Theoretical Study on Rate-Determining Reactions for Constructing Self-Assembling Molecular Cages Controlled by Distorted Ditopic Ligands

Metal–organic cages comprising two Pd ions and four ditopic ligands that can bridge the two Pd ions can encapsulate an anion, such as NO3– and BF4–. Herein, we examined two types of ditopic ligands, 3-(7-pyridin-3-ylnaphthalen-2-yl)pyridine (1) and 3-[2-[3-(2-pyridin-3-ylethynyl)phenyl]ethynyl]pyridine (2), and discussed the following metal–organic cages: Pd214, Pd224, and Pd21222. We analyzed the mechanism underlying ligand-exchange reactions for synthesizing self-assembled molecular cages based on the density functional theory. Particularly, this study focused on rate-determining steps for molecular cage formation, where two leaving ligands are exchanged with ditopic ligands. Furthermore, we demonstrated that rate-determining reactions are controlled by the molecular length and rigidity of ditopic ligands and that the formation energy of molecular cages is affected by distortion of ditopic ligands. Therefore, understanding the distortion effect will help to control the reaction processes and functionalities of molecular cages.