Van der Waals density-functional study of 100% hydrogen coverage on bilayer graphene

We investigate all hydrogen configurations that exist in a 1 × 1 unit cell of bilayer graphene at 100% coverage to find the low energy competing configurations using density functional theory (DFT). Other unique configurations, obtained from a 2 × 1 supercell, are also investigated. The GGA-PBE functional and four variants of non-local van der Waals density functionals namely, vdW-DF, vdW-DF2, vdW-DF-C09x, and vdW-DF2-C09x are used to account for the exchange correlation effects. Ten unique hydrogen configurations are identified for 1 × 1 unit cell bilayer graphene, and nine of these structures are found to be energetically stable with three low energy competing configurations. One arrangement found to exist in both 1 × 1 and 2 × 1 cell sizes is the most energetically stable configuration of all considered. For some of the configurations identified from the 2 × 1 supercell, it is found that the effect of hydrogenation results in greatly distorted hexagonal layers resulting in unequal bond distances between the carbon atoms. Also, interaction between the hydrogen-decorated planes greatly affects the energetics of the structures. The vdW-DF-C09x functional is found to predict the shortest interlayer distances for all the configurations, whereas the GGA-PBE functional predicts the largest. For the most energetically favorable configuration, hydrogenation is found to reduce the elastic properties compared with pristine bilayer graphene.