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

## TL;DR

This study uses computational chemistry to analyze the stability and structure of heterometallic MOFs, revealing how cation size and coordination influence metal mixing and framework stability.

## Contribution

It introduces a systematic DFT-based methodology to understand cation distribution and stability in heterometallic MOFs, specifically MOF-5 and UiO-66.

## Key findings

- Bimetallicity is favored when cation sizes are similar.
- Metal mixing is less favorable with significant size differences.
- Coordination environment impacts mixing stability, especially in UiO-66.

## Abstract

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.