Characterization of the Thermodynamic Stability of Solvated Metal-Organic Framework Polymorphs Using Molecular Simulations

Understanding the factors that govern the thermodynamic stability of metal-organic frameworks (MOFs) is critical to the development of these materials. In this work we present the first theoretical investigation of the stability of MOF polymorphs under solvothermal conditions. We combine thermodynamic integration (TI) and osmotic framework adsorbed solution theory (OFAST) calculations to reliably predict the free energy of immersion, Delta G(imm), of MOFs. We also demonstrate that the configurational free energy can be estimated in the harmonic approximation from the vibrational density of states (VDOS) of the framework. This approach is applied to a set of hypothetical Zn(mIm)(2) polymorphs under ambient conditions using methanol as the solvent to mimic the actual solvothermal synthesis conditions for ZIF-8. Our simulations predict that the relative contribution of Delta G(imm) to the framework stability is minor compared to the configurational free energy relative to the most stable structure for all polymorphs. However, we also find that solvation affects the energetic ordering of metastable polymorphs. We observe good agreement between predictions of Delta G(imm) using the OFAST method and those using the more rigorous TI calculations. The methods developed in this work can be applied to study the effect of the interplay between structural topology, solvent, and temperature on the thermodynamic stability of the framework for a wide range of nanoporous materials.