论文标题
通过相关函数的未结合和假想频率振动的Franck-Condon光谱：无分支切割，数值稳定的推导
Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: a branch-cut free, numerically stable derivation
论文作者
论文摘要
分子电子光谱可以在时域表示为初始振动波袋的自动相关函数。我们提出了谐波振动自动相关函数的推导，该函数对于真实和虚谐频率均有效。推导基于谎言代数技术，该技术将其他复杂的指数运算符算法绘制到更简单的矩阵公式。零和有限温度的谐波自动相关函数的表达式已仔细构造，既没有分支切开的不连续性，又可以在数值上保持有限精确的算术。简单的扩展纠正了最低阶的Anharmonic和Herzberg-Teller效应的谐波Franck-Condon近似。显示了几个示例的定量模拟，包括f $ _2 $，HOCL，CH $ _2 $ NH的电子吸收光谱，以及NO $ _2 $。
Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulae. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F$_2$, HOCl, CH$_2$NH, and NO$_2$.
