Heterometallic Metal–Organic Frameworks of MOF‑5 and UiO-66 Families: Insight from Computational Chemistry

We
study the energetic stability and structural features of bimetallic
metal–organic frameworks. Such heterometallic MOFs, which can
result from partial substitutions between two types of cations, can
have specific physical or chemical properties used for example in
catalysis or gas adsorption. We work here to provide through computational
chemistry a microscopic understanding of bimetallic MOFs and the distribution
of cations within their structure. We develop a methodology based
on a systematic study of possible cation distributions at all cation
ratios by means of quantum chemistry calculations at the density functional
theory level. We analyze the energies of the resulting bimetallic
frameworks and correlate them with various disorder descriptors (functions
of the bimetallic framework topology, regardless of exact atomic positions).
We apply our methodology to two families of MOFs known for heterometallicity:
MOF-5 (with divalent metal ions) and UiO-66 (with tetravalent metal
ions). We observe that bimetallicity is overall more favorable for
pairs of cations with sizes very close to each other, owing to a charge
transfer mechanism inside secondary building units. For cation pairs
with significant mutual size difference, metal mixing is globally
less favorable, and the energy signifantly correlates with the coordination
environment of linkers, determining their ability to adapt the mixing-induced
strains. This effect is particularly strong in the UiO-66 family because
of high cluster coordination number.