Surface energy and stability of stress-driven discommensurate surface structures

A method is presented to obtain ab initio upper and lower bounds to surface energies of stress-driven discommensurate surface structures, possibly nonperiodic or exhibiting very large unit cells. The instability of the stressed, commensurate parent of the discommensurate structure sets an upper bound to its surface energy; a lower bound is defined by the surface energy of an ideally commensurate but laterally strained hypothetical surface system. The surface energies of the phases of the Si(111):Ga and Ge(111):Ga systems and the energies of the discommensurations are determined within +/-0.2 eV.