Reduced-gradient analysis of molecular adsorption on graphene with nonlocal density functionals

Graphene has garnered tremendous interest in the last decade due to its great potential for applications in almost every scientific and engineering discipline. The adsorption of molecules onto graphene is itself also of significant interest, including in catalysis and trace molecule detection. However, density functional theory has traditionally struggled to accurately model surface adsorption involving long-range dispersion interactions between a molecule and a substrate, accentuating the need for comprehensive benchmarking and analysis. Here, we test the accuracy of several functionals in describing the adsorption energy of graphene–molecule adsorption complexes, including several van der Waals density functionals as well as the nonlocal correlation functional rVV10 and the dispersion-corrected PBE-D3. We find that the highest accuracy is provided by vdW–DF2 and the two realizations of vdW–DF3, the most recent generations of the van der Waals density functional family. In addition, we use a reduced-gradient analysis technique to examine the material's exchange energy. This analysis resolves contributions to the exchange interaction energy as a function of the reduced-gradient $s$, revealing regimes of $s$ that are important components of the interaction energy of these systems. In doing so, we identify the best functionals currently available and initiate discussion on desirable traits of each functional for modeling surface adsorption.