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Grand canonical Monte Carlo simulations on a lattice of adsorption sites (L-GCMC) are performed for prediction of adsorption selectivities for three binary mixtures, CO2/CH4, CO2/N2, and CH4/N2, in the metal–organic framework Mg2(dobdc), also known as CPO-27-Mg or Mg-MOF-74. Based on L-GCMC simulated pure gas adsorption data, we evaluated the performance of IAST in conditions where the adsorbed phase is nonideal due to substantial interaction between adsorbed molecules and heterogeneity of adsorption sites. The selectivity for CO2adsorption from the CO2/CH4mixture reaches the maximum of 290 at 298 K and at subatmospheric pressures when mainly the Mg2+sites get populated. For the CO2/N2mixture, with increasing surface coverage up to completing the monolayer, the CO2adsorption selectivity continuously increases up to 800. This shows that for that mixture, the selectivity is not the highest for the open metal sites but for adsorption on Linker sites. Compared to L-GCMC results, the selectivities predicted by IAST are underestimated for subatmospheric pressures for the CO2/CH4mixture and for almost the full pressure range for the CO2/N2mixture. Thus, IAST predicted selectivities are less accurate if the adsorbed phase is not ideal, and the real material can be a much better adsorbent for gas separation than predicted by IAST.

Adsorption of carbon dioxide in the metal–organic framework CPO-27-Mg (Mg-MOF-74) is examined. We use accurate quantum chemical ab initio methods (wave function-type electron correlation methods for cluster models combined with density functional theory for periodic systems) to calculate gas–surface site and gas–gas interactions. At 298 K, the “zero-coverage” enthalpy and Gibbs free energy of CO2adsorption on Mg2+sites are −46 and −9 kJ/mol, respectively; for linker sites these values are −30 and +5 kJ/mol, respectively. For full monolayer coverage lateral interactions from nearby molecules contribute −6 and −5 kJ/mol to the adsorption enthalpy for CO2at Mg2+and linker sites, respectively. The predicted heats of adsorption and free energies of adsorption agree within 2.6 and 0.8 kJ/mol, respectively, with experimental values well within chemical accuracy limits (4.2 kJ/mol). We use two different ways of calculating isotherms from equilibrium constants for individual sites and interaction energies: (i) a Langmuir model, augmented with the mean-field (MF) approximation for lateral interactions, and (ii) grand canonical Monte Carlo (GCMC) simulations on a lattice of sites, which agree very well with each other. We use GCMC data to examine how different isotherm models (Langmuir, dual-site Langmuir, Sips, Toth, and mean-field) fit them. We conclude that the MF model yields the best fit over a wide pressure range with physically meaningful parameters, i.e., adsorption constants for individual sites and lateral interaction energies.

We use quantum chemistry combined with molecular statistics to calculate Gibbs free energies, enthalpies, and entropies of adsorption for carbon dioxide binding to open metal sites in the metal–organic framework Mg2(dobdc), also known as CPO-27-Mg and Mg–MOF-74. For gas–surface interaction energies, we combine periodic MP2 and DFT+D for the full crystal framework with CCSD(T) for the adsorption site. Thermodynamic functions are calculated from anharmonic vibrational frequencies for the isolated sites and for higher surface coverages where adsorbed CO2molecules interact with neighboring molecules. The intermolecular lateral vibrations bring about an additional set of configurations that are not present in the case of molecules at isolated sites. Lateral adsorbate–adsorbate interaction contributions can be calculated separately and taking them into account results in a good agreement (±1 kJ/mol) between thermodynamic functions derived from experimental isotherms and ab initio calculations.

Density functional theory is applied with a hybrid functional to which a parametrized damped 1/r6term has been added to account for dispersion (B3LYP+D*). This method is used with periodic boundary conditions to get the structures of the adsorption complexes. Dispersion has a substantial share on the calculated adsorption energies (46–77%). For these structures, adsorption energies are also calculated with a hybrid high-level (MP2 with complete basis set extrapolation):low level (B3LYP+D*) method. The MP2 calculations are performed on cluster models. Comparison is made with experimental heats of adsorption. B3LYP+D* underestimates heats of adsorption by about 5 kJ/mol, whereas hybrid MP2:B3LYP+D* slightly overestimates them by about 2 kJ/mol. With MP2:B3LYP+D*, also the mean absolute error is somewhat smaller, 3.8 kJ/mol compared to 5.6 kJ/mol for B3LYP+D*. Both the B3LYP+D* and the hybrid MP2/CBS:B3LYP+D* method predict the same sequence of binding energies for carbon monoxide (Ni > Mg > Zn) and carbon dioxide (Mg > Ni > Zn) adsorption on open metal cation sites in the CPO-27 metal–organic frameworks.