Using density functional calculations, we address the energetics of the interface between the SiC(0001) substrate and the first covalently bonded epitaxial graphene layer. We consider a 6 root 3 x 6 root 3R30 degrees geometry showing the experimental periodicity, a simplified root 3 x root 3R30 degrees geometry presenting a strained graphene layer, and an almost commensurate 4 x 4 geometry where SiC and graphene have the same orientation. The total energies of the structurally relaxed interface systems indicate that the 6 root 3 x 6 root 3R30 degrees geometry is the most stable, in agreement with its experimental occurrence. The binding energy is found to correlate with the vertical spread of the C atoms in the graphene layer, with a larger extension corresponding to a higher binding energy. For the 6 root 3 x 6 root 3R30 degrees geometry, the height variation of the graphene layer displays the experimentally observed modulation with an apparent 6 x 6 periodicity. The charge transfer also correlates with the height of the graphene atoms, being more significant in graphene regions which are strongly attached to the SiC substrate. (C) 2011 Elsevier B.V. All rights reserved.