Dispersion-Driven Cooperativity in Alkyl Perylene Diimide Oligomers: Insights from Density Functional Theory

The cooperative mechanism is of paramount importance in the synthesis of supramolecular polymers with desired characteristics, including molecular mass, polydispersity, and morphology. It is primarily driven by the presence of intermolecular interactions, which encompass strong hydrogen bonding, metal-ligand interactions, and dipole-dipole interactions. In this study, we utilize density functional theory and energy decomposition analysis to investigate the cooperative behavior of perylene diimide (PDI) oligomers with alkyl chains at their imide positions, which lack the previously mentioned interactions. Our systematic examination reveals that dispersion interactions originating from the alkyl side-chain substituents play an important role in promoting cooperativity within these PDIs. This influence becomes even more pronounced for alkyl chain lengths beyond hexyl groups. The energy decomposition analysis reveals that the delicate balance between dispersion energy and Pauli repulsion energy is the key driver of cooperative behavior in PDIs. Additionally, we have developed a mathematical model capable of predicting the saturated binding energies for PDI oligomers of varying sizes and alkyl chain lengths. Overall, our findings emphasize the previously undervalued significance of dispersion forces in cooperative supramolecular polymerization, enhancing our overall understanding of the cooperative mechanism.