A method was presented for obtaining  ab initio  upper and lower bounds on the surface energies of stress-driven discommensurate surface structures which were perhaps non-periodic or which exhibited very large unit cells. The instability of the stressed commensurate parent of the discommensurate structure set an upper bound on its surface energy, while a lower bound was defined by the surface energy of an ideally commensurate but laterally strained hypothetical surface system. The surface energies of phases of the Si(111):Ga and Ge(111):Ga systems, and the energies of the discommensurations, were determined to within 0.2eV.

E.Artacho, J.Zegenhagen: Physical Review B, 1995, 52[23], 16373-6