Comparison of methods for inclusion of van der Waals interactions: the case of physisorption of nucleobases on graphene

The physisorption of the nucleobases adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U) on graphene is studied using many flavors of density functional theory (DFT): the generalized gradient approximation (GGA) with the inclusion of van der Waals (vdW) interaction based on the TS approach [A. Tkatchenko and M. Scheffler, \textit{PRL} \textbf{102}, 073005 (2009)], our simplified version of this approach, the vdW density functional (vdW-DF) [M. Dion \textit{et al.}, \textit{PRL} \textbf{92}, 246401 (2004)], and the vdW-DF2 [K. Lee \textit{et al., PRB} \textbf{82}, 081101 (2010)] methods. The binding energies of nucleobases on graphene lie in the range of 496{\-}962 meV and are found to be in the following order G$>$A$>$T$>$C$>$U within vdW-DF, vdW-DF2 and our method and G$>$A$>$T$\sim $C$>$U in the TS approach. The binding separations lie between 3.29{\-}3.53 {\AA} and are found to be about 0.1{\-} 0.2 {\AA} shorter in DFT-D, as compared to vdW-DF approaches. We comment on the efficiency of combining the DFT-D and vdW-DF methods to study vdW interactions in molecular adsorption.