*X*-annulated rylenes

^{1}, Yingli Niu

^{1}, Zhaohui Wang

^{1}, Yuqian Jiang

^{2}, Yan Li

^{1}, Yajun Liu

^{3}and Zhigang Shuai

^{1,2,a)}

### Abstract

The optical properties of rylenes are extremely interesting because their emission colors can be tuned from blue to near-infrared by simply elongating the chain length. However, for conjugated chains, the dipole-allowed odd-parity 1B_{u}excited state often lies above the dipole-forbidden even-parity 2A_{g} state as the chain length increases, thus preventing any significant luminescence according to Kasha's rule. We systemically investigated the 1B_{u}/2A_{g} crossover behaviors with respect to the elongating rylene chain length with various quantum chemistry approaches, such as time-depended density functional theory (TDDFT), complete active space self-consistent field theory (CASSCF/CASPT2), multireference configuration interaction (MRCI)/Zerner's intermediate neglect of diatomic overlap (ZINDO), and MRCI/modified neglect of differential overlap. The calculated results by CASSCF/CASPT2 and MRCI/ZINDO are completely coherent: the optical active 1B_{u} state lies below the dark B_{3g} or 2A_{g} state for perylene and terrylene, which results in strong fluorescence; while a crossover to S_{1} = 2A_{g} occurs and leads to much weaker fluorescence for quaterrylene. Then we put forward a molecular design rule on how to recover fluorescence for the longer rylenes by introducing heteroatom bridges. Several heteroatom-annulated rylenes are designed theoretically, which are predicted to be strongly emissive in the red and near-infrared ranges. These are further confirmed by theoreticalemission spectra as well as radiative and nonradiative decay rate calculations by using the vibration correlation function formalisms we developed earlier coupled with TDDFT.

This work is supported by the Ministry of Science and Technology of China (Grant No. 2009CB623600) and the National Science Foundation of China (Grant Nos. 20903102 and 90921007). Professor Z. Y. Wen of Northwest University is deeply acknowledged for his help in MRCI/MNDO calculations.

I. INTRODUCTION

II. THEORETICAL METHODOLOGY AND COMPUTATIONAL TECHNIQUES

A. Excited state structure calculations

B. Absorption and emission spectroscopy

C. Radiative and nonradiative decay rate

1. Radiative decay rate

2. Internal conversion rate

III. RESULTS AND DISCUSSIONS

A. Vertical excitation energies of oligorylenes

B. Design of heteroatom-annulated quaterrylene derivatives

C. Photophysical properties

1. Absorption and emission spectra

2. Nonradiative and radiative decay rates

IV. CONCLUSION

### Key Topics

- Excited states
- 43.0
- Emission spectra
- 17.0
- Excitation energies
- 13.0
- Correlation functions
- 12.0
- Absorption spectra
- 10.0

## Figures

Molecular structures of (a) rylenes and (b) heteroatom *X*-annulated quaterrylene: *X* _{1} = *X* _{2} = *N*, *N*, *N*, *N*-annulated quaterrylene (QNN); *X* _{1} = *S*, *X* _{2} = *N*, *N*, *S*-annulated quaterrylene (QNS); *X* _{1} = *X* _{3} = *N*, NQN; *X* _{1} = *N*, *X* _{3} = *S*, NQS.

Molecular structures of (a) rylenes and (b) heteroatom *X*-annulated quaterrylene: *X* _{1} = *X* _{2} = *N*, *N*, *N*, *N*-annulated quaterrylene (QNN); *X* _{1} = *S*, *X* _{2} = *N*, *N*, *S*-annulated quaterrylene (QNS); *X* _{1} = *X* _{3} = *N*, NQN; *X* _{1} = *N*, *X* _{3} = *S*, NQS.

The atomic orbital composition of selected molecular orbitals in perylene, terrylene, and quaterrylene at the B3LYP/6–31G*level.

The atomic orbital composition of selected molecular orbitals in perylene, terrylene, and quaterrylene at the B3LYP/6–31G*level.

B3LYP/6–31g* HOMO (left) and LUMO (right) orbitals.

B3LYP/6–31g* HOMO (left) and LUMO (right) orbitals.

The low-lying excited states of quaterrylene and the *X*-annulated quaterrylene calculated by using the MRCI/ZINDO. The transition oscillator strengths are given in parenthesis, and the point groups are shown for the molecules at the ground state at the bottom.

The low-lying excited states of quaterrylene and the *X*-annulated quaterrylene calculated by using the MRCI/ZINDO. The transition oscillator strengths are given in parenthesis, and the point groups are shown for the molecules at the ground state at the bottom.

(a) The absorption spectra at *T* = 20 K of perylene (solid for the calculated spectrum and dash dot for the experimental one); (b) the emission spectra of perylene (solid line for the *T* = 20 K, dash dot for *T* = 300 K) and their assignments of transition (vertical lines) which are labeled as *N* ^{ν} (*N* is the index of the excited normal modes and *ν* is the quantum number).

(a) The absorption spectra at *T* = 20 K of perylene (solid for the calculated spectrum and dash dot for the experimental one); (b) the emission spectra of perylene (solid line for the *T* = 20 K, dash dot for *T* = 300 K) and their assignments of transition (vertical lines) which are labeled as *N* ^{ν} (*N* is the index of the excited normal modes and *ν* is the quantum number).

The dominant normal modes involved in the emission spectra for perylene. The corresponding frequencies of normal modes are shown in parentheses.

The dominant normal modes involved in the emission spectra for perylene. The corresponding frequencies of normal modes are shown in parentheses.

Theoretical emission spectra for the *X*-annulated quaterrylene derivatives at *T* = 300 K.

Theoretical emission spectra for the *X*-annulated quaterrylene derivatives at *T* = 300 K.

Theoretical emission spectra for *tri-N*-annulated hexarylene (HNNN) and tetra-*N*-annulated octerylene.

Theoretical emission spectra for *tri-N*-annulated hexarylene (HNNN) and tetra-*N*-annulated octerylene.

## Tables

Vertical excitation energies (eV) of the four low-lying excited states at the ground state geometry for the oligorylenes. The oscillator strengths of the dipole-allowed states are given in the parenthesis.

Vertical excitation energies (eV) of the four low-lying excited states at the ground state geometry for the oligorylenes. The oscillator strengths of the dipole-allowed states are given in the parenthesis.

The main configurations in CASSCF wave function of the two low-lying states of oligorylenes. The orbital symmetry, and the selected weight (>0.10) in the wave function are given.

The main configurations in CASSCF wave function of the two low-lying states of oligorylenes. The orbital symmetry, and the selected weight (>0.10) in the wave function are given.

The frequencies of active modes involved in the emission process for the *X*-annulated quaterrylene derivatives.

The frequencies of active modes involved in the emission process for the *X*-annulated quaterrylene derivatives.

The calculated radiative and nonradiative transition rates from S_{1} to S_{0} rates for the oligorylenes and the *X*-annulated rylene derivatives.

The calculated radiative and nonradiative transition rates from S_{1} to S_{0} rates for the oligorylenes and the *X*-annulated rylene derivatives.

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