A stochastic model study on the self-assembly process of a Pd₂L₄ cage consisting of rigid ditopic ligands

The coordination self-assembly process of a Pd₂L₄ cage including rigid ditopic ligands, L, was studied numerically. A recently developed experimental approach (QASAP: quantitative analysis of self-assembly process) revealed that the rate-determining steps in the self-assembly of the Pd₂L₄ cage are intramolecular ligand exchanges at the late stages of the self-assembly. In this study, the self-assembly process before the rate-determining steps, which could not be investigated by experiment, was analyzed based on a minimal reaction network model. Only eight variable parameters of rate constants for ligand exchange reactions are sufficient enough to reproduce the time evolution of substrates and the products during the self-assembly of the cage. With these parameters, the major self-assembly pathway was determined. It was also found that a non-negligible amount of an incomplete cage (IC), Pd₂L₃X₂ (X indicates the leaving ligand), which was not suggested by QASAP, should be transiently produced. Numerical tests also suggest that the small rate constant value of the intramolecular ligand exchanges due to a restricted geometry causes the final stage to seemingly become the rate-determining step.