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.