Fluorescence via Reverse Intersystem Crossing from Higher Triplet States

Abstract

A high external quantum efficiency observed for organic light-emitting diodes using PTZ-BZP (PTZ: 10-hexyl-phenothiazin, and BZP:4-phenyl-2,1,3-benzothiadiazole) is attributed to fluorescence from S₁ via reverse intersystem crossing from the T₃ or T₂ state under electrical excitation. The radiative and non-radiative transitions from these higher triplet states to the lower triplet states are suppressed because of their small overlap densities. In this study, a principle to design such an electronic structure is proposed.

1 INTRODUCTION

Thermally activated delayed fluorescence (TADF) is delayed fluorescence via reverse intersystem crossing (RISC) from a thermally activated triplet T₁ state. Recently, TADF has attracted significant attention as a novel light-emitting mechanism for third-generation organic light-emitting diodes (OLEDs) [1]. There is a 25% probability for the generation of a singlet exciton under electrical excitation. On the other hand, there is a 75% probability for the generation of a triplet exciton under electrical excitation. Fluorescent OLEDs utilize singlet excitons, while phosphorescent OLEDs use triplet excitons. On the other hand, TADF OLEDs can exhibit high external quantum efficiencies (EQEs) as they utilize both singlet and triplet excitons.

Sato et al. have proposed a novel light-emitting mechanism for OLEDs based on fluorescence via RISC from triplet states higher than T₁ employing selection rules of an electric dipole moment and spin-orbit coupling, caused by a high molecular symmetry [2].

Yao et al. have reported a high EQE of 1.54% for an OLED using PTZ-BZP (Figure 1) as an emitting molecule [3]. In a fluorescent OLED, EQE is equal to 0.05×PLQY, where PLQY represents the photoluminescence quantum yield. As the PLQY of PTZ-BZP is 16%, the observed EQE cannot be explained as a conventional fluorescent OLED. In addition, as T₁ is low, the emitting mechanism of PTZ-BZP is not TADF. Yao et al. have proposed a fluorescence emitting mechanism via RISC from T₃.

Figure 1.

 PTZ-BZP.

Their mechanism is possible as long as the electric dipole and non-radiative transitions caused by vibronic couplings from T₃ or T₂ to the lower triplet states are suppressed [4,5]. In this Letter, we calculate the off-diagonal vibronic coupling constants (VCCs), which serve as the driving force for non-radiative transitions, and analyze overlap densities for elucidating the suppressed transition dipole moment and VC in PTZ-BZP.

2 METHOD OF CALCULATIONS

The ground and excited states were calculated at the B3LYP/6-31G (d,p) and TD-B3LYP/6-31G (d,p) levels of theory using Gaussian09. The geometries of the relevant triplet states, T₃ and T₂, were optimized. VCC calculations and vibronic coupling density (VCD) analyses were performed using our in-house codes. The off-diagonal VCCs of the non-radiative T₃ → T₁ and T₃ → T₂ transitions were calculated at the optimized geometry for the T₃ state, while those of the non-radiative T₂ → T₁ transition were calculated at the optimized geometry for T₂.

3 RESULTS AND DISCUSSION

Table 1 summarizes the calculated excitation energy and major electronic configurations with configuration interaction (CI) coefficients. The energy gap between T₃ and S₁, $\text{Δ}{E}_{S_1-T_3}$,is −84 meV. Therefore, if the radiative and non-radiative transitions from the T₃ state to the lower triplet states are suppressed, fluorescence from S₁ via RISC from T₃ is expected without temperature dependence because of the negative energy gap.

Table 1.  Excited states at the T₃ optimized structure.

State	Excitation energy	Major configurations
	eV	(CI coefficients)
T1	1.2884	HO-1 → LU (−0.48000)
		HO → LU (0.48227)
T2	1.5929	HO → LU+1 (0.57490)
S1	1.6670	HO → LU (0.70376)
T3	1.7509	HO-1 → LU (0.42134)
		HO → LU (0.50271)

Table 2 lists the calculated results for the T₂ optimized structure. The T₂ state is close to S₁ with a positive energy gap, $\text{Δ}{E}_{S_1-T_2}=66$ meV. Therefore, TADF via RISC from T₂ is expected if the radiative and non-radiative decays T₂ → T₁ are suppressed. Figure 2 shows the off-diagonal VCCs between (a) T₃ and T₁, (b) T₃ and T₂, and (c) T₂ and T₁ for vibrational modes. The off-diagonal VCCs of T₃ → T₂ and T₂ → T₁ are very small. Therefore, the non-radiative decay path T₃ → T₂ → T₁ is suppressed. As the off-diagonal VCCs of T₃ → T₁ are intermediate as an organic π-conjugated molecule, the non-radiative decay path T₃ → T₁ is not significantly suppressed.

Table 2.  Excited states at the T₂ optimized structure.

State	Excitation energy	Major configurations
	eV	(CI coefficients)
T1	0.8864	HO-1 → LU (0.35803)
		HO → LU (0.61205)
T2	1.7311	HO-2 → LU+1 (0.34854)
		HO-1 → LU+1 (−0.31142)
		HO → LU+1 (0.47528)
S1	1.7967	HO → LU (0.70174)
T3	1.9672	HO-1 → LU (0.55826)
		HO → LU (−0.35424)

Figure 2.

 Off-diagonal vibronic coupling constants between (a) T₃ and T₁, (b) T₃ and T₂, and (c) T₂ and T₁ for vibrational modes at the B3LYP/6-31G (d,p) level of theory.

An off-diagonal VCC, V_α, and transition dipole moment, μ, are expressed in terms of overlap (transition) density between the electronic states n and m, ${\rho }^{nm}\left(r\right)$ [4]:   

$V_{\alpha }^{nm}={\int }^{\text{}}{\rho }^{nm}\left(r\right)v_{\alpha }\left(r\right)d^{3}r,$(1)

  

${\mu }^{nm}=-e{\int }^{\text{}}{\rho }^{nm}\left(r\right)r{d}^{3}r,$(2)

where r is a position vector in three-dimensional space, and v_α is a potential derivative with respect to the normal coordinate Q_α of mode α   

$v_{\alpha }\left(r\right)={\left[\frac{\partial }{\partial Q_{\alpha }}\left(-\sum _A\frac{Z_A{e}^2}{\left|r-R_A\right|}\right)\right]}_{R_0},$(3)

where R_A and Z_A denote the position and charge of nucleus A, respectively. The overlap density is defined by   

$\begin{array}{c}{\rho }^{nm}\left(r_1\right)=N{\int }^{\text{}}\cdots {\int }^{\text{}}{\Psi }_n^{*}\left(x_1,\cdots ,x_N\right)\times \\ {\text{Ψ}}_m\left(x_1,\cdots ,x_N\right)d{\omega }_1{d}^3{r}_{2}d{\omega }_2\cdots d^3{r}_{N}d{\omega }_N,\end{array}$(4)

where ${\Psi }_n\left(x_1,\cdots ,x_N\right)$ and ${\Psi }_m\left(x_1,\cdots ,x_N\right)$ are N-electron wave functions for the electronic states n and m, respectively. r_i denotes the space coordinates of electron i, ω_i the spin coordinate of electron i, and $x_i=\left(r_i,{\omega }_i\right)$. The integrand of equation (1) is called off-diagonal VCD ${\eta }_{\alpha }^{nm}\left(r\right)$. $V_{\alpha }^{mn}$ depends on ${\eta }_{\alpha }^{nm}\left(r\right)$, and therefore, on ${\rho }_{mn}\left(r\right)$.

The suppression of the radiative and non-radiative transitions from the T₃ and T₂ states to the lower states can be elucidated on the basis of overlap density. According to equations (1) and (2), if the overlap density between two electronic states is small, V_α and μ^nm are reduced. Therefore, non-radiative and radiative transitions are suppressed.

A TD-DFT wavefunction is written as   

${\text{Ψ}}_m\left(x_1,\cdots ,x_N\right)=\sum _{i\in \text{occ},r\in \text{unocc}}{C}_i^r{\text{Φ}}_i^r\left(x_1,\cdots ,x_N\right),$(5)

where ${\Phi }_i^r$ is a one-electron excitation configuration from the occupied i molecular orbital to the unoccupied r molecular orbital, and $C_i^r$ denotes a CI coefficient. Thus, the overlap density between electronic states is decomposed as a sum of overlap densities between one-electron excitation configurations with a product of CI coefficients. Notably,

1. Overlap density between ${\Phi }_i^r$ and ${\Phi }_j^s$ is zero for $i\ne j$ and $r\ne s$,

2. Overlap density between ${\Phi }_i^r$ and ${\Phi }_j^s$ is equal to orbital overlap between unoccupied orbitals r and s for i = j, $r\ne s$, and equal to orbital overlap between occupied orbitals i and j for $i\ne j$, r = s.

According to Table 1, the T₃ state can be approximately written as   

${\Psi }_{{\text{T}}_3}\approx a{\Phi }_{\text{HO}-1}^{\text{LU}}-b{\Phi }_{\text{HO}}^{\text{LU}},$(6)

and for T₂ and T₁,   

${\Psi }_{{\text{T}}_2}\approx {\Phi }_{\text{HO}}^{\text{LU}+1},\text{and},{\Psi }_{{\text{T}}_1}\approx b{\Phi }_{\text{HO}-1}^{\text{LU}}+a{\Phi }_{\text{HO}}^{\text{LU}}.$(7)

Therefore, the overlap density between ${\Phi }_{\text{HO}-1}^{\text{LU}}$ and ${\Phi }_{\text{HO}}^{\text{LU}+1}$ vanishes and that between ${\Phi }_{\text{HO}}^{\text{LU}}$ and ${\Phi }_{\text{HO}}^{\text{LU}+1}$ is equal to the orbital overlap between the LUMO and NLUMO. As shown in Figure 3, as the LUMO and NLUMO are separately localized, the orbital overlap between them is small. Accordingly, the overlap density between T₃ and T₂ is very small. On the other hand, the overlap density between T₃ and T₁ is not so small. However, if the HOMO and NHOMO are pseudo-degenerate, and these orbitals are separately localized on the BZP units, the overlap density can decrease because of the relations of the CI coefficients: ab − ba = 0 and $a^2-b^2\approx 0$.

Figure 3.

 Frontier orbitals at the T₃ optimized structure.

4 CONCLUDING REMARKS

The high EQE observed in PTZ-BZP is attributed to fluorescence via RISC from the T₃ or T₂ states.

Fluorescence via RISC from a higher triplet state is possible even for asymmetric molecules as long as the transition dipole moments and vibronic couplings are small among the lower triplet states. A small overlap density results in the suppression of transition dipole moments and vibronic coupling. One design principle for realizing such an electronic state is to make use of a pseudo-degenerate electronic structure, namely using molecules in which the same fragments (BZPs in PTZ-BZP) are linked by a linker unit (PTZ in PTZ-BZP).

Acknowledgment

Numerical calculations were partly performed at the Supercomputer Laboratory of Kyoto University and at the Research Center for Computational Science, Okazaki, Japan. This study was also supported by a Grant-in-Aid for Scientific Research (C) (15K05607) from the Japan Society for the Promotion of Science (JSPS).

References

• [1]   As a review article, C. Adachi, Jpn. J. Appl. Phys., 53, 060101 1–11 (2014).
• [2]   T. Sato, M. Uejima, K. Tanaka, H. Kaji, C. Adachi, J. Mater. Chem. C, 3, 870 (2015).
• [3]   L. Yao, S. Zhang, R. Wang, W. Li, F. Shen, B. Yang, Y. Ma, Angew. Chem., 126, 2151 (2014).
• [4]   T. Sato, M. Uejima, N. Iwahara, N. Haruta, K. Shizu, K. Tanaka J. Phys. Conf. Ser., 428, 012010 1–20 (2013).
• [5]   M. Uejima, T. Sato, D. Yokoyama, K. Tanaka, J.-W. Park, Phys. Chem. Chem. Phys., 16, 14244 (2014).