in the ZNX films: −0.23 eV (H) and −0.055 eV (diCl, diBr); in PMMA, they increase to −0.28 eV and −0.11, respectively.

Fig. 2 (A) The excited-state alignment and dominating spin–flip pathways. (B) Arrhenius plots derived from temperature-dependent time-resolved measurements in ZNX (left) and PMMA (right) taken in the 298–150 K range.

Photoluminescence decays

The kinetics of emission decay and its strong temperature dependence unambiguously proves the TADF property of the investigated emitters, as discussed in detail in the ESI.† Well-distinguished time domains of PF and DF decays exhibit different sensitivity to the HA effect (Fig. 1D, and Fig. S8A, S9A, ESI†). Introduction of chlorine and especially bromine atoms leads to the shortening of PF lifetime, because the ISC rate constant (k_ISC) increases up to 1.2 and 8.1 times, respectively (Table 1). The situation is more complex in the case of the DF lifetime, as it is almost twice longer in diCl, but three times shorter in diBr compared to H. The rISC rate constant (k_rISC) thus decreases in diCl, but increases almost three times in diBr in the PMMA films. At this point one can notice that only bromine accelerates both types of intersystem crossing transitions, however it affects ISC more than rISC. This versatile effect of HA is analyzed further using experimental and computational approaches.

Arrhenius and Marcus theories applied to the SOC analysis

Looking for the analysis approach which could help to reveal the TADF mechanism in emitters with complex photophysics, we found that the combination Arrhenius law³⁰ (1) and Marcus–Hush eqn (2) can be a powerful tool for investigations of spin–flip processes.³¹ Transformation of (1) and (2) provides valuable relationships (3, 4):where A is the preexponential factor, E_a is the activation energy, V is the SOC constant, ħ is the reduced Planck constant, λ is the sum of internal and external (λ_solv) reorganization energies for the respective transition, and ΔE_ST is the energy gap between singlet ¹CT and the respective triplet state. First, the k_ISC(1/T) and k_rISC(1/T) dependencies are analyzed according to the Arrhenius law (Fig. 2B, and Section S4, Fig. S13–S15, Tables S5 and S6, ESI†). This enables two types of experimental data: (i) A from which SOC constants V can be extracted and (ii) E_a comprised of ΔE_ST and λ. Importantly, thus obtained V values can be compared to those computed for various spin–flip channels and reveal the TADF mechanism. Within such an approach we discuss ISC and rISC separately and analyze the HA effect on each process.

ISC

In the investigated compounds, ISC is a barrierless process (E_a = 0), which indicates that (i) according to eqn (4), the S₁–T₁ reorganization energy is equal to the energy gap and (ii) according to eqn (2), k_ISC is defined by the SOC constant. V_ISC increases from 0.29 (H) and 0.31 (diCl) to 0.76 cm⁻¹ (diBr) (Table 2). Such an order of magnitude indicates that ISC occurs via a transition or a couple of transitions, so-called as “allowed by El-Sayed rules”.³² The ISC mechanism should thus involve excited states of different nature: ¹CT and ³LE. In H, the key ISC channel is the ¹CT → ³LE(A) transition due to the close energy of the respective states and well-matching computed V_1CT→3LE(A) and experimental V_ISC values (Table 2 and Table S7, ESI†). In the halogenated derivatives, the rates of ¹CT → ³LE(A) transition remain similar because of an identical ΔE_1CT–3LE(A). In fact, the calculations indicate the absence of the HA effect on this transition as neither Cl nor Br increase its SOC (see the ESI† – Section 5, Table S7).

Table 2 Photophysical parameters of the investigated TADF compounds derived from Arrhenius and Marcus–Hush equations

Cmpd	Process	Arrhenius eqn (1)			Marcus–Hush eqn (2)
		A	E a		ΔEST	λ	E a	V
		[s^−1 10^7]	[meV]	[meV]	[meV]	[meV]	[cm^−1]
ZNX
H	ISC	5.09	0		−122	122	0	0.29
diCl		6.12	0	1.1	−127	127	0	0.31	1.0
diBr		38.43	0	2.9	−125	125	0	0.76	2.6
H	rISC	0.12	124		122	122	122	0.05
diCl		0.09	127	0.9	127	127	127	0.04	0.8
diBr		0.16	126	1.2	125	125	125	0.05	1.1
PMMA
H	ISC	3.83	0		−93	93	0	0.29
diCl		4.11	0	1.0	−97	97	0	0.30	1.0
diBr		30.85	0	2.8	−94	94	0	0.76	2.5
H	rISC	0.09	98		93	93	93	0.05
diCl		0.06	95	0.8	97	97	97	0.04	0.8
diBr		0.26	92	1.7	94	94	94	0.07	1.5

---

The observed strong HA effect on ISC correlates with the ¹CT–³LE(D) energy gaps. As compared to PMMA, the decrease of |ΔE_1CT–3LE(D)| in ZNX films leads to the increase of k_ISC. Theoretical calculations support this conclusion: the predicted SOC constants and rates of the ¹CT → ³LE(D) transition evidence its sufficient role in diCl and diBr (Table S8, ESI†). For example, in PMMA films, the mean k_1CT–3LE(D) increases drastically from 2.5 × 10³ s⁻¹ (H) to 1.8 × 10⁶ s⁻¹ (diCl) and 1.8 × 10⁷ s⁻¹ (diBr). Regarding the ¹CT-energy distribution, in diBr species with minimal ΔE_1CT–3LE(D), the maximal k_1CT–3LE(D) value exceeds 1.5 × 10⁸ s⁻¹ (Table S8, ESI†). The HA effect on ISC is thus realized mainly via³LE(D)-state influenced directly by the heavy halogens (Table S9, ESI†). From the point of view of TADF efficiency, one can conclude the energetic closeness of the HA-affected ³LE state to the ¹CT one and it is a negative factor, as it leads to strong acceleration of ISC.

rISC

A similar approach applied for rISC reveals that for all three compounds, thermal activation E_a is roughly constant (Table 2). According to eqn (4), this indicates that neither Cl nor Br change the energy gap or reorganization energy for rISC. As compared to ZNX, in PMMA films, E_a decreases by 30 meV from ca. 125 to 95 meV (Table 2). The SOC constant V_rISC is significantly lower than that for ISC: in diBr, the HA effect is more than 2 times higher for ISC than for rISC (V_hal/V_H, Table 2). Together with unexpected V_rISC decrease in diCl, these observations indicate different mechanisms for ISC and rISC.

In H, V_rISC does not exceed 0.05 cm⁻¹ evidencing a dominating role of the “forbidden” channel: the ³CT → ¹CT transition. Similarly the low V_rISC of the halogenated derivatives indicate that neither the ³LE(D) nor ³LE(A) state contribute significantly to rISC. Despite the strong HA effect on the calculated V_3LE(D)–1CT, in ZNX, where ³LE(D) is closer to ¹CT (Table 1 and Table S1, ESI†), diBr exhibits a lower experimental V_rISC value than in PMMA. This indicates the insignificant role of the ³LE(D)-state in rISC due to its almost negligible population (Fig. 2A, Fig. S16 and Tables S10 and S11, ESI†). Neither the ³LE(A) → ¹CT transition contributes noticeably, because the calculated rate constants and SOC of the ³LE(A) → ¹CT transition decrease in the row diCl – H ≈ diBr (Table S11, ESI†), which is not the case for V_rISC. Moreover, due to the large reorganization energies, k_3LE(A)→1CT should exhibit much sharper temperature dependence than the experimental one (Fig. S14 and S15, ESI†).

The above-mentioned analysis indicates that rISC occurs mainly via the ³CT → ¹CT transition. The analysis of molecular vibrations and inhomogeneity reveals why the effect of heavy halogens on the ³CT → ¹CT spin–flip is so peculiar. Within our previously developed TADF model, in DMAC-TRZ,¹⁹ the ³CT → ¹CT transition is efficient in rotamers with various θ-deviation due to non-zero SOC, low energy gap and reorganization energy. Surprisingly, in θ-rotamers, the increase in the atomic number of the substituent results in the decrease of SOC (Fig. 3C). As a consequence, the rotational model predicts that the statistical sum of the ³CT → ¹CT transition rate constants (k_3CT→1CT) for all θ-rotamers decreases in the row H–diCl–diBr (see the ESI† – Section S6, Fig. 3B, 4 and Fig. S17–S19, Tables S12–S14). Interestingly, this correlates with the observed rISC inhibition in diCl, but contradicts the rISC acceleration in diBr.

Fig. 3 The most important vibrational modes for SOC enhancement (A), contributions of low-energy vibrational modes to rISC (B), and dependence of ³CT → ¹CT SOC constants on their amplitudes (C–E).

Fig. 4 Comparison of the experimental and model rISC values (see Table S19, ESI†).

The analysis of vibrational modes explains this discrepancy. In the case of the most stable 90°-rotamer, the k_3CT–1CT values calculated taking into account eight lowest vibrational modes (ω₁–ω₈, see the ESI† – Section S7, Fig. 3A and Fig. S20–S25, Tables S15–S18, and the supporting animation file) follow the experimental trend of k_rISC (Fig. 4). Thus the calculated rISC rates are underestimated, because other rotamers are not taken into account. The complete TADF model should thus combine rotational and vibronic models via vibrational SOC analysis for all θ-rotamers, which unfortunately requires expensive and time-consuming computations. Assuming that vibrational SOC enhancement in all rotamers is similar to the 90°-rotamer, the rotational model was completed by the correction on vibrations (see the ESI† – Section S8). Thus the obtained corrected k_3CT–1CT values better matched the experimental ones (Fig. 4 and Table S19).

Positive verification of such a rotational-vibronic model enables the analysis of key vibronic modes for rISC. In H, the ω₁ mode leading to the θ-deviation is almost exclusive ³CT → ¹CT channel (Fig. 3A). This supports our previous findings, that in the orthogonal TADF emitters without heavy atoms, rISC via³CT → ¹CT transition is correctly predicted by the θ-rotamer model which takes into account only relative rotations of the D and A fragments.¹⁹ In diCl and diBr, however, k_3CT→1CT realized via the ω₁ mode decreases down to 1.6 and 2.0 times, respectively (Fig. 3B). In diBr, the enhanced rISC is due to the activated ω₄ and ω₈ channels of the ³CT → ¹CT transition. The ω₄ and ω₈ modes distort the planarity of the donor, causing motions of bromine atoms and SOC enhancement up to three times (Fig. 3A–E). As a result, diBr gains a four-fold increase of k_3CT→1CT initially activated by ω₁. For diCl, the ω_3–5 and ω₈ modes also activate SOC but their contribution to k_3CT→1CT is only 40%.

The activation of ω₄ and ω₈ vibronic rISC channels in diBr indicate the importance of the position of HA in the emitter. Obviously, HA should be involved in the low-energy vibrations to increase V_3CT→1CT. On the other hand, diCl serves as an example of an unfortunate decrease of SOC via ω₁ and weak compensation from other vibrations resulting in the rISC inhibition.

Conclusions

In summary, using heavy-halogen derivatives of the DMAC-TRZ emitter, we verified an approach for the photoluminescence data analysis within Arrhenius and Marcus theories to explain the heavy-atom effect on blue TADF materials. Such an approach provides experimental electronic data on spin–flip transitions, among which spin–orbit coupling constants are especially helpful for the analysis of the TADF mechanism.

Triplet states of the LE character play an important role in the ISC process, especially in blue emitters like diCl and diBr. The introduction of such halogens into the donor fragment decreases the energy of the donor-localized T₃-state in such a manner that it becomes close to the ¹CT state of the blue emitters and thus decreases the S₁–T₃ energy gap. Together with the heavy atom effect which enhances SOC of the ¹CT → ³LE(A) transition, this results in strong acceleration of ISC. From the point of view of potential application in OLED, the ISC rate should, however, be low to avoid competition with the radiative deactivation of singlet excitons. The first criterion of the molecular design of HA-containing emitters can thus be formulated as: avoid energetic closeness of singlet and triplet states of different nature directly affected by HA.

For the studied emitters, rISC is realized via the ³CT → ¹CT transition, proving the appropriateness of the two-level model described in ref. 19 In the light-atom emitter H, the ³CT → ¹CT SOC is enhanced by θ-rotations. For rISC modelling in heavy-atom emitters, the two-level model should take into account molecular vibrations involving HAs. In contrast to the commonly used three-level model, our results evidence the negligible role of local ³LE states in rISC.

Heavy atoms in the donor unit inhibit spin–orbit coupling of the ³CT → ¹CT transition via the θ-rotational channel. However, SOC and rISC are activated by the low-energy vibrations which cause HA motions. Whilst in diCl, the former effect dominates causing rISC inhibition, in diBr, the latter effect is strong enough to accelerate rISC up to three times. Our second criterion of molecular design of TADF materials with HA is: the heavy atom should be involved in low-energy molecular vibrations to enhance the ³CT → ¹CT transition.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

I. E. S. is grateful to the National Science Centre, Poland for financial support within the Sonata 16 project No. UMO-2020/39/D/ST5/03094 and the Polish Ministry of Science and Higher Education within the Mobility Plus project No. 1637/MOB/V/2017/0. M.M is grateful to the National Centre for Research and Development for financial support within the CHEMFIZ program (WND-POWR.03.02.00-00-I059/1). Quantum chemical calculations were performed on the computers of the Wroclaw Centre for Networking and Supercomputing (WCSS), Poland. The work at Seoul National University was partially supported by the research grant of Samsung Display Co., Ltd.

References

1. F. B. Dias, T. J. Penfold and A. P. Monkman, Methods Appl. Fluoresc., 2017, 5, 012001.
2. P. K. Samanta, D. Kim, V. Coropceanu and J.-L. Bredas, J. Am. Chem. Soc., 2017, 139, 4042–4051.
3. H. Uoyama, K. Goushi, K. Shizu, H. Nomura and C. Adachi, Nature, 2012, 492, 234–238.
4. T. J. Penfold, E. Gindensperger, C. Daniel and C. M. Marian, Chem. Rev., 2018, 118, 6975–7025.
5. Y.-F. Xiao, J.-X. Chen, W.-C. Chen, X. Zheng, C. Cao, J. Tan, X. Cui, Z. Yuan, S. Ji, G. Lu, W. Liu, P. Wang, S. Li and C.-S. Lee, Chem. Commun., 2021, 57, 4902–4905.
6. D. R. Lee, K. H. Lee, W. Shao, C. L. Kim, J. Kim and J. Y. Lee, Chem. Mater., 2020, 32, 2583–2592.
7. C. E. Housecroft and E. C. Constable, J. Mater. Chem. C, 2022, 10, 4456–4482.
8. C. Sun, L. Llanos, P. Arce, A. Oliver, R. Wannemacher, J. Cabanillas-Gonzalez, L. Lemus and D. Aravena, Chem. Mater., 2021, 33, 6383–6393.
9. IUPAC. Compendium of Chemical Terminology, 2nd ed. (the “Gold Book”). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. 10.1351/goldbook.
10. T. Huang, X. Song, M. Cai, D. Zhang and L. Duan, Mater. Today Energy., 2021, 21, 100705.
11. Y. Ren, Y. Wada, K. Suzuki, Y. Kusakabe, J. Geldsetzer and H. Kaji, Appl. Phys. Express, 2021, 14, 071003.
12. D. Song, Y. Yu, L. Yue, D. Zhong, Y. Zhang, X. Yang, Y. Sun, G. Zhou and Z. Wu, J. Mater. Chem. C, 2019, 7, 11953.
13. T. Hua, L. Zhan, N. Li, Z. Huang, X. Cao, Z. Xiao, S. Gong, C. Zhou, C. Zhong and C. Yang, Chem. Eng. Sci., 2021, 426, 131169.
14. S. Gan, S. Hu, X.-L. Li, J. Zeng, D. Zhang, T. Huang, W. Luo, Z. Zhao, L. Duan, S.-J. Su and B. Z. Tang, ACS Appl. Mater. Interfaces, 2018, 10, 17327–17334.
15. Y. Xiang, Y. Zhao, N. Xu, S. Gong, F. Ni, K. Wu, J. Luo, G. Xie, Z.-H. Lu and C. Yang, J. Mater. Chem. C, 2017, 5, 12204–12210.
16. D. Pereira, D. R. Lee, N. A. Kukhta, K. H. Lee, C. L. Kim, A. S. Batsanov, J. Y. Lee and A. P. Monkman, J. Mater. Chem. C, 2019, 7, 10481–10490.
17. K. Matsuo and T. Yasuda, Chem. Sci., 2019, 10, 10687–10697.
18. I. S. Park, K. Matsuo, N. Aizawa and T. Yasuda, Adv. Funct. Mater., 2018, 28, 1802031.
19. I. E. Serdiuk, M. Mońka, K. Kozakiewicz, B. Liberek, P. Bojarski and S. Y. Park, J. Phys. Chem. B, 2021, 125, 2696–2706.
20. I. E. Serdiuk, C. H. Ryoo, K. Kozakiewicz, M. Mońka, B. Liberek and S. Y. Park, J. Mater. Chem. C, 2020, 8, 6052–6062.
21. A. A. Kubicki, P. Bojarski, M. Grinberg, M. Sadownik and B. Kukliński, Opt. Commun., 2006, 269, 275–280.
22. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, et al., Gaussian 16, Revision C.01 Gaussian, Inc., Wallingford, CT, 2016.
23. A. D. Becke, J. Chem. Phys., 1993, 98, 1372–1377.
24. F. Neese, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2012, 2, 73–78.
25. S.-J. Woo, Y.-H. Kim and J.-J. Kim, Chem. Mater., 2021, 33, 5618–5630.
26. M. Hempe, N. A. Kukhta, A. Danos, M. A. Fox, A. S. Batsanov, A. P. Monkman and M. R. Bryce, Chem. Mater., 2021, 33, 3066–3080.
27. K. Stavrou, L. G. Franca and A. P. Monkman, ASC Appl. Electron. Mater., 2020, 2, 2868–2881.
28. L. G. Franca, A. Danos and A. Monkman, J. Mater. Chem. C, 2022, 10, 1313–1325.
29. L.-S. Cui, H. Nomura, Y. Geng, J. U. Kim, H. Nakatomani and C. Adachi, Angew. Chem., 2016, 56, 1571–1575.
30. F. B. Dias, K. N. Bourdakos, V. Jankus, K. C. Moss, K. T. Kametekar, V. Bhalla, J. Santos, M. R. Bryce and A. P. Monkman, Adv. Mater., 2013, 25, 3707–3714.
31. J. Gibson and T. J. Penfold, Phys. Chem. Chem. Phys., 2017, 19, 8428–8434.
32. M. A. El Sayed, J. Chem. Phys., 1963, 38, 2834–2838.

---

Footnote

† Electronic supplementary information (ESI) available: Synthetic procedures and results of analyzes, description of methods used and procedure for the determination of photophysical parameters; detailed discussion on spectral properties; details of the analysis approach based on Arrhenius and Marcus theories; computational details and theoretical prediction of ISC and rISC rate constants within rotational, vibrational, and rotational-vibronic models; animation file for the key molecular vibrations. See DOI: https://doi.org/10.1039/d2tc00476c

---