  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.
