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

Abstract

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 S(0)((1)A(1)) and the first excited S(1)((1)B(2)) states of fluorobenzene (FB) were calculated. The dispersed fluorescence spectrum and internal conversion (IC) rate of the A(1)B(2)→X(1)A(1) 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 ν(9) and ν(10) which belong to totally symmetry modes. Anharmonic corrections simultaneously improve the intensity order of 9(1)(0) and 10(1)(0) bands and diminish 1(1)(0) 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 C(1). By choosing dephasing width as 10 cm(-1) that is consistent with spectral simulation, we obtained the lifetimes of the A(1)B(2)→X(1)A(1) de-excitation as 11 and 19 ns, respectively, from TD(B3LYP) and HF∕CIS calculations in comparison with the experimental value 14.75 ns.