An assessment of density functionals for predicting CO₂ adsorption in diamine-functionalized metal–organic frameworks

Diamine-functionalized M₂(dobpdc) (M = Mg, Mn, Fe, Co, Zn) metal–organic frameworks (MOFs) are among a growing class of crystalline solids currently being intensively investigated for carbon capture as they exhibit a novel cooperative and selective CO₂ adsorption mechanism and a step-shaped isotherm. To understand their CO₂ adsorption behavior, ab initio calculations with near-chemical accuracy (∼6 kJ/mol, an average experimental error) are required. Here, we present density functional theory (DFT) calculations of CO₂ adsorption in m-2-m–Zn₂(dobpdc) (m-2-m = N,N′-dimethylethyle-nediamine and dobpdc⁴⁻ = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) with different exchange–correlation functionals, including semilocal functionals [Perdew–Burke–Ernzerhof (PBE) and two revised PBE functionals], semiempirical pairwise corrections (D3 and Tkatchenko–Scheffler), nonlocal van der Waals (vdW) correlation functionals—vdW-optB88 (or vdW-DF-optB88), vdW-DF1, vdW-DF2, vdW-DF2-B86R (or rev-vdW-DF2), vdW-DF-cx (and vdW-DF-cx0), and revised VV10—and the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA). Overall, we find that revPBE+D3 and RPBE+D3 show the best balance of performance for both the lattice parameters and the CO₂ binding enthalpy of m-2-m–Zn₂(dobpdc). revPBE+D3 and RPBE+D3 predict the m-2-m–Zn₂(dobpdc) lattice parameters to within 1.4% of experiment and predict CO₂ binding enthalpies of −68 kJ/mol, which compare reasonably well with the experiment (−57 kJ/mol). Although PBE (−57.7 kJ/mol), vdW-DF1 (−49.6 kJ/mol), and vdW-DF2 (−44.3 kJ/mol) are also found to predict the CO₂ binding enthalpy with good accuracy, they overestimate lattice parameters and bond lengths. The other functionals considered predict the lattice parameters with the same accuracy as revPBE+D3 and RPBE+D3, but they overbind CO₂ by around 26–50 kJ/mol. We find that the superior performance of revPBE+D3 and RPBE+D3 is sustained for the formation enthalpy and the lattice parameters of ammonium carbamate, a primary product of the cooperative CO₂ insertion in diamine-functionalized M₂(dobpdc) MOFs. Moreover, we find that their performance is derived from their larger repulsive exchange contributions to the CO₂ binding enthalpy than the other functionals at the relevant range of the reduced density gradient value for the energetics of CO₂ adsorption in the m-2-m–Zn₂(dobpdc) MOF. A broader examination of the performance of RPBE+D3 for the structural parameters and CO₂ binding enthalpies of 13 diamine-functionalized Mg₂(dobpdc) MOFs further demonstrates that RPBE+D3 successfully reproduces experimental CO₂ binding enthalpies and reveals a logarithmic relationship between the step pressure and the CO₂ binding enthalpy of the diamine-functionalized Mg₂(dobpdc) MOFs, consistent with experiments where available. The results of our benchmarking study can help guide the further development of versatile vdW-corrected DFT methods with predictive accuracy.