Performance of van der Waals Corrected Functionals for Guest Adsorption in the M₂(dobdc) Metal-Organic Frameworks

Small-molecule binding in metal-organic frameworks (MOFs) can be accurately studied both experimentally and computationally, provided the proper tools are employed. Herein, we compare and contrast properties associated with guest binding by means of density functional theory (DFT) calculations using nine different functionals for the M₂(dobdc) (dobdc^4- = 2,5-dioxido,1,4-benzenedicarboxylate) series, where M = Mg, Mn, Fe, Co, Ni, Cu, and Zn. Additionally, we perform Quantum Monte Carlo (QMC) calculations for one system to determine if this method can be used to assess the performance of DFT. We also make comparisons with previously published experimental results for carbon dioxide and water and present new methane neutron powder diffraction (NPD) data for further comparison. All of the functionals are able to predict the experimental variation in the binding energy from one metal to the next; however, the interpretation of the performance of the functionals depends on which value is taken as the reference. On the one hand, if we compare against experimental values, we would conclude that the optB86b-vdW and optB88-vdW functionals systematically overestimate the binding strength, while the second generation of van der Waals (vdW) nonlocal functionals (vdw-DF2 and rev-vdW-DF2) correct for this providing a good description of binding energies. On the other hand, if the QMC calculation is taken as the reference then all of the nonlocal functionals yield results that fall just outside the error of the higher-level calculation. The empirically corrected vdW functionals are in reasonable agreement with experimental heat of adsorptions but under bind when compared with QMC, while Perdew-Burke-Ernzerhof fails by more than 20 kJ/mol regardless of which reference is employed. All of the functionals, with the exception of vdW-DF2, predict reasonable framework and guest binding geometries when compared with NPD measurements. The newest of the functionals considered, rev-vdW-DF2, should be used in place of vdW-DF2, as it yields improved bond distances with similar quality binding energies.