Method for Analyzing Structural Changes of Flexible Metal−Organic Frameworks Induced by Adsorbates

Metal−organic frameworks (MOFs) have crystal structures that exhibit unusual flexibility. An extreme example is that of the “breathing MOF” MIL-53 that expands or shrinks to admit guest molecules like CO2 and water. We present a powerful simulation tool to quickly calculate unit cell shape and size at 0 K for structures loaded with adsorbates. The method can be applied to unit cell minimization of periodic systems such as metal−organic frameworks and zeolites for vibrational analysis (IR spectra and mode analysis), force field development, and computation of elastic constants at 0 K. The expressions for first- and second-derivatives for rigid guest molecules that are missing in the literature are described in this paper. In addition, two case studies about determination of the structure of IRMOF-1 at 0 K and about the influence of water on the structure of MIL-53 showed that the simulation results correspond well with experimental results and other computational results. Our analysis scheme has significant advantages over other schemes, and the IRMOF-1 case study shows how these methods could potentially fail.