  We present a comparative study of DNA nucleobases [guanine (G), adenine (A),
thymine (T), and cytosine (C)] adsorbed on hexagonal boron nitride
(\textit{h}-BN) sheet and graphene, using local, semilocal, and van der Waals
(vdW) energy-corrected density-functional theory (DFT) calculations.
Intriguingly, despite the very different electronic properties of BN sheet and
graphene, we find rather similar binding energies for the various nucleobase
molecules when adsorbed on the two types of sheets. The calculated binding
energies of the four nucleobases using the local, semilocal, and DFT+vdW
schemes are in the range of 0.54 ${\sim}$ 0.75 eV, 0.06 ${\sim}$ 0.15 eV, and
0.93 ${\sim}$ 1.18 eV, respectively. In particular, the DFT+vdW scheme predicts
not only a binding energy predominantly determined by vdW interactions between
the base molecules and their substrates decreasing in the order of
G$>$A$>$T$>$C, but also a very weak hybridization between the molecular levels
of the nucleobases and the ${\pi}$-states of the BN sheet or graphene. This
physisorption of G, A, T, and C on the BN sheet (graphene) induces a small
interfacial dipole, giving rise to an energy shift in the work function by 0.11
(0.22), 0.09 (0.15), $-$0.05 (0.01), and 0.06 (0.13) eV, respectively.
