Quantifying vibronic couplings in molecular excited states is crucial for the elucidation of a broad range of photophysical phenomena. In this study, we compare different theoretical approaches for the calculation of reorganization energy, a measure of vibronic coupling strength, and provide a rigorous derivation to show that molecular transition density characterizing electron–hole excitation could be used to quantify the magnitude of reorganization energy. The theory enables a descriptor based on molecular-orbital coefficients and atomic transition densities to quantify the magnitude of reorganization energies in molecular excited states. Applying the approach to low-lying excited states of polyacenes, we demonstrate that transition density distribution explains the difference in the magnitude of the reorganization energy of different excited states. Furthermore, to clarify the applicability of the transition density descriptor in molecular design for small-reorganization energy molecules, we investigate a broad range of molecular chromophores to show the effectiveness of the proposed theory. With this perspective on the relationship between reorganization energy and transition density, we successfully provide a quantitative rule to identify π-conjugated systems with small reorganization energy in the excited state, which should be useful for the development of novel optoelectronic materials.

中文翻译：

---

从跃迁密度的角度阐明分子激发态内部重组能的大小。

量化分子激发态的振动耦合对阐明广泛的光物理现象至关重要。在这项研究中，我们比较了用于计算重组能量（一种测量振动耦合强度）的不同理论方法，并提供了严格的推论，以表明表征电子-空穴激发的分子跃迁密度可用于量化重组能量的大小。该理论使基于分子轨道系数和原子跃迁密度的描述符能够量化分子激发态中重组能的大小。将该方法应用于聚乙烯的低激发态，我们证明了跃迁密度分布解释了不同激发态的重组能量大小的差异。此外，为了阐明过渡密度描述符在小重组能量分子的分子设计中的适用性，我们研究了多种分子发色团，以证明所提出理论的有效性。基于重组能量与跃迁密度之间关系的观点，我们成功地提供了定量规则，以识别激发态下重组能量小的π共轭体系，这对开发新型光电材料应是有用的。我们研究了广泛的分子发色团，以证明所提出理论的有效性。基于重组能量与跃迁密度之间关系的观点，我们成功地提供了定量规则，以识别激发态中重组能量小的π共轭体系，这对开发新型光电材料应是有用的。我们研究了广泛的分子发色团，以证明所提出理论的有效性。基于重组能量与跃迁密度之间关系的观点，我们成功地提供了定量规则，以识别激发态下重组能量小的π共轭体系，这对开发新型光电材料应是有用的。