A kinetics study of ligand substitution reaction on dinuclear platinum complexes: Stochastic versus deterministic approach

Theoretical and computational methodologies for understanding coordination self-assembly complexes

This perspective highlights three theoretical and computational methods to capture the coordination self-assembly processes at the molecular level: quantum chemical modeling, molecular dynamics, and reaction network analysis. These methods cover the different scales from the metal-ligand bond to a more global aspect, and approaches that are best suited to understand the coordination self-assembly from different perspectives are introduced. Theoretical and numerical researches based on these methods are not merely ways of interpreting the experimental studies but complementary to them.

Cyclization or bridging: which occurs faster is the key to the self-assembly mechanism of Pd6L3 coordination prisms

The self-assembly processes of Pd₆L₃ coordination prisms consisting of cis-protected Pd(II) complexes and porphyrin-based tetratopic ligands with four 3-pyridyl or 4-pyridyl groups (L) were investigated by experimental and numerical methods, QASAP (quantitative analysis of self-assembly process) and NASAP (numerical analysis of self-assembly process), respectively. It was found that contrary to common intuition macrocyclization takes place faster than the bridging reaction in the prism assembly and that the bridging reaction occurring before the macrocyclization tends to produce kinetically trapped species. A numerical simulation demonstrates that the relative magnitude of the rate constants between the macrocyclization and the bridging reaction is the key factor that determines whether the self-assembly leads to the thermodynamically most stable prism or to kinetically trapped species. Finding the key elementary reactions that largely affect the selection of the major assembly pathway is helpful to rationally control the products under kinetic control via modulation of the energy landscape.

Unexpected Self-Assembly Pathway to a Pd(II) Coordination Square-Based Pyramid and Its Preferential Formation beyond the Boltzmann Distribution

Experimental and theoretical investigations of the self-assembly process of a Pd(II) coordination M₆L₄ square-based pyramid (SP) were conducted. It was found that the probable self-assembly pathway, in which the dimerization of M₂L₂ with two M leads to SP, expected from the connectivity of the building blocks is not a major self-assembly pathway to the M₆L₄ SP. Whether the M₆L₄ SP is assembled or M₂L₂ is trapped is determined by an inter- or intramolecular reaction in a chain-like M₂L₂X, where X is a leaving ligand. The kinetically trapped state where the M₆L₄ SP is produced from M₂L₂ beyond the Boltzmann distribution was realized by a concentration-induced process and was kept for at least 2 months at 298 K.

Towards kinetic control of coordination self-assembly: a case study of a Pd3L6 double-walled triangle to predict the outcomes by a reaction network model

Numerical analysis of self-assembly process (NASAP) was performed for a [Pd3L6]6+ double-walled triangle (DWT) complex. With a chemical reaction network and a parameter set of the reaction rate constants obtained from a numerical search in an eighteen-dimensional parameter space to obtain a good fit to the data from the experimental counterpart (quantitative analysis of self-assembly process, QASAP), a refined calculation resulted in a detailed time evolution of each molecular species. Analysis based on those clues revealed dominant self-assembly pathways and a balance between inter- and intramolecular reactions, and enabled prediction of the reaction outcomes depending on the initial stoichiometric ratio under kinetic control.

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

Numerical analysis considering explicit conformational difference revealed the self-assembly process of a Pd₂L₄ cage containing rigid ditopic ligands.