Atomistic Model for Water Adsorption in Mg-MOF-74: Quantum Chemical Prediction of Structures and Isotherms

The design of improved metal-organic frameworks (MOFs) for water harvesting requires the reliable prediction of adsorption isotherms, i.e., Gibbs free energies of adsorption, with no other input than the atomic positions. We employ density functional theory (DFT) and show that, in Mg-MOF-74, well-defined adsorption structures exist for water loadings of <i>n</i> = 1, 2, 3, 4, and 5 molecules per Mg²⁺ ion. The first water molecule attaches to the open metal site, while on adsorption of subsequent molecules, structures with an increasing number of hydrogen bonds per molecule form: dimers (<i>n</i> = 2), chains in pore direction (<i>n</i> = 3), and a monolayer on the pore wall (<i>n</i> = 4). For <i>n</i> = 5, a tube-like stack of water trimers connected to the monolayer fills the pore completely, and all water molecules are 4-fold coordinated. For isotherm predictions, we use a <i>Multisite Langmuir</i> model with Gibbs free energies of -33, -19, -13, -10, and -21 kJ/mol for the steps leading to adsorption states with <i>n</i> = 1, 2, 3, 4, and 5 molecules, respectively. The close agreement of the predicted total isotherm with experiment corresponds to an accuracy of ±2 kJ/mol for Gibbs free energies. This is achieved only after adding "high-level" Coupled Cluster corrections (0, 3, 9, 8, and 11 kJ/mol for <i>n</i> = 1, 2, 3, 4, and 5, respectively) to the DFT energies. We show that the large variations observed between different experimental isotherms can be explained by sample imperfections or incomplete evacuation of samples before isotherm measurements.