Modulation of luminescence properties of circularly polarized thermally activated delayed fluorescence molecules with axial chirality by donor engineering

Abstract

Multifunctional thermally activated delayed fluorescence (TADF) materials are currently a trending research subject for luminescence layer materials of organic light-emitting diodes (OLEDs). Among these, circularly polarized thermally activated delayed fluorescence (CP-TADF) materials have the advantage of being able to directly achieve highly efficient circularly polarized luminescence (CPL). The simultaneous integration of outstanding luminescence efficiency and excellent luminescence asymmetry factor (g_lum) is a major constraint for the development of CP-TADF materials. Therefore, on the basis of first-principles calculations in conjunction with the thermal vibration correlation function (TVCF) method, we study CP-TADF molecules with different donors to explore the feasibility of using the donor substitution strategy for optimizing the CPL and TADF properties. The results indicate that molecules with the phenothiazine (PTZ) unit as the donor possess small energy difference, a great spin–orbit coupling constant and a rapid reverse intersystem crossing rate, which endow them with remarkable TADF features. Meanwhile, compared with the reported molecules, the three designed molecules exhibit better CPL properties with higher g_lum values. Effective molecular design strategies by donor engineering to modulate the CPL and TADF properties are theoretically proposed. Our findings reveal the relationship between molecular structures and luminescence properties of CP-TADF molecules and further provide theoretical design strategies for optimizing the CPL and TADF properties.

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1. Introduction

Organic light-emitting diodes (OLEDs) with light weight and bendable properties have been extensively used in optoelectronic lighting and display fields widely.^1–3 As one of the most popular choices for light-emitting layer materials in OLEDs, thermally activated delayed fluorescence (TADF) materials can utilize the reverse intersystem crossing (RISC) process to achieve efficient use of excitons, which is due to the small energy difference between their singlet excited states and the triplet excited states.^4–8 Recently, multifunctional TADF materials have emerged to meet the needs of society. These include multi-stimulus-responsive TADF materials,⁹ circularly polarized thermally activated delayed fluorescence (CP-TADF) materials,^10–12 and aggregation-induced TADF materials.¹³ Among these, CP-TADF materials show promising development prospects due to their circularly polarized luminescence (CPL), and are widely used in the fields of three-dimensional displays and information encryption.^14,15 Moreover, CPL materials are independent of the polarizing film and 1/4 wave plate, avoiding complex device structures and the loss of luminance intensity.¹⁶ In recent years, more and more attention has been paid to CPL research. In 1997, Meijer et al. discovered the circularly polarized electroluminescence (CPEL) effect in chiral polymers.¹⁷ Since then, various CPL materials have been found. However, all of these materials inevitably exhibit efficiency roll-off, which limits the further development of circularly polarized organic light-emitting diodes (CP-OLEDs).

To address this issue, Imagawa et al. combined a chiral skeleton with a TADF molecule for the first time, which had a sufficiently small energy difference (ΔE_ST) between the first singlet excited state (S₁) and the first triplet excited state (T₁). Moreover, fast RISC could be achieved efficiently, which guaranteed high exciton utilization.¹⁸ They synthesized CP-TADF molecules with central chirality, namely 12-(2-(diphenylamino)phenyl)-12-hydroxynaphthacen-5(12H)-one (DPHN), with which CPL can be achieved with large luminescence asymmetry factor (g_lum) and considerable exciton utilization. Recently, Chen et al. realized that the large distance between the chiral skeleton and the emitting unit makes the perturbation of the chiral unit small, which limits the enhancement of the CPL properties. Therefore, they designed axially chiral CP-TADF molecules, (−)-(S)-Cz-Ax-CN and (+)-(R)-Cz-Ax-CN, synthesized by coupling two fluorophores 3-(9H-carbazol-9-yl)benzonitrile (Cz-CN). The CP-TADF molecules achieved a g_lum of 10⁻² orders of magnitude and a photoluminescence quantum yield (PLQY) of 68.2%.¹⁹ In 2020, Zheng et al. achieved better CPL and TADF properties by replacing one of the carbazole (Cz) units with phenoxazine (PXZ) based on the same chiral skeleton.²⁰ Therefore, achieving CPL while maintaining high exciton utilization has become a popular research topic in CP-TADF materials.

By changing the donor unit, it is possible to balance the properties of both CPL and TADF. This motivated us to explore the strategy of developing efficient molecules by designing and testing the luminescence properties of CP-TADF molecules with different donor units. The molecular structures in the ground and excited states are optimized using the BMK functional coupled with the 6-31G(d) basis set based on the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methods, respectively. The photophysical properties including molecular transition properties, intersystem crossing (ISC) and RISC processes, and CPL properties have been investigated in detail theoretically. The effects of donor substitutions on these properties have also been studied. The aim of our study is to propose design strategies for modulating CPL and TADF properties and offer rational suggestion for designing efficient CP-TADF molecules.

2. Theoretical methods and computational details

First, we construct all structures of molecules and use the polarizable continuum method by the Integral Equation Formalism model (IEFPCM) to simulate the liquid phase environment in toluene.^21,22 In order to make our theoretical calculations more reliable, we use different functionals (B3LYP, BMK, M062X, PBE0, and WB97XD)^23–25 combined with the 6-31G(d) basis set²⁶ for the optimization and frequency analysis of the S₁ state of Cz-Ax-CN in toluene. Fluorescence emission wavelengths are obtained and the corresponding results are listed in Table 1. It is found that the computational data (449 nm) by BMK can well match the experiment result (458 nm). In the DFT and TD-DFT calculations, some approximate methods are adopted to simplify the calculations, such as the case of two-electron integrals and Tamm–Dancoff approximation. Thus, some acceptable differences between theoretical calculations and experimental measurements are generated, such as the difference between 449 nm (computational data) and 458 nm (experiment result). This makes us to think that using the 6-31G(d) basis set to calculate the emission wavelength and other photophysical properties of molecules is reliable, and this method has been recognized in related research studies.^27,28 Therefore, for the subsequent discussion, we employ the BMK functional with the 6-31G(d) basis set. We optimize the structure of S₀ based on the structure we constructed. Then, based on the optimized S₀ structure, the S₁ and T₁ states of the four chiral TADF molecules are optimized by using DFT and TD-DFT to obtain the corresponding molecular structures. All the molecular structures are with no imaginary frequency, which determines the stability of the structures, so we can use the obtained structures to analyze the photophysical properties of the molecules. All the calculations are carried out using the Gaussian 16 program suite.²⁹

Table 1 The fluorescence emission wavelengths (nm) of Cz-Ax-CN in toluene calculated using different functionals and experimentally measured wavelengths

	B3LYP	BMK	M062X	PBE0	WB97XD	Exp.
Cz-Ax-CN	572	449	408	534	379	458

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Decay rates should also be obtained. The main formulas used in this study are summarized below.

The fluorescence radiative rate is obtained using the Einstein spontaneous emission equation:³⁰

Here, f represents the oscillator strength of S₁, ΔE_fi represents the vertical emission energy (cm⁻¹) between the S₁ and the ground states (S₀) and k_r is defined as the radiative decay rate (s⁻¹).³¹

For the non-radiative process between S₁ and S₀, the non-radiative decay rate (k_nr) is obtained from the Fermi's golden rule and Condon approximation:

Here, P_iv represents the Boltzmann distribution function of the initial state and Ĥ_fu,iv represents the interaction between two Born–Oppenheimer states. The Ĥ can be expressed as:

ĤΨ_iν = Ĥ^BOΦ_i(r, Q)Θ_iν(Q) + Ĥ^SOΦ_i(r, Q)Θ_iν(Q) (3)

Ĥ^BO represents the non-adiabatic coupling. Ĥ^SO represents the spin–orbit coupling (SOC) obtained by the quadratic response function method in the Dalton program.^32,33r and Q stand for the normal coordinates of electrons and nuclei, respectively. Φ and Θ stand for the electron wave function and nuclear vibration wave function, respectively. Then, according to the Fourier transform of the delta function, we calculate k_nr from S1 to S0 as:Here, represents the thermal vibration correlation function (TVCF) in the non-radiative process. All calculation methods and application of these formulas are also used in Shuai, Peng, Cui and our previous works.^34–43 The MOMAP program is used to perform these calculations.⁴⁴ The calculations of the SOC constant and frequency analyses are performed based on the optimized molecular structures of T₁.

Then, in order to characterize the geometric structures of different states, we calculate the root mean squared displacement (RMSD). The calculation formula is as follows:

Here i is the atomic number, and x_i and are the x-coordinates of the ith atom in the first and the second structures, respectively. y and z have a similar meaning to x. Through this analysis, we can preliminarily predict and compare the photophysical properties of molecules such as the k_nr.

Furthermore, to quantitatively characterize the CPL properties, the g_lum values can be calculated with the equation:

Here, μ and m are the electronic transition dipole moment and magnetic transition dipole moment, respectively, and θ is the angle between them.

Then, the frontier molecular orbital (FMO) analyses and natural transition orbital (NTO) analyses are both achieved using Multiwfn.⁴⁵

3. Results and discussion

Based on the proposed molecule Cz-Ax-CN synthesized by Chen's group,²⁰ we chose three different donor moieties, 9,10-dihydro-9,9-dimethylacridine (DMAC), PTZ and PXZ, to design new axial chiral TADF molecules named DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN by donor substitution engineering, and the corresponding structures are shown in Fig. 1. Then, molecular structures and transition properties as well as radiative and non-radiative decay processes are studied, and the CPL and TADF properties are revealed.

Fig. 1 The structures of the skeleton and donors for all molecules.

3.1. Molecular structures and RMSD values

Identifying the geometry of the CP-TADF molecule is the first step in studying its photophysical properties. Therefore, the structures of the ground and excited states of the four molecules are optimized by applying the BMK functional and the 6-31G(d) basis set and the stability of the structures is ensured by frequency analysis. To compare the structural differences of the molecules in different states, we calculate the RMSD values between the S₀, S₁ and T₁ states of the four molecules. The corresponding results are displayed in Fig. 2. The results show that the RMSD value between S₀ and S₁ is smaller for the Cz-Ax-CN (0.163 Å) and PTZ-Ax-CN (0.193 Å) molecules than the other two molecules (0.853 Å and 0.387 Å). This suggests that these two molecules may have smaller non-radiative quenching rates, which is consistent with our subsequent calculations of k_nr. It is found that the RMSD value between S₁ and T₁ is smaller for all molecules. Additionally, the RMSD value of the PTZ-Ax-CN (0.022 Å) molecules is significantly smaller than that of the other three molecules (0.064 Å, 0.086 Å and 0.026 Å), indicating a smaller recombination energy, which may result in a more desirable RISC process.

Fig. 2 Geometry comparisons and RMSD values of all molecules between S₀ (red), S₁ (blue), and T₁ (green) in toluene, respectively.

3.2. Thermally activated delayed fluorescence properties

The performance of TADF materials can be evaluated using the k_RISC and k_r values. The variations in the molecular geometry result in differences in the electronic structure, such as energy levels and transition properties, which ultimately affect the TADF process. Thus, we examine these characteristics by investigating the excited state and luminescence properties of the four chiral TADF molecules.

3.2.1. Energy gaps and the frontier molecular orbitals. ΔE_ST has a significant impact on the TADF properties of a molecule.^46,47 A small energy difference promotes the RISC process, resulting in a more efficient TADF. To obtain the adiabatic energy of the molecules at S₁ and T₁ states, we optimize the molecular structures to calculate the energy difference. The corresponding data are presented in Table 2. To provide a more intuitive comparison of the energy differences between the four molecules, the ΔE_ST diagram is shown in Fig. S1 (ESI†). The results indicate that the energy difference of the three designed molecules (0.06 eV, 0.04 eV and 0.05 eV) is significantly smaller than that of the original molecule (0.12 eV), making it more likely for exciton transitions from T₁ to S₁. Therefore, it is conducive to achieving efficient TADF and luminescence efficiency. To investigate the reason for the change in the energy difference, we calculate the FMOs and the corresponding results are shown in Fig. 3. According to the equation:

ΔE_ST = E_S − E_T = 2J (7)

where J is the exchange energy of the two unpaired electrons at the excited states, and E_S and E_T are adiabatic energies of S₁ and T₁, respectively. It can be observed that the HOMO of all molecules is primarily located on the donor unit, whereas the LUMO is predominantly situated on the acceptor group and chiral skeleton. Moreover, the overlap of molecular frontier orbitals is quantitatively compared using the Multiwfn program, and the corresponding results are listed in Table S1 (ESI†). Therefore, there is more distinct separation of the HOMO and LUMO for the three designed molecules (26.43%, 25.58% and 25.60%) compared to the original molecule (28.31%). This distribution of molecular orbitals is one of the reasons for the decrease in the energy difference for TADF molecules.⁴⁸

Table 2 Detailed data for Cz-Ax-CN, DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN. λ_em (nm) is the emission wavelength of the molecule, E_S is the adiabatic energy of the S₁ state, E_T is the adiabatic energy of the T₁ state, ΔE_ST is the adiabatic energy difference between the S₁ state and the T₁ state of the molecules, and f is the oscillator strength of the molecules in toluene

	λ em (nm)	E S (eV)	E T (eV)	ΔEST (eV)	f
Cz-Ax-CN	449.20	3.08	2.96	0.12	0.0347
DMAC-Ax-CN	537.27	2.87	2.81	0.06	0.0094
PTZ-Ax-CN	600.68	2.48	2.44	0.04	0.0031
PXZ-Ax-CN	603.16	2.46	2.41	0.05	0.0090

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Fig. 3 Energies and distributions of the HOMO and LUMO for all molecules in toluene.

To further determine the transition properties of the molecule,⁴⁹ we calculate the NTO based on its structures for S₁ and T₁ and the results are presented in Fig. 4, and the enlarged images are shown in Fig. S2 and S3 (ESI†). Chen's group concluded that according to the local-excited (LE) proportion, excited states can be categorized into three types of excitations: the charge-transfer (CT) state (0–40%), the hybrid local-excited and charge-transfer (HLCT) state (40–75%), and the LE state (75–100%).^50–52 According the result, the LE components of the S₁ state for the four molecules are 32.11%, 27.19%, 25.79% and 27.07%, indicating that the S₁ state of all four molecules is the CT state. However, it is worth noting that the T₁ state of all three designed molecules is the CT state and the T₁ state of the CZ molecule is the HLCT state. According to previous investigation of Penfold,^53–56 when the T₁ state of the molecule is the CT state, such a molecule usually has a smaller ΔE_ST. Combining our previous calculations of ΔE_ST and current orbital information, our calculations fit well with that conclusion. For the TADF molecule, the electronic properties are more favorable for smaller ΔE_ST and facilitate a more desirable RISC process. Moreover, by regulating the geometric structures by donor engineering, which affects the electronic structure and the ΔE_ST, it is expected to regulate the TADF properties.

Fig. 4 Natural transition orbitals (NTOs) of the S₁ and T₁ states for Cz-Ax-CN, DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN in toluene, respectively.

3.2.2. Spin–orbit coupling and decay rates. In addition to the ΔE_ST, the TADF properties are also related to the SOC between S₁ and T₁.^57,58 The SOC values of the molecule are calculated and the results are presented in Table 3. Among the four molecules, PTZ-Ax-CN (0.134 cm⁻¹) has a larger SOC value than the other three (0.055 cm⁻¹, 0.066 cm⁻¹ and 0.050 cm⁻¹), suggesting a more efficient RISC process. To enhance the intuitive comparison of the conversion processes of the molecules, we calculate the k_ISC and k_RISC values between S₁ and T₁ using data of SOC and ΔE_ST. The corresponding results are listed in Table 4 and are plotted as shown in Fig. S4 (ESI†). It is found that the three designed molecules (3.76 × 10⁶ s⁻¹, 7.67 × 10⁶ s⁻¹ and 1.73 × 10⁵ s⁻¹) exhibit a significantly higher k_RISC compared to the original molecule (5.62 × 10⁴ s⁻¹). This is closely related to their smaller ΔE_ST and larger SOC, which ensures ideal TADF properties. To investigate the energy consumption process, we calculate the k_nr of the four molecules. According to the data in Table 4, we discover that the k_nr of the three designed molecules (6.82 × 10⁷ s⁻¹, 3.31 × 10⁷ s⁻¹ and 5.62 × 10⁷ s⁻¹) is slightly increased compared to that of the Cz-Ax-CN (2.45 × 10⁷ s⁻¹), which is caused by the stronger vibrational coupling effect with smaller energy difference between S₁ and S₀ (shown in Fig. S1, ESI†). In addition, the values of k_r are calculated by combining the oscillator strength (f) obtained from the optimized S₁, and the corresponding data are shown in Table 4. The Cz-Ax-CN has a higher k_r (1.15 × 10⁷ s⁻¹) due to its stronger f (0.0347). Moreover, the DMAC-Ax-CN (0.0094), PTZ-Ax-CN (0.0031), and PXZ-Ax-CN (0.0090) have smaller f, and they also demonstrate considerable k_r (2.17 × 10⁶ s⁻¹, 5.73 × 10⁵ s⁻¹ and 1.65 × 10⁶ s⁻¹). Thus, it can be seen that all four molecules have large k_r and efficient emission can be achieved. In summary, based on the donor engineering strategy, three new efficient TADF molecules are proposed.

Table 3 Calculated SOC constants between S₁ and T₁ states for Cz-Ax-CN, DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN in toluene based on optimized T₁ structures

Unit: cm^−1	〈T1|Ĥsoc|S1〉
Cz-Ax-CN	0.055
DMAC-Ax-CN	0.066
PTZ-Ax-CN	0.134
PXZ-Ax-CN	0.050

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Table 4 Rate constants of radiative and non-radiative processes from S₁ to S₀ states as well as the ISC and RISC rates between S₁ and T₁ states for all studied molecules in toluene

	k ISC (s^−1)	k RISC (s^−1)	k r (s^−1)	k nr (s^−1)
Cz-Ax-CN	4.94 × 10^5	5.62 × 10^4	1.15 × 10^7	2.45 × 10^7
DMAC-Ax-CN	6.47 × 10^6	3.76 × 10^6	2.17 × 10^6	6.82 × 10^7
PTZ-Ax-CN	1.90 × 10^7	7.67 × 10^6	5.73 × 10^5	3.31 × 10^7
PXZ-Ax-CN	1.17 × 10^6	1.73 × 10^5	1.65 × 10^6	5.62 × 10^7

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3.3. Circularly polarized luminescence properties

In order to evaluate the CPL properties of the molecules, the electron circular dichroism spectra (ECD) are calculated using the Multiwfn program based on the optimized ground state and the corresponding results are shown in Fig. 5.^59,60 The plotted lines in all molecules are symmetric about the X-axis, indicating the presence of the cotton effect and verifying the success of the chiral perturbation strategy. This suggests that the molecules are chiral and can achieve circularly polarized luminescence. To compare the CPL properties of the four molecules, we also conduct vertical emission calculations based on the S₁ structure. Combining the result of vertical excitation and vertical emission, we calculate the circularly polarized absorption asymmetry factor (g_abs) and the circularly polarized luminescence asymmetry factor (g_lum), respectively, and the data are listed in Table S2 (ESI†) and Table 5. Based on these data, it can be observed that the angles between the electronic transition dipole moment (μ) and magnetic transition dipole moment (m) of the four molecules are approximately 180°, with cosine values of −1. This indicates that the two dipole moments are oriented in opposite directions. Research has shown that the CPL properties of chiral molecules can be measured using the g_lum. The larger the absolute value of this factor, the better the circularly polarized properties of the molecule. Combined with the theoretical formulas, it is evident that the value of the g_lum is primarily influenced by three factors: the μ, m and θ. Our previous study has indicated that the angle between the two dipole moments has the greatest impact on the luminescence asymmetry factor,⁶¹ and we aim to obtain a dipole moment angle with a larger cosine value. From this perspective, for these four axially chiral molecules with some symmetry, their dipole moment angles are almost always optimal, demonstrating the advantage of this design strategy. Simplifying the calculation formula, we can get , i.e., the g_lum is proportional to the absolute value of the μ and inversely proportional to the absolute value of the m. As the μ is two orders of magnitude larger than that of the m, decreasing the former may be an effective strategy for obtaining better circular polarization properties. To verify this, we plotted a line graph of the g_lum and the μ, as shown in Fig. 6. This is consistent with our conjecture and confirms the effect of μ on the nature of CPL. We find that the three designed molecules have a more desirable g_lum than the original molecules due to their smaller μ. PTZ-Ax-CN has the smallest μ and the largest g_lum. Thus, using the donor engineering strategy, the CPL properties are modulated. Compared with the reported molecule (Cz-Ax-CN), three new efficient CP-TADF molecules (DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN) with large RISC rates and large g_lum values are theoretically proposed.

Fig. 5 ECD spectra of Cz-Ax-CN, DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN in toluene. The rotatory strength is also illustrated.

Table 5 The data of luminescence asymmetry factor (g_lum) for Cz-Ax-CN, DMAC-Ax-CN, PTZ-Ax-CN and PXZ-Ax-CN in toluene

	|μ| (×10^−18 esu cm)	|m| (×10^−20 erg G^−1)	cos θ	g lum (×10^−2)
Cz-Ax-CN	1.806	0.471	−1	−1.04
DMAC-Ax-CN	1.028	0.379	−1	−1.47
PTZ-Ax-CN	0.623	0.348	−1	−2.23
PXZ-Ax-CN	1.058	0.382	−1	−1.45

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Fig. 6 Calculated luminescence asymmetry factor (g_lum) and transition electric dipole moments (μ) of the molecules.

4. Conclusion

In summary, through first-principles calculations with the TVCF method, this work validates the design strategy for efficient CP-TADF molecules by donor engineering. The results show that modulation of the donor unit can achieve a smaller ΔE_ST and a smaller μ for the axial chiral TADF molecule. The former facilitates the RISC process and thus promotes the efficient utilization of the triple excitons, which is essential for effective TADF emission. The latter ensures the desired g_lum, which indicates that the molecule can achieve better CPL properties. For three designed molecules, we also observed that the S₁ and T₁ all possess CT features, and this results in smaller ΔE_ST required for an efficient RISC process. Additionally, we have computationally verified the relationship between the μ and the g_lum. Therefore, it is possible to modulate the μ by regulating the donor unit of CP-TADF materials to achieve a large g_lum. Thus, three new efficient molecules with dominant CPL and TADF properties are theoretically proposed, and wise molecular design strategies by donor engineering to modulate the CPL and TADF properties are illustrated. This work reveals the inner relationship between molecular structures and luminescence properties, and could provide theoretical guidance for designing new efficient CP-TADF molecules.

Author contributions

S. L.: writing-original draft; S. L.: visualization; Y. G.: methodology; L. L.: conceptualization and formal analysis; C.-K. W.: supervision; J. F.: writing-review & editing; Y. S.: writing-review & editing.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 11874241, 12274266, 11874242, 21933002 and 12374269). Thanks to Professor Yingli Niu for his great help in the usage of MOMAP.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cp00341a

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