速報

Fluorescence via Reverse Intersystem Crossing from Higher Triplet States

キーワード:
organic light-emitting diode (OLED),
vibronic coupling,
thermally activated delayed fluorescence (TADF),
non-radiative transition,
overlap density

2016 年 14 巻 6 号 p. 189-192

詳細

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 S_{1} via reverse intersystem crossing from the
T_{3} or T_{2} 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 T_{1} 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 T_{1} 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
T_{1} is low, the emitting mechanism of PTZ-BZP is not TADF. Yao *et
al*. have proposed a fluorescence emitting mechanism via RISC from
T_{3}.

Figure 1.

PTZ-BZP.

Their mechanism is possible as long as the electric dipole and non-radiative transitions
caused by vibronic couplings from T_{3} or T_{2} 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,
T_{3} and T_{2}, 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 T_{3} → T_{1} and T_{3} → T_{2} transitions
were calculated at the optimized geometry for the T_{3} state, while those of the
non-radiative T_{2} → T_{1} transition were calculated at the optimized
geometry for T_{2}.

3 RESULTS AND DISCUSSION

Table 1 summarizes the calculated excitation
energy and major electronic configurations with configuration interaction (CI) coefficients.
The energy gap between T_{3} and S_{1}, _{3} state to the lower triplet states are suppressed,
fluorescence from S_{1} via RISC from T_{3} is expected without temperature
dependence because of the negative energy gap.

Table 1.
Excited states at the T_{3} optimized structure.

State | Excitation energy | Major configurations |

eV | (CI coefficients) | |

T_{1} |
1.2884 | HO-1 → LU (−0.48000) |

HO → LU (0.48227) | ||

T_{2} |
1.5929 | HO → LU+1 (0.57490) |

S_{1} |
1.6670 | HO → LU (0.70376) |

T_{3} |
1.7509 | HO-1 → LU (0.42134) |

HO → LU (0.50271) |

Table 2 lists the calculated results for the
T_{2} optimized structure. The T_{2} state is close to S_{1} with
a positive energy gap, _{2} is expected
if the radiative and non-radiative decays T_{2} → T_{1} are suppressed.
Figure 2 shows the off-diagonal VCCs between (a)
T_{3} and T_{1}, (b) T_{3} and T_{2}, and (c)
T_{2} and T_{1} for vibrational modes. The off-diagonal VCCs of
T_{3} → T_{2} and T_{2} → T_{1} are very small. Therefore,
the non-radiative decay path T_{3} → T_{2} → T_{1} is suppressed. As
the off-diagonal VCCs of T_{3} → T_{1} are intermediate as an organic
*π*-conjugated molecule, the non-radiative decay path T_{3} →
T_{1} is not significantly suppressed.

Table 2.
Excited states at the T_{2} optimized structure.

State | Excitation energy | Major configurations |

eV | (CI coefficients) | |

T_{1} |
0.8864 | HO-1 → LU (0.35803) |

HO → LU (0.61205) | ||

T_{2} |
1.7311 | HO-2 → LU+1 (0.34854) |

HO-1 → LU+1 (−0.31142) | ||

HO → LU+1 (0.47528) | ||

S_{1} |
1.7967 | HO → LU (0.70174) |

T_{3} |
1.9672 | HO-1 → LU (0.55826) |

HO → LU (−0.35424) |

Figure 2.

Off-diagonal vibronic coupling constants between (a) T_{3} and T_{1},
(b) T_{3} and T_{2}, and (c) T_{2} and T_{1} 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*,

(1) |

(2) |

(3) |

(4) |

The suppression of the radiative and non-radiative transitions from the T_{3} and
T_{2} 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

(5) |

1. Overlap density between

2. Overlap density between *r* and *s* for *i* = *j*, *i* and *j* for *r* = *s*.

According to Table 1, the T_{3} state
can be approximately written as

(6) |

(7) |

Therefore, the overlap density between _{3} and T_{2} is very small. On the other hand, the
overlap density between T_{3} and T_{1} 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

Figure 3.

Frontier orbitals at the T_{3} optimized structure.

4 CONCLUDING REMARKS

The high EQE observed in PTZ-BZP is attributed to fluorescence via RISC from the
T_{3} or T_{2} 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).

© 2016 Society of Computer Chemistry, Japan