(218h) Modeling Self-Assembly of Metal-Organic Frameworks with Enhanced Sampling Techniques

Self-assembly is a process by which building blocks form functional materials. In principle, instructions can be imparted onto the building blocks to engineer and design the final structure. One class of materials which takes advantage of this building block approach is metal-organic frameworks (MOFs), nanoporous crystalline materials formed in solution through coordination-driven self-assembly of inorganic nodes and organic linkers. Experimental observations of MOF self-assembly reveal complex and interesting phenomena where synthetic conditions (solvent, temperature, concentration of building blocks) alter the final MOF structure as well as intermediate metastable states. However, computational efforts to elucidate MOF self-assembly are scarce. For this study, we focus on the self-assembly of MOF-5.

We employ a combination of enhanced sampling techniques to study MOF self-assembly for different scenarios and system sizes. We model MOF-5 with an atomistic model as either a discrete unit cell or four unit cells in explicit solvent. To validate the model, we perform replica exchange with solute scaling (REST2) simulations and calculate the free energy profile using the average distance and average angle between nodes as collective variables. The free energy minima observed in these systems are close to the values in the experimental unit cell, therefore validating that the chosen model represents at least a metastable state.

To model self-assembly, we perform finite temperature string (FTS) method calculations using the average distance and angle between nodes and the total coordination between nodes and linkers. The process was modeled for both single and four unit cells systems from two starting points: fully disassembled and amorphous. The self-assembly starting from the disassembled state was found to be downhill in free energy for both the single unit cell and four unit cells systems. In contrast, the self-assembly starting from the amorphous state reveals energetic barriers on the way to the final MOF structure. Finally, we discuss the mechanism of self-assembly of MOF-5 for the scenarios and system sizes considered.