  We report diffusion quantum Monte Carlo calculations of the interlayer
binding energy of bilayer graphene. We find the binding energies of the AA- and
AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9)
meV/atom, respectively. The out-of-plane zone-center optical phonon frequency
predicted by our binding-energy curve is consistent with available experimental
results. As well as assisting the modeling of interactions between graphene
layers, our results will facilitate the development of van der Waals
exchange-correlation functionals for density functional theory calculations.
