An effective method in modulating thermally activated delayed fluorescence (TADF) emitters from green to blue emission: the role of the phenyl ring

Abstract

Developing efficient blue emitters with high performance and low cost is crucial for the further development of organic light-emitting diodes (OLEDs). Based on the two experimentally reported green thermally activated delayed fluorescence (TADF) emitters, which are thioxanthone derivatives consisting of carbazole as an electron donor and 9H-thioxanthen-9-one-S,S-dioxide (SOXO) as an electron acceptor with donor–acceptor (D–A) or donor–acceptor–donor (D–A–D) structures, two new blue TADF emitters are designed by simply inserting a phenyl ring between D and A units. The TADF processes of the four thioxanthone derivatives are studied systematically through first-principles calculations. The role of the introduced phenyl ring in the excited state properties of the designed molecules is explored by analyzing the changes in molecular geometries, frontier molecular orbital distributions, the lowest singlet–triplet energy splitting (ΔE_ST), the spin orbit coupling (SOC) constants, the radiative decay rates (k_r) and the nonradiative decay rates (k_nr), as well as the intersystem crossing rates (k_ISC) and reverse intersystem crossing rates (k_RISC). The results show that when incorporating phenyl units into the D–A and D–A–D structures, both high k_r and enhanced k_RISC are achieved in Cz-Ph-SOXO and DCz-DPh-SOXO, demonstrating that incorporating the phenyl unit in D–A and D–A–D structures is an efficient way for developing new SOXO-based TADF molecules. It is worth noting that the k_RISC values for Cz-Ph-SOXO and DCz-DPh-SOXO are significantly increased with respect to those of the experimental molecules. The present results would provide helpful guidelines for developing new SOXO-based TADF molecules experimentally.

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1. Introduction

As the third generation of organic light emitting diode (OLED) emitters, thermally activated delayed fluorescence (TADF) materials, which can harvest both the singlet and triplet excitons through the efficient reverse intersystem crossing (RISC) process, have drawn more and more attention in recent years.^1–3 Unlike the conventional fluorescent and phosphorescent materials, the TADF emitters can utilize all the singlet and triplet excitons and realize high efficiency without the assistance of noble metals. Thus, there is a high potentiality to develop lower cost, but more promising OLED devices based on this class of materials. For an efficient TADF emitter, two key parameters, a small singlet–triplet energy splitting (ΔE_ST) and high photoluminescence quantum yield (Φ_PL), are requisite.^4–7 To achieve a small ΔE_ST, the spatial separation of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the molecules are required and thereby the exchange integral (J) will be reduced based on the equation .^8,9 However, the demand of the separated distribution of the HOMO/LUMO for a narrow ΔE_ST can suppress the transition dipole moment between the ground state (S₀) and the first singlet excited state (S₁), leading to a small oscillator strength (f) and low Φ_PL. Therefore, the delicate balance between the spatial separation of the HOMO–LUMO wave function and the large f could be a compromise design strategy for efficient TADF emitters.^4–7 So far, versatile molecular systems with TADF properties have been developed, including spiro-acidine,¹⁰ triazine,¹¹ spirobifluorene,¹² phthalonitrile,¹³ triptycene,⁸ diphenyl sulfone derivatives,^14–17 and so on. Highly efficient sky-blue OLEDs with 37% external quantum efficiency have been achieved, which can be comparable to the excellent performance of phosphorescent OLEDs.¹⁸ Despite significant progress having been made in recent years, developing highly efficient new TADF emitters with both small ΔE_ST and high Φ_PL is still a great challenge. The traditional design strategy for TADF emitters is combining an electron donor (D) and an electron acceptor (A) unit to spatially separate the HOMOs and LUMOs.^19,20 Generally, a phenyl linker is demanded to increase the D–A spatial separation distance and relieve the twisted angle between the D and the A.^21,22 Compared with the D–A-type TADF emitters, D–A–D-type TADF emitters can facilitate a stronger intramolecular charge transfer and therefore smaller ΔE_ST, which can promote the highly efficient RISC progress and achieve excellent OLED performance.^23–31

Thioxanthone (TXO) and 9-H-thioxanthen-9-one-10,10-dioxide (SOXO) units are excellent acceptor units for constructing highly efficient TADF materials. The ΔE_ST of SOXO is reported to be lower than 0.3 eV,^32,33 and the SOXO core contains a ketone moiety which is alone able to produce delayed fluorescence.^34,35 Several kinds of SOXO systems have been reported to exhibit excellent TADF properties. In 2014, Wang and co-workers reported two efficient TADF emitters of SOXO based derivatives with the D–A structure, using SOXO as the electron acceptor unit, and triphenylamine (TPA)/N-phenylcarbazole (PhCz) as the electron donor unit.³⁶ Later on, they demonstrated a remarkable divergence in the photophysical properties of the SOXO based TADF emitters with different substitution positions of the PhCz donor.³⁷ In 2019, they designed four D–A–D region isomers with TADF properties by connecting two PhCz as donors at the different substituted positions of the phenyl group in the SOXO unit, highlighting the beneficial role of the different substituted positions of the acceptor unit in facilitating the adjustment of ΔE_ST and f.³⁸ In 2016, Su et al. investigated the structure–performance relationship of thioxanthone-based TADF emitters with substituted carbazole donors and inferior OLED performance was achieved for the symmetric D–A–D molecules with 2,7-substitutions.²⁷ Interestingly, in the same year, they reported blue and yellow TXO-based TADF emitters with the D–A–D structure with an external quantum efficiency (EQE) of over 20%, in which they introduced two triphenylamine (TPA) donor units at the 3 and 6 position of the TX (9-H-thioxanthen-9-one) unit. Ultrahigh EQE values of 23.7% and 24.3% are achieved for the symmetrical blue emitter 3,6-2TPA-TX and the yellow emitter 3,6-2TPA-TXO, respectively.³⁹ Although the SOXO-based TADF emitters have achieved excellent performance in OLED devices, the electroluminescence mechanism of this kind of material is still unclear. For the singlet-harvesting mechanism, both the singlet and triplet excited states are involved in the emission process, and the overall emission behavior relates to the individual properties of these states, ΔE_ST, f, the spin orbit coupling (SOC) and the related intersystem crossing (ISC) and RISC processes. All of these properties should be considered sufficiently when engineering the chemical structures of the TADF emitters.^9,40,41 Therefore, a detailed understanding of the structural–property relationship of the organic TADF emitters is crucial for effective materials engineering, which facilitates the development of new efficient TADF emitters and promotes their applications in OLEDs.

In this work, the electroluminescence mechanisms of two experimentally reported D–A and D–A–D type SOXO based TADF emitters (the chemical structures are plotted in Fig. 1) are systematically investigated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). Two new SOXO derivatives are designed via simply introducing the phenyl ring between donor and acceptor units with D–π–A and D–π–A–π–D structures to further establish the structure–property relationship. The influence of the phenyl ring on the excited state properties of the SOXO-based molecules is investigated. The photophysical properties, the radiative and nonradiative decay rates, the ISC and RISC rates, as well as SOC constants of the investigated molecules, are explored in detail. It was found that the TADF emitters are modulated from green to blue emission, and the radiative decay rates and the rates of the RISC process are also enhanced through simply incorporating phenyl rings into the experimental molecules.

Fig. 1 Chemical structures of the studied thioxanthone-based molecules with D–A (CzSOXO), D–π–A (Cz-Ph-SOXO), D–A–D (DCzSOXO) and D–π–A–π–D (DCz-DPh-SOXO) structures, θ and l denote the main dihedral angles and bond lengths.

2. Theoretical methods

The decay rate constants from the S₁ to S₀ states and the interconversion rate constants between the S₁ and T₁ states are key parameters in determining the electroluminescence mechanism of the SOXO-based TADF molecules. The radiative decay rate k_r is calculated by the Einstein spontaneous emission equation as follows:^42–44where f is the oscillator strength and ΔE_fi is the vertical emission energy with the unit of wavenumber (cm⁻¹).

The nonradiative decay rate k_nr can be obtained based on Fermi's golden rule and the first-order perturbation theory^45,46

Here, the delta function δ is to ensure the conservation of energy; P_iv is the Boltzmann distribution function for the initial vibronic manifold; Ĥ_fu,iv is the interaction operator between two different Born–Oppenheimer states, consisting of two contributions as below⁴⁶

here, Ĥ^BO is the nonadiabatic coupling and Ĥ^SO is the spin–orbit coupling, r and Q are the electronic and normal mode coordinates. Φ_i is the electron wave function, and Θ_iv is the nuclear vibrational wave function.

The internal conversion rate constant between two electronic states with the same spin multiplicity can be evaluated by using the first-order perturbation theory as⁴⁵

Here, the nonadiabatic electronic coupling matrix element , is the normal momentum operator of the k_th normal mode in the final electronic states. Φ_f and Φ_i are the wavefunctions of the final state and the initial states, respectively. ρ^ic_fi is the thermal vibration correlation function (TVCF),^42–44 which is Here, Z_i represents the partition function.

The intersystem crossing rate constant between the singlet and triplet states can be evaluated based on the following equation:^42,43

The detailed derivation of these equations can be found in Peng and Shuai's work.^45–47

3. Computational details

The geometric optimizations and frequency calculations of the S₀ states are performed via density functional theory (DFT), while the excited singlet and triplet states are optimized through the time-dependent DFT (TD-DFT) approach. Since the excited state properties of TADF molecules with charge transfer character are functional dependent, several exchange–correlation functionals, including B3LYP,⁴⁸ PBE0,⁴⁹ PBE0-1/3,⁵⁰ BMK⁵¹ and M062X⁵² with different HF exchange percentages in the XC functional of 20%, 25%, 33.33%, 42% and 54%, and two range-separated hybrid functionals, CAM-B3LYP⁵³ and ωB97XD,⁵⁴ are used to calculate the absorption and emission wavelengths of CzSOXO and DCzSOXO combining with the 6-31G(d)^55–57 basis set (see Table 1). It was shown that the results based on the PBE0-1/3 functional agree well with the experimental values. The PBE0-1/3 functional and 6-31G(d) basis sets are therefore used to evaluate the ground and excited state properties of the studied molecules. All calculations are performed in a toluene solvent with the Polarizable Continuum Model (PCM)⁵⁸ using the Gaussian 09 software package.⁵⁹

Table 1 The calculated absorption (λ_ab) and emission (λ_em) wavelengths of CzSOXO and DCzSOXO based on different functionals, together with the experimental values for comparison

	CzSOXO		DCzSOXO
	λ ab (nm)	λ em (nm)	λ ab (nm)	λ em (nm)
B3LYP	521	700	543	730
PBE0	478	617	498	642
PBE0-1/3	423	524	440	542
BMK	393	474	408	476
M062X	361	421	372	425
CAM-B3LYP	352	411	364	415
ωB97XD	341	389	349	395
Expt.^26	404	536	406	546

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Based on the electronic properties, the calculations of the radiative and nonradiative decay rates, as well as the intersystem crossing rate and reverse intersystem crossing rate constants are finished through the Molecular Material Property Prediction Package (MOMAP).^60–65 The SOC matrix elements are computed from the quadratic response function by the Dalton program package.^66,67

In addition, to characterize the geometric changes between the S₀ and S₁ states and between the S₁ and T₁ states, the root of the mean of squared displacement (RMSD) is calculated using the following equation:

where i is the atomic ordinal number. To analyze the excitation properties of the investigated molecules, the electron–hole (e–h) distributions and the overlaps of e–h of the S₁ states are calculated through the Multiwfn^68,69 software.

4. Results and discussions

4.1 Molecular geometric structures

The molecular geometric structures play a crucial role in determining both the electronic structures and photophysical properties. A large distorted dihedral angle between D and A units generally allows efficient spatial separation of the HOMO and the LUMO to achieve a small ΔE_ST value. The geometric structures of the S₀, S₁ and excited triplet states for all the investigated molecules are optimized based on the PBE0-1/3/6-31G(d) level in a toluene solvent. The main dihedral angles and bond lengths (as shown in Fig. 1) of CzSOXO, DCzSOXO, Cz-Ph-SOXO and DCz-DPh-SOXO based on the optimized S₀, S₁ and T₁ geometries in toluene are listed in Table 2. It can be seen that the molecular geometries between the S₀ and S₁ states are significantly altered when changing the molecular types. In the S₀ states, the dihedral angle (θ₁) between D and A moieties of CzSOXO is 50°, which is almost the same as that of DCzSOXO. However, when inserting the phenyl rings between the D and A unit in CzSOXO and DCzSOXO, the dihedral angles between the SOXO group and the phenyl ring are decreased to 37° for Cz-Ph-SOXO and DCz-DPh-SOXO, respectively. The corresponding bond lengths (l₁) are also 0.08 Å larger than those of CzSOXO and DCzSOXO. When comparing the dihedral angles in Table 2 between the S₀ and S₁ states, it can be found that the dihedral angles between D and A units are increased by around 14° for CzSOXO and DCzSOXO. While the largest dihedral angle deviations between the S₀ and S₁ states for Cz-Ph-SOXO and DCz-DPh-SOXO have occurred between the carbazole unit and the inserted phenyl ring, and the value at S₁ states is decreased by 6° with respect to those of S₀ states. The decreased dihedral angles at S₀ and S₁ states make the geometries of Cz-Ph-SOXO and DCz-DPh-SOXO become more planar compared with those of CzSOXO and DCzSOXO. It can also be found that the T₁ geometries of the studied molecules change significantly compared with the S₁ geometries, and the selected dihedral angles of Cz-Ph-SOXO and DCz-DPh-SOXO at the T₁ state show greater changes than those of CzSOXO and DCzSOXO with respect to those at the S₁ state.

Table 2 The main dihedral angles (in degree) and bond lengths (in angstrom) of the designed SOXO-based molecules based on the optimized S₀ and S₁ geometries in toluene

Molecules	Bond parameters	S0 geometry	S1 geometry	T1 geometry
CzSOXO	θ 1	50	64	42
	l 1	1.40	1.43	1.38
DCzSOXO	θ 11/θ12	49/49	64/53	49/43
	l 11/l12	1.40/1.40	1.43/1.41	1.40/1.38
Cz-Ph-SOXO	θ 3/θ2	37/54	33/48	46/2
	l 3/l2	1.48/1.41	1.47/1.40	1.41/1.39
DCz-DPh-SOXO	θ 31/θ32/θ21/θ22	36/37/53/126	35/33/56/132	4/36/46/126
	l 31/l32/l21/l22	1.48/1.48/1.41/1.41	1.48/1.47/1.41/1.40	1.41/1.48/1.39/1.41

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To quantitatively characterize the geometry changes between S₀ and S₁ states and between S₁ and T₁ states, the RMSD analysis of the investigated molecules is performed and the results are presented in Fig. 2. It can be found that the RMSD values between S₀ and S₁ states for CzSOXO and DCzSOXO are 0.344 and 0.394 Å, respectively. When bringing the phenyl ring between D and A units, the RMSD values decrease to 0.118 and 0.122 Å, respectively. The geometric changes between S₁ and T₁ states show much larger RMSD values than those between S₀ and S₁ states. The large geometry changes will lead to large reorganization energy between the corresponding two states and consequently lead to larger nonradiative decay rates. The geometry changes of the ground state and the excited states via changing the molecular types will definitely affect the distributions of the frontier molecular orbitals and the photophysical properties as discussed below.

Fig. 2 Comparison of the geometries between S₀ (pink), S₁ (blue) and T₁ (red) states in toluene for investigated molecules (RMSD values are presented).

4.2 Frontier molecular orbitals

The distributions of the frontier molecular orbitals play an important role in determining ΔE_ST, which is closely related to the steric hindrance of the molecular geometry. The more separated distributions between HOMOs and LUMOs, the smaller ΔE_ST will be. On the other hand, the spatial overlap between HOMO and LUMO is essential to achieve high radiative decay rates (k_r). The distributions and energy levels of HOMOs and LUMOs for the investigated molecules in the S₀ state are plotted in Fig. 3. It can be clearly seen that the HOMOs of CzSOXO and DCzSOXO are predominantly located on the donor units, and partially on the acceptor groups, and the LUMOs are mainly distributed on the acceptor moieties, and a small portion is distributed on the donor unit, ensuring a partial overlap between the distributions of HOMOs and LUMOs. When inserting the phenyl ring between D and A groups, smaller overlaps between HOMOs and LUMOs for Cz-Ph-SOXO and DCz-DPh-SOXO can also be found, which facilitates obtaining small ΔE_ST. It can also be found that the energy gaps between HOMOs and LUMOs for Cz-Ph-SOXO and DCz-DPh-SOXO are decreased by 0.14 and 0.10 eV compared with CzSOXO and DCzSOXO, respectively.

Fig. 3 The distributions and energy levels of the frontier molecular orbitals for the studied molecules at the S₀ state (isovalue is 0.02).

To analyze the excitation properties and quantitatively predict the degree of overlap between HOMOs and LUMOs, the electron–hole (e–h) distribution and overlap of e–h for the S₁ state of the investigated molecules are provided in Fig. 4. It can be seen that there are obvious overlaps of e–h for CzSOXO and DCzSOXO, mainly occurring on the acceptor unit. For the designed molecules Cz-Ph-SOXO and DCz-DPh-SOXO, the e–h overlap became smaller than those of CzSOXO and DCzSOXO, indicating that they may possess smaller ΔE_ST. It can also be noticed that the e–h distributions are separated significantly for all the investigated molecules, indicating that the charge transfer process can occur in all the molecules. To further analyze the inside mechanisms, the spatial separation of holes and electrons S_r, the charge transfer (CT) length D, the degree of separation of holes and electrons t, the reflection of the overall average distribution breadth of electrons and holes H, and the Δr index for the S₁ and S₂ states used to measure the charge transfer length during the electron excitation, are calculated via Multiwfn software⁶⁸ and the results are listed in Table 3. The calculated parameters in Table 3 also verify the above findings. When the t index is larger than zero, this implies that the distributions of holes and electrons are effectively separated because of the CT process. The Δr index for the S₁ and S₂ states is used to measure the charge transfer length during the electron excitation, and the larger the Δr value is, the more likely the excitation is a CT mode. It can be found that the S_r index of CzSOXO (0.32) and DCzSOXO (0.38) is larger than Cz-Ph-SOXO (0.24) and DCz-DPh-SOXO (0.29), indicating the larger overlap between holes and electrons, which is in accord with the e–h distributions as discussed above. It can also be found that t indices are all greater than zero, suggesting that sufficient hole and electron separations occurred in these molecules due to the CT process. However, the t index of DCzSOXO is as small as 0.08, demonstrating that there is some overlap between the hole and the electron. For the S₁ and S₂ states, Δr of all the molecules is larger than the threshold distinguishing the local excited (LE) state and the CT excited states of 2 Å, except that of DCzSOXO, indicating that they are LE states. It is also illustrated in Table 3 that the e–h overlaps can be decreased when incorporating the phenyl ring in Cz-Ph-SOXO and DCz-DPh-SOXO with respect to those of CzSOXO and DCzSOXO.

Fig. 4 The electron–hole (e–h) distributions and overlaps of e–h for the S₁ states of CzSOXO, DCzSOXO, Cz-Ph-SOXO and DCz-DPh-SOXO (isosurface value is 0.002).

Table 3 The S_r, D, t, H, and Δr index of the investigated molecules

Molecules	S r/a.u.	D/Å	t/Å	H/Å	ΔrS1/Å	ΔrS2/Å
CzSOXO	0.32	5.08	4.62	2.81	5.66	6.49
DCzSOXO	0.38	1.44	0.08	4.40	1.58	1.62
Cz-Ph-SOXO	0.24	8.75	6.26	3.15	9.50	4.45
DCz-DPh-SOXO	0.29	3.52	1.78	6.02	4.88	4.94

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4.3 ΔE_ST and transition properties

The singlet–triplet energy gap (ΔE_ST) for TADF molecules is one of the key parameters for the RISC process, which is correlated to the distributions of the HOMO and the LUMO. The excitation energies of S₁ and T₁ states based on the S₀, S₁ and T₁ geometries and the vertical and adiabatic energy splitting between the S₁ and T₁ states for the investigated molecules are provided in Table 4. It can be noticed that the adiabatic energy gaps between the S₁ and T₁ states for CzSOXO and DCzSOXO are 0.35 and 0.31 eV, respectively. When inserting the phenyl ring between D and A units in CzSOXO and DCzSOXO, these values are increased to 0.63 and 0.59 eV, respectively. The results are in agreement with the analysis of the geometric changes. However, the energy gap of Cz-Ph-SOXO between the T₃ and S₁ states is much smaller than that of CzSOXO between T₁ (T₂) and S₁ states (see Fig. 5), demonstrating that the ISC and the RISC processes may occur from the S₁ to T₃ states for Cz-Ph-SOXO. Similarly, for DCzSOXO and DCz-DPh-SOXO, the nearest triplet states to the S₁ state are T₂ (T₃) and T₃ (T₄) states, respectively. So, the ISC process may occur from S₁ to T₂ (T₃) and T₃ (T₄) states, respectively.

Table 4 The excitation energies of the S₁ and T₁ states based on S₀ and S₁ geometries and the energy difference between the S₁ and T₁ states for the investigated molecules (in unit of eV)

Molecules	S0 geometry			S1 geometry			T1 geometry			Adiabatic
	S1	T1	ΔEST	S1	T1	ΔEST	S1	T1	ΔEST	ΔEST
CzSOXO	2.93	2.63	0.30	2.37	2.24	0.13	2.49	1.85	0.64	0.35
DCzSOXO	2.82	2.54	0.28	2.29	2.16	0.13	2.41	1.85	0.56	0.31
Cz-Ph-SOXO	3.11	2.71	0.40	2.65	2.35	0.30	2.75	1.77	0.98	0.63
DCz-DPh-SOXO	3.06	2.68	0.38	2.61	2.33	0.28	2.71	1.77	0.94	0.59

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Fig. 5 The energy landscape of the vertical excitation of CzSOXO (a), Cz-Ph-SOXO (b), DCzSOXO (c) and DCz-DPh-SOXO (d).

The transition properties of excited states are also vital in determining the excited state properties. The natural transition orbital (NTO) analyses of the S₁ and T₁ states in toluene are performed for the investigated molecules. As shown in Fig. S1–S4 (ESI†), the highest occupied natural transition orbital (hole) and the lowest unoccupied natural transition orbital (particle) predominate the transition for S₁ and T₁ states. The S₁ states of the studied molecules generally exhibit charge transfer (CT) characters. For the T₁ and higher triplet states (T₂, T₃ or T₄ states), it can be found that all the molecules not only show significant local excited (LE) properties, but also partial CT characters. The CT characters can help to achieve larger k_RISC, therefore realizing a more efficient RISC process.²²

4.4 Photophysical property

The photophysical property is vital in exploring the TADF process of the investigated molecules. The absorption and emission wavelength as well as the oscillator strength of the S₁ state in a toluene solvent are provided in Table 5, together with the available experimental data. It can be found that the deviation between the theoretical and experimental absorption wavelengths of CzSOXO and DCzSOXO is less than 34 nm (with a relative difference of 7.7%). The calculated emission wavelengths are also in good agreement with the experimental results, and the deviations are within 12 nm. The emission wavelengths of CzSOXO and DCzSOXO are 524 and 542 nm, respectively, which are green emitters. While introducing the phenyl rings between the D and the A to CzSOXO and DCzSOXO make the emission wavelengths of Cz-Ph-SOXO and DCz-DPh-SOXO blue-shifted to 468 and 475 nm, respectively, which are blue emitters. When introducing the phenyl ring to CzSOXO and DCzSOXO between the D and A groups, the oscillator strengths of Cz-Ph-SOXO and DCz-DPh-SOXO are increased by 1.5 and 2 times, respectively, with respect to those of CzSOXO and DCzSOXO for the absorption process. While for the emission process, the oscillator strengths of Cz-Ph-SOXO and DCz-DPh-SOXO are also enhanced by 6 times than those of CzSOXO and DCzSOXO. From the perspective of oscillator strengths, it can be determined that the designed molecules (Cz-Ph-SOXO and DCz-DPh-SOXO) possess much better TADF properties compared with the experimental molecules (CzSOXO and DCzSOXO). Therefore, incorporating the phenyl ring between D and A moieties could be an efficient way for designing new efficient SOXO-based TADF molecules.

Table 5 The calculated absorption (λ_ab) and emission (λ_em) wavelengths as well as the oscillator strength based on the PBE0-1/3/6-31G(d) level in a toluene solvent for the investigated molecules (the experimental values are also listed in the parentheses for comparison)

Molecules	λ ab (nm)	f VA	λ em (nm)	f VE
CzSOXO	423 (404^26)	0.0405	524 (536^26)	0.0145
DCzSOXO	440 (406^26)	0.0431	542 (546^26)	0.0157
Cz-Ph-SOXO	399	0.0613	468	0.0622
DCz-DPh-SOXO	405	0.0838	475	0.0665

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4.5 Excited state dynamics

For TADF emitters, the rate constants of radiative (k_r) and nonradiative (k_nr) processes from the S₁ to S₀ state, as well as the intersystem crossing (k_ISC) and reverse intersystem crossing (k_RISC) rates play an important role in the dynamic process of the excited states. It is widely known that the ISC and RISC processes are related to not only the adiabatic energy gap between the S₁ and T₁ states, but also the SOC between the singlet and triplet states. The SOC constants between the S₁ and T₁ (T₂, T₃ and T₄) states are calculated based on the S₁ geometries through the Dalton^66,67 package, as shown in Table 6. The k_r and k_nr from the S₁ to S₀ state as well as k_ISC and k_RISC between the S₁ and T₁ (T₂, T₃ and T₄) states in toluene are provided in Table 7. The radiative decay rates of CzSOXO and DCzSOXO are 3.52 × 10⁶ and 3.56 × 10⁶ s⁻¹, respectively. While this value for Cz-Ph-SOXO and DCz-DPh-SOXO is increased to 1.89 × 10⁷ and 1.96 × 10⁷ s⁻¹, respectively, which agrees with the values of oscillator strengths. However, the nonradiative decay rates (k_nr) are all larger than the radiative rates (k_r) for CzSOXO and DCzSOXO, which is not beneficial for the light-emitting process. This is because the nonradiative process is sensitive to the environment, and the calculated results are based on the single molecule model and without considering the intermolecular interaction. So when made into OLEDs, the nonradiative rates of the designed molecules can be reduced significantly than the calculated values as illustrated in previous studies.^70–72 While k_nr of Cz-Ph-SOXO and DCz-DPh-SOXO is significantly decreased compared with k_r, which is beneficial for the light-emitting process. It is also found in Table 6 that the calculated SOC values between the S₁ state and the triplet state closest to the S₁ state are larger than those values between the S₁ and other triplet states.

Table 6 The spin–orbit coupling (SOC) constants between the S₁ state and the selected triplet states in toluene for the investigated molecules (all the SOC values are in unit of cm⁻¹)

Molecules	〈S1|HSO|T1〉	〈S1|HSO|T2〉	〈S1|HSO|T3〉	〈S1|HSO|T4〉
CzSOXO	0.228	0.358	—	—
DCzSOXO	0.215	0.183	0.366	—
Cz-Ph-SOXO	0.158	0.432	0.374	—
DCz-DPh-SOXO	0.141	0.158	0.043	0.365

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Table 7 The rate constants of radiative (k_r) and nonradiative (k_nr) from the S₁ to S₀ state as well as the ISC (k_ISC) and RISC (k_RISC) between the S₁ and T₁ (T₂, T₃ and T₄) states in toluene (all the rates are in unit of s⁻¹)

Molecules	CzSOXO	DCzSOXO	Cz-Ph-SOXO	DCz-DPh-SOXO
k r (S1 → S0)	3.52 × 10^6	3.56 × 10^6	1.89 × 10^7	1.96 × 10^7
k nr (S1 → S0)	5.14 × 10^10	8.40 × 10^10	7.50 × 10^5	3.83 × 10^6
k ISC (S1 → T1)	8.27 × 10^6	1.02 × 10^6	7.00 × 10^4	5.65 × 10^4
k RISC (T1 → S1)	9.89 × 10^0	1.80 × 10^0	6.58 × 10^−5	1.82 × 10^−2
k ISC (S1 → T2)	2.06 × 10^7	2.53 × 10^6	5.09 × 10^5	1.59 × 10^4
k RISC (T2 → S1)	2.39 × 10^1	6.82 × 10^2	3.01 × 10^−4	6.32 × 10^−5
k ISC (S1 → T3)	—	1.01 × 10^7	5.56 × 10^5	1.43 × 10^3
k RISC (T3 → S1)	—	2.92 × 10^3	1.41 × 10^6	2.66 × 10^4
k ISC (S1 → T4)	—	—	—	1.02 × 10^5
k RISC (T4 → S1)	—	—	—	2.50 × 10^6

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For CzSOXO, the T₁ and T₂ states are degenerate, and both the T₁ and T₂ states participate in the ISC and RISC processes. The k_ISC (2.06 × 10⁷ s⁻¹) and k_RISC (2.39 × 10¹ s⁻¹) between the S₁ and T₂ states are more effective than those between the S₁ and T₁ states due to the larger SOC values between the S₁ and T₂ states. It can be seen in Table 7 that the T₁, T₂ and T₃ states of DCzSOXO are all involved in the ISC and RISC processes. The most efficient route of the ISC and RISC processes for DCzSOXO is between the S₁ and T₃ states, and k_ISC and k_RISC are 1.01 × 10⁷ s⁻¹ and 2.92 × 10³ s⁻¹, respectively. It can also be found in Fig. 5 that the T₂ and T₃ states of DCzSOXO are degenerate. However, the energy gap between T₁ and T₂ (T₃) states is as small as 0.19 eV, so the internal conversion process will occur quickly from the T₂ (T₃) to the T₁ state, and the RISC process might also happen from the T₁ to S₁ state. For Cz-Ph-SOXO and DCz-DPh-SOXO, k_ISC values of the most effective route are decreased to 5.56 × 10⁵ and 1.02 × 10⁵ s⁻¹, respectively. However, k_RISC values of Cz-Ph-SOXO (1.41 × 10⁶ s⁻¹) and DCz-DPh-SOXO (2.50 × 10⁶ s⁻¹) of the most effective routes are significantly increased compared with those of CzSOXO (2.39 × 10¹ s⁻¹) and DCzSOXO (2.92 × 10³ s⁻¹), demonstrating that Cz-Ph-SOXO and DCz-DPh-SOXO are more facilitated to the occurrence of the RISC process. It can also be found that the RISC from the T₁ (T₂) to S₁ state is very small for Cz-Ph-SOXO, which is due to the larger energy gap (0.46 eV) between the T₃ and T₁ (T₂) states. Therefore, the internal conversion process from the T₃ to T₁ (T₂) state will be slow and the RISC process for Cz-Ph-SOXO mainly occurs from the T₃ to S₁ state. Similarly, for DCz-DPh-SOXO, the energy gap between T₃ (T₄) and T₁ states is also as large as 0.46 eV, so the main ISC and RISC processes have happened between the S₁ and T₃ (T₄) states.

In addition, the phosphorescence rates (k_p) from the T₁ to S₀ states calculated through MOMAP^60–65 software for all the investigated molecules are presented in Table S1 (ESI†). It can be found that the values of k_RISC are apparently much larger than the corresponding k_p, indicating that the reverse intersystem crossing process can successfully compete with the phosphorescence process. Based on the analysis of the dynamics of the excited states, it can be concluded that the designed molecules Cz-Ph-SOXO and DCz-DPh-SOXO with high k_r and efficient k_RISC can be used as excellent TADF emitters. Therefore, incorporating phenyl units into D–A and D–A–D type molecules is a good strategy for developing new efficient SOXO-based TADF emitters, and the emission color can also be modulated from green to blue simply by introducing the phenyl ring.

5. Conclusions

In summary, the photophysical processes and excited state dynamics of four SOXO-based molecules are investigated based on the first principles calculation. It is found that incorporating phenyl units between the donor and acceptor groups and changing the molecular types can significantly modulate the excited state properties of these molecules. The TADF mechanisms of the studied molecules are revealed by calculating k_r, k_nr, k_ISC and k_RISC, ΔE_ST and SOC based on the thermal vibration correlation function method and TD-DFT approach. Results show that the emission wavelengths of Cz-Ph-SOXO and DCz-DPh-SOXO are also modulated from green to blue by simply inserting the phenyl ring between the donor and acceptor groups. For the designed molecules Cz-Ph-SOXO and DCz-DPh-SOXO, the k_r values increased significantly compared with those of CzSOXO and DCzSOXO. The k_ISC values of Cz-Ph-SOXO and DCz-DPh-SOXO are relatively smaller than those of CzSOXO and DCzSOXO. However, the k_RISC values of Cz-Ph-SOXO and DCz-DPh-SOXO are significantly increased compared with those of CzSOXO and DCzSOXO, demonstrating that Cz-Ph-SOXO and DCz-DPh-SOXO are more facilitated to achieve the TADF process. In particular, the k_RISC values of Cz-Ph-SOXO and DCz-DPh-SOXO reached up to 1.41 × 10⁶ s⁻¹ and 2.50 × 10⁶ s⁻¹, respectively, which is beneficial to the occurrence of delayed fluorescence. Our results would be helpful for developing new SOXO-based TADF materials experimentally.

Conflicts of interest

The authors have no conflicts to disclose.

Acknowledgements

This work was supported by the Natural Science Foundation of Shandong, China, Grant No. ZR2020QB074, the National Natural Science Foundation of China, Grant No. 21503056, the Fundamental Research Funds for the Central Universities, Grant No. HIT. NSRIF. 2016090. The authors gratefully acknowledge HZWTECH for providing computational facilities.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp05632e

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