Theoretical insights into the vibrational spectra and chemical bonding of Ln(<scp>iii</scp>) complexes with a tripodal N₄O₃ ligand along the lanthanide series

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/MWB<i>n</i>(Ln)/6-311++G** (<i>n</i> 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.