Density functional theory is applied with a hybrid functional to which a parametrized damped 1/r6 term 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.