This study provides new theoretical insights into the vibrational spectra of Ln(III) complexes, along the lanthanide series by utilizing the LModeAGen protocol and integrating cutting-edge topological ideas. It provides a quantitative interpretation of the vibrational spectra of [Ln(trensal)] complexes at the B3LYP/MWBn(Ln)/6-311++G** (n from 46 (La) to 60 (Lu)) level using the characterization of normal modes from the local vibrational mode theory. This involves decomposing normal vibrational modes related to the complex formation, distortions in the coordination sphere, and C–H vibrations into local mode contributions, offering particularly promising results aimed at the design of highly luminescent lanthanide complexes. This study also delivers key theoretical insights into the chemical bonding of the coordination sphere of [Ln(trensal)] by combining the local vibrational mode theory and the bond overlap model to achieve relationships between bond properties, including those of the Badger-type. Altogether, we present the theoretical framework necessary to quantitatively interpret the vibrational spectra of [Ln(trensal)] complexes along the lanthanide series and gain a better understanding of the lanthanide-ligand chemical bonds, thereby enhancing our understanding of their chemistry and guiding future design efforts.

中文翻译：

---

Ln（III） 配合物与沿镧系元素的三脚 N4O3 配体的振动光谱和化学键合的理论见解


本研究利用 LModeAGen 协议并整合了前沿的拓扑思想，为沿镧系元素的 Ln（III） 配合物的振动光谱提供了新的理论见解。它使用局部振动模态理论中的法则模态表征，对 B3LYP/MWBn（Ln）/6-311++G** （n from 46 （La） 到 60 （Lu）） 水平的 [Ln（trensal）] 配合物的振动谱进行了定量解释。这包括将与配合物形成、配位球的扭曲和 C-H 振动相关的正常振动模式分解为局部模式贡献，为设计高发光镧系元素配合物提供了特别有希望的结果。本研究还通过结合局部振动模态理论和键重叠模型来实现键性质之间的关系，包括 Badger 型键性质之间的关系，为 [Ln（trensal）] 配位球的化学键提供了关键的理论见解。总之，我们提出了定量解释沿镧系元素系列 [Ln（trensal）] 配合物的振动光谱所需的理论框架，并更好地了解镧系元素-配体化学键，从而增强我们对它们化学的理解并指导未来的设计工作。