The analysis of the photoabsorption spectra of molecules shows that the band maximum is usually redshifted in comparison to the vertical excitation. We conducted a throughout analysis of this shift based on low-dimensional analytical and numerical model systems, showing that its origin is rooted in the frequency change between the ground and the excited states in multidimensional systems. Moreover, we deliver a benchmark of ab initio results for the shift based on a comparison of vertical excitations and band maxima calculated with the nuclear ensemble approach for the 28 organic molecules in the Mülheim molecular dataset. The mean value of the shift calculated over 60 transitions is 0.11 ± 0.08 eV. The mean value of the band width is 0.32 ± 0.14 eV.

.

中文翻译：

---

关于分子光吸收中垂直激发和谱带最大值之间的转换的起源。

分子的光吸收光谱分析表明，与垂直激发相比，最大能带通常发生红移。我们基于低维分析和数值模型系统对这种位移进行了全面分析，表明其起源是多维系统中基态和激发态之间频率变化的根本原因。此外，我们基于Mülheim分子数据集中28种有机分子的垂直激发和能带最大核对计算得出的位移，从头计算结果的基准。在60个转换中计算出的偏移平均值为0.11±0.08 eV。带宽的平均值为0.32±0.14 eV。

。