Franck–Condon simulation of the A 1B2 → X 1A1 dispersed fluorescence spectrum of fluorobenzene and its rate of the internal conversion

He, Rongxing; Yang, Ling; Zhu, Chaoyuan; Yamaki, Masahiro; Lee, Yuan-Pern; Lin, Sheng Hsien

doi:doi:10.1063/1.3559454

By using three different hybrid exchange-correlation functionals containing 20%, 35%, and 50% of exact Hartree–Fock (HF) exchange of the density functional theory and its time-dependent extension plus the Hartree–Fock and the configuration interaction of single excitation methods, equilibrium geometries, and their 30 vibrational–normal-mode frequencies of the ground S₀(¹A₁) and the first excited S₁(¹B₂) states of fluorobenzene (FB) were calculated. The dispersed fluorescence spectrum and internal conversion (IC) rate of the A ¹B₂ → X ¹A₁ transition were simulated by Franck–Condon (FC) calculations within the displaced harmonic oscillator approximation plus anharmonic and distorted corrections. The simulated spectral profile is primarily described by the Franck–Condon progression from the ring-breathing modes v₉ and v₁₀ which belong to totally symmetry modes. Anharmonic corrections simultaneously improve the intensity order of 910 and 1010 bands and diminish 110 transition that is fairly strong in harmonic simulations. It is concluded that the amount of Hartree–Fock exchange does impact the geometries and vibrational frequencies of FB molecule, but not the relative intensities of the transitions. It is anharmonic corrections that make the relative intensities of the transitions in good agreement with experimental results. Distorted corrections could assign most of the dominant overtones of out-of-plane nontotally symmetry modes, and the results agree well with the experimental assignments. Furthermore, it was found that the internal conversion rate is dominated by three promoting modes that are computed with lowing symmetry to C₁. By choosing dephasing width as 10 cm⁻¹ that is consistent with spectral simulation, we obtained the lifetimes of the A ¹B₂ → X ¹A₁ de-excitation as 11 and 19 ns, respectively, from TD(B3LYP) and HF/CIS calculations in comparison with the experimental value 14.75 ns.

Article Outline

INTRODUCTION
COMPUTATIONAL METHODS
1. Ab initio methods for electronic properties
2. Franck–Condon simulation for DF spectra
3. Franck–Condon simulation for internal conversion
RESULTS AND DISCUSSIONS
1. Equilibrium geometries and vibrational frequencies
2. Electronic structures and excitation energies
3. Franck–Condon simulation of the DF spectrum
4. Internal conversion and the lifetime of S ₁ state
CONCLUDING REMARKS

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KEYWORDS and PACS

Keywords

configuration interactions, density functional theory, electron correlations, excited states, fluorescence, Franck-Condon factors, ground states, harmonic oscillators, HF calculations, nonradiative transitions, organic compounds, vibrational states

PACS

33.70.Ca

Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors
33.50.Hv

Radiationless transitions, quenching
33.50.Dq

Fluorescence and phosphorescence spectra
31.15.ve

Electron correlation calculations for atoms and ions: ground state
31.15.vj

Electron correlation calculations for atoms and ions: excited states
31.15.xr

Self-consistent-field methods