State Key Laboratory of Organic Electronics and Information Displays & Jiangsu Key Laboratory for Biosensors, Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing University of Posts & Telecommunications, Nanjing 210023, China
Thermally activated delayed fluorescence (TADF) materials have attracted significant attention due to their promising performance in organic light-emitting diodes (OLEDs) with theoretical 100% internal quantum efficiency through upconversion of triplet excitons into singlet excitons via reverse intersystem crossing (RISC) process. However, the experimental development of high-performance TADF materials is complicated and time-consuming. Theoretical calculations could intrinsically establish the structure-performance relationship, predict the properties and provide molecular design strategies. In this paper, aiming to develop high-performance TADF materials, started from the principle of luminescence, we systematically expound the molecular design strategies, and the calculation principles, methods and research progress of the photophysical parameters such as the single-triplet energy gap (ΔEST), the (reverse) intersystem crossing rate, absorption/emission spectrum and radiation/non-radiation rate. Finally, the opportunities and challenges faced by the theoretical research of TADF materials are discussed. Through the overview of the theoretical research of TADF materials and the outlook of the research prospects, we look forward to attracting more researchers and promoting the development and breakthrough of this field.
Zhang Yewen, Yang Qingqing, Zhou Cefeng, Li Ping, Chen Runfeng.
The Photophysical Behavior and Performance Prediction of Thermally Activated Delayed Fluorescent Materials.
Progress in Chemistry, 2022, 34(10): 2146-2158 DOI:10.7536/PC211229
4.2 Evaluation of(reverse)intersystem crossing process
4.3 Simulation of absorption and emission spectra
4.4 Calculation of radiation rate and non-radiation rate
4.5 Prediction of LE and CT characteristics
5 Conclusion and outlook
1 Introduction
The discovery of Thermally activated delayed fluorescence (TADF) can be traced back to 1961. Parker and Hatchard first observed the phenomenon of delayed fluorescence in eosin dye, but it did not attract much attention[1]. It was not until 2009 that TADF materials were used in Organic light-emitting diode (OLED) devices[2]. In 2012, Adachi et al. Used TADF materials as the active layer, and the maximum External quantum efficiency (EQE) of OLED devices was as high as 30%, which broke the efficiency limitation of traditional fluorescent OLEDs and was comparable to the efficiency of devices containing heavy metals, causing a wave of research on TADF materials[3]. Consistently, the reported TADF materials focus on the Donor-Acceptor (D-A) type structure, which realizes a small singlet-triplet energy level difference (the highest occupied molecular orbital) through the spatial separation of the highest occupied molecular orbital (the highest occupied molecular orbital, HOMO) and the lowest unoccupied molecular orbital (the lowest unoccupied molecular orbital, LUMO) electron cloud density distributions to meet the realization of efficient interantisystem crossing (Reverse intersys te. In 2016, Hatakeyama et al. Synthesized a new type of Multiple resonance TADF (MR-TADF) material by introducing boron/nitrogen atoms and combining adjacent phenyl groups to construct a rigid polycyclic aromatic skeleton[4]. Due to the opposite resonance effect of the nitrogen atom and the boron atom, the electron cloud distribution of the HOMO and LUMO orbitals is obviously separated without introducing a donor or acceptor group, and the material can realize narrow-band emission and obviously improve the color purity. In addition, the luminescent color of TADF materials has also experienced the development from blue to red, showing great application potential in OLED, but the traditional development of TADF materials is based on the trial and error of experiments and the intuition of chemists.The diversity of organic functional fragments will hinder the screening of high-performance TADF materials, so the experimental development of high-performance TADF materials is very time-consuming, and there is an urgent need for forward-looking molecular design strategies to guide the development of new high-performance materials[5⇓⇓⇓⇓⇓⇓⇓~13][14⇓⇓⇓~18].
Theoretical calculation can study the microstructure of compounds in advance, predict their photophysical properties, establish the structure-property relationship of materials from the microscopic point of view, and provide some guidance and suggestions for the design of molecules. In this paper, the design and development of high performance TADF materials are focused on, and the theoretical research progress of TADF materials is described from the aspects of molecular structure design strategy, calculation method of photophysical properties and performance prediction.
2 Photophysical Processes and Molecular Design Strategies of TADF
Delayed fluorescence can be divided into E-type and P-type delayed fluorescence according to the type of triplet-to-singlet conversion process. In E-type delayed fluorescence, when the energy of the lowest triplet (T1) is close to that of the lowest singlet (S1), that is, the ΔEST is small, the triplet exciton can be partially converted into a singlet exciton, which is also called the TADF process[19,20][21,22]. P-type delayed fluorescence originates from the formation of a singlet exciton by triplet-triplet annihilation (TTA)[23⇓~25]. This paper will mainly discuss the E-type delayed fluorescence, whose photoluminescence and electroluminescence processes are shown in Fig. 1.
In the photoluminescence process of TADF, only singlet excitons are generated after photoexcitation, singlet excitons decay to the ground state (Ground state,S0) through radiative (fluorescence) or non-radiative (internal conversion), and some singlet excitons decay through Intersystem crossing.The triplet exciton is converted into a singlet exciton through the RISC process, and the singlet exciton is converted into a singlet exciton again through the RISC process, and the formed singlet exciton emits light, namely Delayed fluorescence (DF). In the process of electroluminescence, holes and electrons form excitons under the action of an applied electric field. According to the spin selection rule, the formation ratio of singlet and triplet excitons is 1 ∶ 3[26]. Under an electric field, 25% of singlet excitons decay to the Internal quantum efficiency, which can emit Prompt fluorescence (PF) with nanosecond lifetime; 75% of triplet excitons are converted into singlet excitons through RISC under thermal activation, which can produce DF with microsecond or even millisecond lifetime, and theoretically achieve 100% Internal quantum efficiency (IQE)[27].
From the luminescence mechanism, it can be concluded that the triplet-to-singlet RISC process of TADF molecules is essential for the EQE of their devices. In addition to the device efficiency, the device lifetime, the Full color coverage of the emission color, and the Full width at half maximum (FWHM) of the emission spectrum are also strongly dependent on the performance of the TADF material[28]. For conventional D-a type TADF materials, the electron density distribution of HOMO and LUMO can be effectively separated, and a small ΔEST can be obtained, which is conducive to achieving a large RISC rate[29,30]. However, D-a molecules are excited to form an intramolecular charge transfer (ICT) state, which results in a broad emission spectrum (FWHM 70 ~ 100 nm), thus affecting the color purity of the device[31]. At the same time, the stability of material molecules will affect the lifetime of the device. For MR-TADF materials, the multiple resonance effect makes the materials obtain narrow band emission, but the MR system is limited and the red light materials are scarce. Therefore, how to obtain materials with new structures to regulate the properties of TADF materials, so as to balance the device efficiency, lifetime and color, is a key scientific issue in this field.
The current molecular design strategies for TADF materials can be roughly summarized as follows (Figure 2): 1) introducing a structure with large steric hindrance, destroying the conjugation of the linking group between the donor and the acceptor, designing an X-shaped molecular structure, and constructing an asymmetric structure, so as to effectively separate the electron density distribution of HOMO and LUMO orbitals, thereby obtaining a small Δ and achieving a highly efficient T1→S1→S0 process[32⇓~34][35,36]; 2) increase that Photoluminescence quantum yield (PLQY) by increasing the phenyl connection, expand the dispersion of HOMO in the molecular orbital, and adopting a dual-emission core structure[37,38]; 3) designing a rigid donor/acceptor structure to improve FWHM, constructing multiple resonance structures such as boron/nitrogen, carbonyl/nitrogen and the like to realize short-range charge transfer, obtaining narrow-band emission, and improving color purity[39,40]; 4) Design donor and acceptor materials with triazine, benzonitrile, and carbazole derived chemical groups, etc., to increase the bond dissociation energy of the materials to ensure stability[41,42].
In a word, the effective separation of HOMO and LUMO electron density of TADF materials can ensure a small ΔEST value and achieve an effective RISC. A certain degree of orbital overlap can improve the radiative transition efficiency and increase the PLQY to achieve a higher EQE. The use of rigid skeleton and resonance effect is beneficial to the improvement of FWHM. The stability of the material itself will affect the lifetime of the device. Considering the above factors and balancing the requirements of various factors on the molecular structure, we can design and develop high-performance TADF materials.
3 Computational theory of TADF materials.
The accurate description of the ground state and excited state structure of pure organic light-emitting materials is the basis and guarantee of theoretical research and prediction of their photoelectric properties. At present, there are many theoretical prediction methods reported. Although the semi-empirical configuration interaction with single substitute (CIS) method has high computational efficiency, its accuracy is relatively low. The full coupled-cluster singles and doubles model (EOM-CCSD) method, which considers both single and double excitations, has greatly improved accuracy, but is very expensive. Considering timeliness and accuracy, Density functional theory (DFT) is the most recognized and widely used[43,44]. Time-dependent density functional theory (TD-DFT) is used to study the properties of excited States, but the system depends on the functional and basis set, so it is very important to choose the appropriate functional and basis set for different systems. Common DFT functionals and their HF content are listed in Table 1.
DFT functionals can be divided into three types: the first type is single functional (pure functional), including PBE, SVWN, etc. The second type is hybrid functional, including B3LYP, PBE0, M06-2X, etc. The third category is the long-range correction functional, including ωB97X, LC-ωPBE, etc. An accurate and quantitative description of the energy and properties of molecules requires that the functional used can not only take into account the Localized excitation (LE) States, but also correct the CT States. The Range-separation parameter can be adjusted by the modern long-range correction functional. The Coulomb operator is decomposed into a long-range part and a short-range part by using the standard error function (1), and the boundary between the long-range part (Hartree-Fock exchange energy representation) and the short-range part (local density approximation representation) is determined by the separation parameter ω (unit :Bohr-1). It realizes the accurate correction of the long-range Coulomb interaction asymptote in the physical sense, and provides a theoretical guarantee for the accurate quantitative description of the properties of excited States.
Where erf is the error function, r12 is the distance between electrons, and the parameter ω depends on the electron density distribution of the system, and different systems have different values of ω. The parameter ω is usually determined by the method of forced DFT self-consistent Koopmans' theorem, that is, by adjusting the parameter ω, the vertical Ionization potential (IP) of the system is consistent with the eigenvalue of the HOMO orbital of the neutral system, as shown in formula (2).
In the above formula, Δip(ω) is the absolute value of the difference between the vertical ionization energy of the system and the HOMO orbital eigenvalue, is the HOMO orbital eigenvalue, Egs(ω,N) is the energy of the ground state, and Egs(ω,N-1) is the ground state geometric upper cation state energy. Finally, the Δip(ω) is minimized to obtain the optimized value of ω parameter.
DFT theory and TD-DFT theory are widely used in the study of ground state and excited state properties of large and medium-sized molecular systems[45,46]. The hybrid functional is widely applicable to the ground state properties of TADF molecules, and B3LYP, as a comprehensive hybrid functional, is reliable for the optimization of the ground state configurations of medium-scale molecules[47]. But in the calculation of excited States, the choice of functional is different due to the characteristics of excited States. For different TADF molecular systems, different hybrid functionals or long-range correction functionals should be selected to calculate the related properties, and compared with the experimental values or high-precision calculated values, so as to select a reliable theoretical calculation method that can quantitatively describe the related properties, and discuss the effects of different functionals on the related properties.
4 Theoretical Prediction of TADF Material Properties
Based on the selected theoretical methods, the ground state and excited state properties are calculated and simulated, such as the intersystem/antisystem crossing rate is measured by calculating the ΔEST and Spin-orbit coupling (SOC), and the peak value and peak width are discussed by simulating the absorption/emission spectra. Some parameters are used to predict the properties of TADF materials, and the structure-property relationship of materials is established, which provides theoretical guidance and suggestions for the design of high performance TADF materials.
4.1 Calculation of ΔEST.
The ΔEST is one of the most important physical parameters of TADF luminescent materials, and a small value of ΔEST is the main characteristic of TADF materials, which greatly affects the RISC process:
It can be seen from the equation that a small ΔEST can increase the triplet exciton to singlet exciton conversion efficiency, which is beneficial to increase the EQE of TADF materials. Therefore, accurately predicting the ΔEST value of molecules is essential for screening potential high-efficiency TADF materials. ΔEST is defined as the energy level difference between the singlet energy level and the triplet energy level, usually considering the S1 energy level and the T1 energy level, which depends on the exchange energy between the singlet excited state and the triplet excited state, as shown in (4).
Where ES is the singlet energy, ET is the triplet energy, E is the orbital energy, and K is the electron repulsion energy. In the same molecule, the electron arrangement of the singlet and triplet States is the same, so the E and K values of the singlet and triplet States are the same. However, the triplet state is stabilized by the presence of an unpaired electron in a different orbital, while the singlet state is relatively unstable due to the presence of a paired electron in the same orbital. The degree of stabilization and destabilization is J, so the energy gap of the singlet and triplet States is 2 J. The J value is determined by the overlap integral of the HOMO and LUMO of the TADF molecule, and a smaller overlap of the HOMO and LUMO is beneficial to obtain a small J value, that is, the ΔEST can be reduced by reducing the overlap of the HOMOs and LUMOs. The materials reported so far are realized by spatially separating the HOMO and LUMO through donor-acceptor structures, multiple resonance structures, and conjugated structures.
Accurately predicting the ΔEST value of a molecule is one of the important theoretical criteria for judging it as a potential TADF material. Huang Shuping et al. Proposed a set of theoretical prediction methods for calculating ΔEST for a series of CT molecules, as shown in Fig. 3[48]. Firstly, the stable ground state structure was obtained by B3LYP, and the charge transfer (Q) from HOMO to LUMO was calculated by Multiwfn[49]. Secondly, According to the optimized HF (OHF) relation OHF% = 42q, the functional close to the proportion of OHF is selected, and the vertical absorption energy EVA(S1)-HF% curve of the S1 level is simulated.EVA(S1,OHF) is obtained, and according to the relationship between EVA and E0-0, E0-0(S1) is obtained.Where ΔEV is the vibrational level difference between the vertical transitions and is about 0.15 eV,ΔEStokes for the conjugated molecule is the Stokes shift energy loss (0.09 eV); Then, since the T1state can be either the CT state or the LE state,The relationship between EVA and E0-0 is different, and E0-0(3CT) and E0-0(3LE) are calculated respectively through the correction factor C=EVA(S1,OHF)/EVA(S1,BLYP). Finally, the ΔEST is calculated according to whether the T1state is the CT state or the LE state. They used the OHF method to calculate the ΔEST values of the series of molecules (Fig. 4), and the theoretical and experimental values are listed in Table 2. It can be seen from the data that the theoretical value is in good agreement with the experimental value, which shows the effectiveness of the method to predict the ΔEST value of TADF molecule.
When OHF chooses the best HF content, the electronic structure of the molecule is uncertain, and the density of excited States is highly dependent on the HF content, so there will be uncertainty in choosing the best HF ratio, and the division of molecular fragments has a certain degree of randomness. Zhang Qisheng et al. Developed the K-OHF method on the basis of OHF. Based on the ground state structure optimized by B3LYP, the PBEα method was used to calculate the HOMO-LUMO energy level difference Δε and the vertical excitation energy difference ΔEVA(S1) of the S1 energy level under α = 0.1 and α = 0.9, respectively. According to formula (5), the optimal HF% was calculated[50].
Sun et al. Used a tunable long-range functional to study traditional TADF materials with ΔEST less than 0.1 eV[51]. They used functionals with different HF hybridization ratios, including PBE, B3LYP, M062X, M06HF, LC-ωPBE and LC-ωPBE *, to calculate the TADF molecules studied, and analyzed the average absolute error, relative error and linear correlation coefficient between the theoretical value and the experimental value. Where all single-point calculations have been performed for the N and N ± 1states using the default SCF convergence criterion in Gaussian, and the optimal ω value is obtained with the method of "golden ratio". The results show that the optimal range separation parameter ω of these TADF molecules is less than the 0.2 Bohr-1. This work confirms the importance of controlling the value of ω for accurately describing the properties of TADF molecules, and provides a theoretical basis for calculating the triplet energy levels and ΔEST of TADF molecules. This kind of control makes the calculated HOMO orbital energy approximately equal to the ionization energy by controlling the ω value, which is called IP control. This requires several self-consistent field calculations in the anionic, neutral, and cationic States to determine the optimal ω, but this regulatory approach is relatively time consuming, especially for larger molecules.
The localized orbital locator (LOL) is used to divide the electron density, which can quickly obtain a ω value equivalent to that of IP regulation only by using the localized orbital locator to calculate the single point energy, thus greatly reducing the computational cost[52]. Since hybrid functionals, such as B3LYP, significantly underestimate the EVE(S1), while RS functionals, such as LC-ωPBE, overestimate it, the use of LC-ωPBELOL can significantly improve the accuracy, and the Tamm-Dancoff Approximation (TDA) is used for triplet calculations to avoid triplet instability[53][54]. Fig. 5 shows the specific method: (1) using TD-DFT to optimize the S1structure by CAM-B3LYP/6-31G (d) under the PCM model; (2) optimize that structure of the T1 by CAM-B3LYP/6-31G (d) under the PCM model by TDA-DFT; (3) Based on the optimized structure of the S1, the LOL method is used to make the EVE(S1) close to the ionization energy, and the appropriate ω value is selected to obtain the energy of the S1; (4) to calculate the energy of T1 using LC-ωPBELOL at the determined value of ω; (5) The ΔEST of adiabatic excitation is obtained by the calculation of the LC-ωPBELOL method.
4.2 Calculation of intersystem crossing rate and antisystem crossing rate
The process of exciton conversion in TADF materials is closely related to the intersystem/antisystem crossing process, which is a non-radiative transition between two equal energy vibrational levels of electronic States with different multiplicities[55]. In general, the S1state exciton is converted to the T1 state by ISC, because the S1 energy level is higher than the T1 energy level.The exciton in the T1state can be converted to the S1 state by RISC in a thermally assisted manner, and then the delayed fluorescence is emitted from the S1 state. Exciton conversion will be affected if the intersystem crossing rate is too high or the antisystem crossing rate is too low. Reasonable intersystem crossing rate and antisystem crossing rate are beneficial to improve the efficiency of TADF materials. According to the first-order perturbation theory, Fermi's golden rule (FGR), the intersystem crossing rate and the antiintersystem crossing rate are related to the SOC and the Fermi's golden rule by the following equations:
Where <S1|ĤSOC|T1> is the spin-orbit coupling constant matrix element between S1 and T1 States with different spin multiplicities, while ρFC represents the Frank-Condon weighted density of States. Under high temperature conditions (usually room temperature), the ρFC can be expressed by the semiclassical Marcus theory as Eq. (7):
Where λ is the reorganization energy associated with the ISC/RISC process, kB is the Boltzmann constant, T is the temperature, and ΔE is the energy difference between the initial and final States at the optimized structure, ΔEST for adiabatic. λ can be calculated by the classical four-point method or the normal-mode analysis method (NMA).
The reorganization energy between singlet and triplet excited States is one of the important factors affecting intersystem/antisystem crossing, which can be simply calculated by the four-point method proposed by Nelsen et al[56][57]. The potential energy surfaces of the lowest singlet and triplet excited States are shown in Fig. 6, and the reorganization energy of the ISC process corresponds to λISC and the reorganization energy of the RISC process corresponds to λRISC, as shown in Eq.
Where ES(GS) and ET(GS) represent the energy of S1 and T1 at the stable configuration of S1, respectively,ES(GT) and ET(GT) then represent the energy of S1 and T1 at the stable configuration of T1, respectively.
In addition to the four-point method, NMA can also be used to calculate the reorganization energy. NMA takes into account the relationship between the vibrational frequency and the reorganization energy. The total reorganization energy is the sum of the contributions of each vibrational mode, and the formula is as follows:[58]
Where ΔQi is the displacement between the two state minima contributed by the ith mode, Si is the Huang-Kun factor corresponding to the ith vibration mode, and (Huang-Rhys factor),ki and ωi are the force constant and vibration frequency of the corresponding vibration mode, respectively. The stable configurations of S1 and T1 were input using the DUSHIN program, and the output contained the contribution of each vibrational mode to the reorganization energy as well as the total reorganization energy[59].
Spin-orbit coupling is the result of the interaction between the spin and orbital motion of electrons, which can mix singlet and triplet excitons. The Hamiltonian operator of spin-orbit coupling is given by the following formula:[60,61]
Where, is the fine structure constant; The is the effective nuclear charge of the atom; and are the electron spin and orbital angular momentum, respectively. Using first order perturbation theory, the spin-orbit coupling constant between the singlet and triplet States can be estimated with the zeroth order vector:
Fig. 7 and Table 3 show the chemical structures of the four studied molecules and the relevant data for the calculated ISC/RISC rates. It can be found that there is still a gap between the calculated rates and the experimental rates, but it can provide a predictive trend[55]. In addition, the related theoretical parameters can also qualitatively describe the effectiveness of the RISC process[62]. Such as Δαn, represents the change in the n-orbital composition of the highest occupied natural transition orbital when the exciton switches from the S1 state to the T1 state. As shown in Table 3, the Δαn values well reproduce the effectiveness of different molecular ISC processes, which provides an effective method for predicting ISC rate trends. The overlap (I) or the separation distance (R) of the frontier molecular orbitals can also describe the ISC/RISC process. The smaller the overlap (I) and the larger the separation distance (R), the smaller the ΔEST, and thus promote the ISC/RISC process.
The intersystem crossing rate and antisystem crossing rate are of great significance to the exciton conversion process of TADF materials. At present, it is still difficult to predict the ISC/RISC rate accurately by theoretical calculation, and new theoretical models need to be developed to predict the ISC/RISC rate of materials.
4.3 Calculation of absorption and emission spectra.
The simulation calculation of the spectrum can not only obtain the position and intensity of the peak, but also predict the half-peak width, which provides a theoretical basis for the design of materials with high color purity. The essence of light absorption and light emission is that when a molecule is in the S0, it absorbs a part of its energy to the excited state (Sn,n≥1), reaches the S1 through energy relaxation, and returns to the S0 from the S1, releasing part of its energy in the form of light. Absorption (UV) and emission (PL) spectra are the basic optical characterization methods of material molecules in experiments. Accurate simulation of the spectrum can not only get the position and intensity of the peak, but also get the FWHM, and then predict the color purity of the material. The structural relaxation of the ground state and excited state involved in the luminescence process of the material will affect the FWHM of the emission spectrum, and the smaller the relaxation energy is, the smaller the FWHM is. At the same time, the weak vibrational coupling between the excited state and the ground state can not only realize the narrow emission of the spectrum, but also suppress the non-radiative transition process, which is conducive to obtaining high-performance narrow-band luminescent materials (Fig. 8)[11].
The measurement and calculation of absorption and emission spectra are important to reflect the excited state of molecules, and the accurate simulation of the spectra is also one of the difficulties in the theoretical study of TADF performance. Because the excited state is an unstable state with high energy, it is difficult to observe its specific properties and States in experiment. In recent years, with the innovation of experimental instruments, some equipment for in-depth study of excited States has been available, such as transient spectroscopy, but it is expensive, complex to operate and difficult to popularize. Theoretical calculation can solve this kind of problem relatively well. In view of the dependence of the calculation of excited state properties on the functional, it is an important basis to evaluate and select the applicable functional by simulating the absorption and emission spectra of TADF molecules and comparing them with the experimental values.
The solvent effect has many effects on the excited state, such as the position of the peak, the intensity of the absorption/emission, the width of the peak, and the structure of the excited state. Solvent should be taken into account in the calculation of problems related to electronic excitation that actually occur in solution, and the stronger the polarity of the solvent, the greater the necessity of consideration[63,64]. The solute polarizes the solvent, including the electronic structure and molecular orientation of the solvent, which correspond to the fast and slow parts of the solvent relaxation, respectively. For a system in a certain electronic state, if both parts of the solvent have relaxed for it, it is called an equilibrium solvent (eq); If only the fast part relaxes, it is called a non-equilibrium solvent (neq). The process of vertical absorption and vertical emission is very short. In the final state, only the electrons of the solvent molecules have time to be repolarized, and the orientation has time to be repolarized and remains in the initial state. Therefore, the initial state should be calculated in the equilibrium solvent, while the final state should be calculated in the non-equilibrium solvent. The adiabatic absorption/emission process can be considered as the complete relaxation of the solvent in the initial and final States, that is, in the equilibrium solvent. The calculation of absorption/emission energy in solvent is strictly required to account for non-equilibrium solvent effects, although their influence may not be very large. The absorption and emission processes are shown in Figure 9, and the calculation method is shown in Equation (14).
Where λ1 represents the vertical absorption energy, λ2 represents the vertical emission energy, and λ3 and λ4 represent the adiabatic absorption energy and adiabatic emission energy, respectively. In Fig. 9, a, B, C and d represent EGS(RGS,eq), EGS(RES,neq), EES(RES,eq) and EES(RGS,neq);EES and EGS represent excited and ground state energies, respectively; RES and RGS represent the excited state minimum structure and the ground state minimum structure, respectively. For example, the EES(RGS,neq) represents the excited state energy in the ground state minimum structure and in the non-equilibrium solvent.
4.4 Calculation of radiative and non-radiative rates.
In the luminescence process of TADF materials, there is a competitive relationship between the radiation process and the non-radiation process, so it is necessary to minimize the energy loss in the non-radiation process and increase the fluorescence rate and intensity of the materials. Therefore, TADF materials not only have small ΔEST, but also need large radiation rate, both of which are the key to ensure efficient TADF materials[65]. The radiation rate (kr) of the excited state in the radiative transition process is mainly related to the energy level of the excited state and the oscillator strength, which can be simply estimated by using Einstein's formula:[66]
Where f is the oscillator strength and is a dimensionless quantity; ΔE is the radiation energy of the excited state in units of cm-1;kr in units of s-1. Einstein's formula is applicable to the calculation of both fluorescence and phosphorescence rates, and generally agrees well with the experimental values. If the calculated results are quite different from the experimental values, it may be that significant non-radiative transitions have occurred in the molecule.
In addition, considering the coupling effect between the electronic state and the vibrational multilevel, a more universal method for calculating the radiative rate is to integrate the emission spectrum:
Where ufi is the transition dipole moment, Piv is the Boltzmann distribution function, Φ is the nuclear vibrational wave function, and u and V are the vibrational quantum numbers.
For the non-radiative rate knr, the reorganization energy of the ground state and the excited state structural relaxation needs to be obtained, and the sum of the contributions of the normal mode relaxation in the resonant approximation represents the reorganization energy of knr. Based on the first-order perturbation theory and FGR, the formula is derived as follows:
Where Qizhong is Planck's constant, the delta function δ is to preserve energy conservation, and H is the interaction between two different Born-Oppenheimer States. Based on the Fourier transform to the delta function, which in turn can be converted to Equation 19.
Where ρIC(t,T) is the thermal vibrational correlation function (TVCF),Rkl is the non-adiabatic electronic coupling and Zi is the partition function.
In general, the non-radiative rate of molecules in the same system will gradually increase with the red shift of wavelength, as shown in Fig. 10 and Table 4. When carbon atoms are replaced by oxygen atoms, the wavelength shifts from 533 nm to the 577nm,knr and increases by two orders of magnitude[6]. Therefore, red-emitting materials need to overcome certain non-radiative processes to achieve the highest possible efficiency.
The above radiative and non-radiative rates can be calculated by the MOMAP package developed by Shuai Zhigang et al[67].
4.5 LE and CT characteristic prediction
The excited state of TADF materials is usually the charge transfer (CT) state, the localized excitation (LE) state, or a mixture of the two. Efficient TADF materials generally have two triplets with different characteristics, and the current research on CT/LE States is mainly focused on traditional TADF materials[68]. In this regard, the characteristics of the excited state can be described and judged by some parameters, and different characteristics have an important impact on the exciton conversion process.
In 2016, Gibson et al. Used quantum dynamics method to study the lowest singlet excited state (1CT) and the lowest triplet excited state (3CT and 3LE) of TADF molecule.Exploring the effect of vibrational coupling on the RISC process, it is demonstrated that vibrational (non-adiabatic) coupling between 3LE and 3CT provides the potential for second-order coupling effects and exhibits an order of magnitude increase in kRISC[69]. They also divided the effects of the three forms on the RISC process according to the location of the 3LEstate, as shown in Fig. 11 for the :(a)3LE state in the 3CT state; The (b)3LEstate is degenerate with the 3CT state. The (c)3CTstate is in the 3LE state. For these three forms, (a) shows that the 3LEstate first reaches the 3CT state, and then the direct second-order coupling occurs through the 3LEstate; While (B, C) show that there is no need to reach the 3CTstate first. For the three modes, the vibrational coupling between the 3LEstate and the 3CT state can promote the RISC process.Because of the large vibrational coupling, the 3LEstate and the 3CT state can be quickly balanced, and the effective vibrational overlap between the 3CT and the 1CT makes the exciton conversion between them take place effectively. In the same year, Etherington et al. Further demonstrated that 3LE enhances SOC between singlet-triplet States, thereby promoting the RISC process[70]. The efficiency of the TADF material reaches the maximum by controlling the energy level sequence of the molecular 3LE and 3CT of the material, which confirms the RISC process model and the importance of the 3LEstate with energy close to the S1 state for achieving efficient TADF. The characteristics of the excited state also affect the ΔEST, and Kim et al. Showed that the T1 state has obvious CT characteristics, which is beneficial to reduce the Δ. Br BrÉdas et al. Studied a series of TADF molecules reported, and discussed the influence of singlet-triplet characteristics on the up-conversion of triplet excitons to singlet excitons.The results show that the T1 has obvious CT characteristics or the smaller energy gap of 3LE and 3CT is beneficial to obtain smaller ΔEST,S1.And that CT component in the T1state has a great contribution to the ΔEST and SOC,This is advantageous for the RISC process of the material[72].
Excited state properties play an important role in the performance of TADF materials, and the theory proposes parameters to predict the excited state properties, which are closely related to the geometric structure and its fluctuations near equilibrium. These parameter classes can be divided into two categories: molecular orbit-based measures and density difference-based measures. At the same time, from a quantitative point of view, the use of relaxed and non-relaxed densities may cause differences in the results. Table 5 summarizes the relevant parameters and their limiting values that are commonly used in current theory. Where the parameter I represents the overlap between a pair of occupied orbital (I) and unoccupied orbital (a); The parameter Δr represents the separation distance of the center of mass of the hole and the electron after the molecule is excited; The t index indicates the degree of separation of holes and electrons, and t < 0 indicates that there is no obvious separation of holes and electrons; The density-based descriptor DCT represents the distance between the centers of gravity of the densities associated with the electronic transitions; ϕS represents the overlap between electron-withdrawing/electron-donating densities[73]. Among them, the parameters based on orbitals need to be further considered. For example, the excited state may involve multiple pairs of orbitals, and the meaning of I value will be different. For traditional TADF materials, the amount of CT-LE mixing is determined by the size of the electronic coupling between the donor and acceptor, which in turn is determined by the molecular structure (such as the torsion angle between the two groups), usually in the structure close to D-A orthorhombic, showing larger CT characteristics, that is, small ϕS and large Δr. For the D-A-D type symmetric structure, if the molecule has strong CT excited state characteristics, the hole centroid and the electron centroid coincide to some extent due to symmetry, and the final Δr may be less than 22 Å. Fig. 12 demonstrates the excited state properties of two D-A-D type TADF molecules, S1 and T1 of 2PXZ-OXD are CT properties, where Δr of T1 state is 1.8585 Å (Δr < 22 Å); However, the T1 of 2PTZ-TAZ is CT-LE, which is close to the orthorhombic structure, but the donor shows LE characteristics[74]. Ciofini et al. Proposed a new descriptor to quantify the electron-hole distance associated with charge transfer, even for symmetric molecules[75]. DCT results in quantitative analysis by calculating the electron density of the ground and excited States and can be calculated at any level of theory, such as density functional and wave function based methods, but this descriptor exhibits the same dilemma as the Δr descriptor for symmetric systems. The new descriptor ADCT, interpreted as a weighted average of distances between holes and electrons, is universal for symmetric and asymmetric systems. Since ADCT takes into account all possible physical distances between opposite charges, instead of estimating the unique distance between the average center of gravity of an electron and a hole as DCT, DCT is less than or equal to ADCT in absolute value, and ADCT is an average concept, essentially a scalar. The charge transfer distance value of ADCT is more accurate than that of DCT, and it is believed that there will be more applications in the future. In addition, the excited state characteristics can also be judged by the analysis of charge transfer amount[58]. To put it simply, taking the D-A type TADF molecule as an example, there may be three types of charge transfer: D → D, A → A, and D → A. Through the percentage of charge transfer in these three forms, we can know the composition of CT and LE, and then judge the type of excited state characteristics or which characteristics are dominant. The characteristics represented by the percentage range of charge transfer need to be evaluated by researchers according to their own experience. The study of excited state properties is of positive significance for the design of materials. The study shows that 3LE is more stable than 3CT, which is consistent with the increase of electron exchange energy with the spatial overlap of related wave functions. The ΔEST of excited state is generally larger than that of excited state CT in the same kind of materials[76]. In addition, the different excited state characteristics of S1 and T1 will produce a larger SOC, which is also applicable to S1 and T2, and the different excited state characteristics will also induce a significant SOC value.
5 Conclusion and prospect
TADF materials exhibit excellent performance in the field of organic electroluminescence due to their high exciton utilization, making them a very promising candidate for next-generation OLED technology. The prediction of the structure and properties of TADF materials by quantum chemistry method can clarify the relationship between structure and properties from the microscopic point of view, and provide theoretical guidance for screening high-performance materials. In this paper, the general strategy of TADF molecular structure design is introduced from three aspects of efficiency, color and lifetime, and different kinds of DFT functionals and their HF contents are listed. The calculation principles, methods and research progress of photophysical properties of TADF materials, such as ΔEST, intersystem/antisystem crossing rate, absorption/emission spectrum, radiative/non-radiative rate, are reviewed. However, there are still some problems to be solved in the current research in related fields.
(1) Small ΔEST and efficient ISC/RISC are the two keys to implement TADF. For the calculation of ΔEST of traditional TADF materials, OHF or IP control method can be chosen, but for MR-TADF materials, especially materials containing boron atoms, the error of the above methods is large, and the accuracy of the calculation may be improved by fitting a large number of data or using a more accurate method. For ISC/RISC, considering the participation of high-energy triplet is beneficial to the understanding and accurate prediction of ISC/RISC mechanism.
(2) Accurate spectral simulation can intuitively show many properties of TADF materials, such as peak, FWHM and so on. At present, the simulation of the peak position is relatively accurate, but the prediction of FWHM is rarely studied, and there is a lack of molecular design strategies for red narrow-band TADF luminescent materials. Considering the structural relaxation and vibrational coupling of the ground and excited States involved in the luminescence process will be a potential direction to study the FWHM of the emission spectrum of the material, and the cooperative narrow band emission skeleton and spectral red shift strategy will be a possible molecular design strategy to obtain the red narrow band luminescence material.
(3) The diversity and flexibility of the combination of organic fragments will pose a problem for the screening of high-performance TADF materials. Quantum chemical calculation combined with machine learning methods provides the possibility for the rapid and efficient screening of potential materials on a large scale. Among them, the development of independent and easy-to-calculate property descriptors plays an important role in the effectiveness of screening materials.
National Natural Science Foundation of China(61875090)
National Natural Science Foundation of China(91833306)
National Natural Science Foundation of China(21772095)
Key giant project of Jiangsu Educational Committee(19KJA180005)
fifth 333 project of Jiangsu Province of China(BRA2019080)
1311 Talents Program of Nanjing University of Posts and Telecommunications, the Scientific Starting Fund from Nanjing University of Posts and Telecommunications (No.NUPTSF)(NY219160)
Natural Science Foundation of Nanjing University of Posts and Telecommunications(NY221092)
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