Deciphering Self-Assembly Mechanisms of IRMOF-n-Inspired Three-Dimensional Cubic-Symmetry Nanoporous Crystals from Multiscale Simulations

Abstract

The formation mechanisms of metal−organic frameworks (MOFs) are not fully understood. Therefore, experimental realization of potential “breakthrough” MOFs is hindered by uncertainty in the synthesis conditions that would allow the constituent nodes and linkers to self-assemble into the targeted MOF structure. Here, a multiscale endeavor using density functional theory (DFT) calculations, followed by metadynamics with DFT-informed classical atomistic potentials, followed by standard molecular dynamics (MD) and Hamiltonian replica exchange (HREX) simulations with a metadynamics-informed, coarse-grained (CG) model, was used to study the self-assembly mechanism of cubic-symmetry porous crystals inspired by the IRMOF-n family of MOFs. Mechanistic differences were examined for different values of node–linker coordination strength─understood as the free energy penalty for breaking a coordination bond in a solvated environment. Our integrated analyses of HREX-derived free energy surfaces and standard MD trajectories indicate that at coordination strengths typical of the IRMOF-n family in dimethylformamide (DMF) (i.e., 52 kJ/mol), disassembled nodes and linkers are favored to overcome a small 1.3 kJ/mol free energy barrier to first form solid amorphous clusters, which then overcome a series of barriers (the largest of which is 3.7 kJ/mol) to heal and form ordered, more stable, cubic-symmetry crystals. This healing seems to occur through the splintering/reattaching of small clusters from/to large clusters. Our analyses also suggest that if coordination strength is moderately weakened (e.g., to 40 kJ/mol), crystals form without the preliminary formation of amorphous clusters. However, further coordination strength weakening (e.g., to 36 kJ/mol) makes the formation of sizable crystals unfavorable thermodynamically. On the other hand, strengthening the coordination would increase the free energy barrier to heal the amorphous clusters into crystals. Accordingly, if coordination becomes too strong (e.g., 65+ kJ/mol), then healing may become unlikely. In practical terms, our study suggests that MOF formation is favored only when the free energy of coordination, accounting for solvent effects, falls within a relatively narrow range (approximately 40 to 65 kJ/mol), at least at 300 K, for MOFs with cubic symmetries.