Department of Applied Chemistry, Institute of Molecular Science and Center for Interdisciplinary Molecular Science, National Chiao-Tung University, Hsinchu 30050, Taiwan.
J Chem Phys. 2011 Mar 7;134(9):094313. 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 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.
采用三种不同的混合交换相关泛函，其中包含密度泛函理论及其时间相关扩展的 20%、35%和 50%的精确 Hartree-Fock（HF）交换，以及 Hartree-Fock 和单激发方法的组态相互作用，计算了氟苯（FB）基态 S(0)((1)A(1))和第一激发态 S(1)((1)B(2))的平衡几何形状及其 30 个振动正则模式频率。在位移谐振子近似加非谐和畸变修正的 Franck-Condon（FC）计算中，模拟了分散荧光光谱和 A(1)B(2)→X(1)A(1)跃迁的内转换（IC）速率。模拟的光谱轮廓主要由属于完全对称模式的环呼吸模式 ν(9)和 ν(10)的 Franck-Condon 级联描述。非谐校正同时改善了 9(1)(0)和 10(1)(0)带的强度顺序，并减小了在谐波模拟中相当强的 1(1)(0)跃迁。结果表明，HF 交换的量确实会影响 FB 分子的几何形状和振动频率，但不会影响跃迁的相对强度。正是非谐校正使跃迁的相对强度与实验结果很好地吻合。畸变校正可以分配出大部分非平面非完全对称模式的主要泛音，结果与实验分配吻合良好。此外，还发现内转换速率主要由三个促进模式主导，这些模式以较低的对称性计算到 C(1)。通过选择与光谱模拟一致的退相宽度为 10 cm(-1)，我们从 TD(B3LYP)和 HF∕CIS 计算中得到 A(1)B(2)→X(1)A(1)去激发的寿命分别为 11 和 19 ns，与实验值 14.75 ns 相比。
