Stacking and band structure of van der Waals bonded graphane multilayers

We use density functional theory and the van der Waals density functional (vdW-DF) method to determine the binding separation in bilayer and bulk graphane and study the changes in electronic band structure that arise with the multilayer formation. The calculated binding separation (distance between center-of-mass planes) and binding energy are $4.5\ensuremath{-}5.0$ \AA{} ($4.5\ensuremath{-}4.8$ \AA{}) and $75\ensuremath{-}102$ meV/cell ($93\ensuremath{-}127$ meV/cell) in the bilayer (bulk), depending on the choice of vdW-DF version. We obtain the corresponding band diagrams using calculations in the ordinary generalized gradient approximation for the geometries specified by our vdW-DF results, so probing the indirect effect of vdW forces on electron behavior. We find significant band-gap modifications by up to \ensuremath{-}1.2 eV (+4.0 eV) in various regions of the Brillouin zone, produced by the bilayer (bulk) formation.