Anisotropy of Elastic Properties of Metal–Organic Frameworks and the Breathing Phenomenon

Metal–organic
frameworks (MOFs) need a high mechanical stability
to be robust for industrial applications, like gas storage and catalysis.
Their adsorption properties also correlate with the structure flexibility,
which leads to the so-called breathing phenomenon. Finding relations
between geometrical and topological descriptors and mechanical properties
is important for explaining and predicting mechanical behavior of
both synthesized and hypothetical MOFs. To address this, we present
the full tensor DFT analysis of the second-order elastic constants
for 22 either rigid or flexible MOFs assembled from rod secondary
building units (rod MOFs) and related to 7 topological types of underlying
nets: 4/5/t1, bik, crb, dia, gis, cda, and mog. The calculated values of the Young’s and shear moduli, linear
compressibility, and Poisson’s ratio have found a good agreement
with experimental observations. We have shown that the geometrical–topological
features of the coordination framework predetermine the general form
of the elastic tensor, while variations in the MOF composition tune
the mechanical properties in specific directions. We report for the
first time a negative linear compressibility for the CAU-10-OCH3, NOTT-401, MIL-60, MIL-116, and MIL-118 frameworks. We have
also revealed that the breathing behavior of six rod MOFs of the MIL-53,
MIL-118, and CAU-10 families is caused by compliant geometrical–topological
patterns and ligand–ligand interactions. The proposed classification
of the geometrical–topological patterns into compliant and
noncompliant can be used to search for and to design breathing MOFs.