Interactions of CO₂ with cluster models of metal-organic frameworks

The interactions between carbon dioxide and cluster models of coordinatively unsaturated metal-organic frameworks (MOFs) were studied using a variety of ab initio methods. Three metal species and three organic linkers in four structures were considered in these models as a representation of the tunable nature of MOFs and the potential multireference character of such systems. Common single-reference methods, such as MP2 and CCSD(T), were compared with multireference methods based on complete active space self-consistent field theory, going as far as multireference configuration interaction with single and double excitations (MRCISD). Special consideration is taken to avoid issues of size inconsistency in the CI results, where an alternate reference is used in the interaction energy definition. The benchmark values are used to judge the adequacy of a selection of density functionals for the current systems. Symmetry-adapted perturbation theory (SAPT) decomposition was performed to elucidate the important effects that comprise the binding interactions. The systems proved to have very limited multireference character, and MP2 values were closer to the CCSD(T) benchmark than the more difficult MRCISD results. Though the SAPT total energies prove to be relatively poor approximations to the benchmark interaction energies, they reveal (in most cases) the correct trends with respect to the choice of the metal. The SAPT energy decompositions indicate that the CO₂ binding is primarily driven by electrostatics, but induction and dispersion also provide sizable, and quite similar, attractive contributions. Importantly, the small diformate model provides a faithful representation of complexes with large aromatic linkers, both in terms of the total interaction energy and the SAPT decomposition.