Theoretical Study on the Mechanism of Ru(II)-Catalyzed Intermolecular [3 + 2] Annulation between <i>o</i>-Toluic Acid and 3,5-Bis(trifluoromethyl)benzaldehyde: Octahedral vs Trigonal Bipyramidal

Density functional theory was utilized to investigate the mechanism of Ru(II)-catalyzed aromatic C-H activation and addition of aromatic aldehydes. The proposed catalytic cycle consists of C-H bond activation, aldehyde carbonyl insertion for C-C coupling, lactonization for the formation of the final product, product separation, and catalyst recovery. Our calculations suggest that Ru(OAc)₂(PCy₃) (referred to as <b>CAT</b>) is the most favorable active catalyst, facilitating the C-H bond activation to form a five-membered ring cycloruthenium intermediate (<b>INT2</b>). Subsequently, the aromatic aldehyde reactant <b>2a</b> enters the Ru coordination sphere, accelerating the C-C coupling and lactonization for the formation of the final product. The involvement of acetate assists in the final product separation, while <b>INT1</b> re-enters the Ru coordination sphere to initiate a new catalytic cycle. Utilizing the energetic span model, the apparent activation free energy barrier was computed to be 34.3 kcal mol^-1 at 443 K. Furthermore, exploration of the reaction mechanism in the absence of phosphine ligands identified Ru(OAc)₂(<i>p</i>-cymene) as the most favorable active catalyst. The derived apparent activation free energy barrier offers a comprehensive explanation for the experimentally observed yields. Additionally, we have examined the disparities between the octahedral and trigonal bipyramidal structures of the catalysts concerning their effects on the reaction mechanisms and apparent activation free energy barriers.