We present the first ab initio determination of the surface structure and electronic properties of Ge(lll)c(2x8). New features emerge, in addition to the basic adatom-rest-atom architecture. In agreement with LEED, which shows weak but nonvanishing quarter-order reflections, we find that an asymmetry is present in the surface unit cell, related to a small buckling between the two rest atoms, as well as to in-plane asymmetries of the rest atoms, adatoms, and first bilayer atoms. This inequivalence also produces a splitting of both the rest-atom and the adatom dangling-bond states, which explains the difference in their apparent heights as seen recently with scanning tunneling microscopy.PACS numbers: 68.35.Bs, 73.20.AtThe low-temperature stable surface of Si(lll) has a (7x7) structure, while that of Ge(lll) is c(2x8). In both reconstructions a crucial role is played by the adatom-rest-atom mechanism [1-11]: About j of the ideal surface dangling bonds are saturated by "adatoms," where extra electrons are mainly captured away by the remaining j of surface atoms ("rest atoms"). In the simplest adatom-rest-atom structure [with either a (2x2) or a (2x4) unit cell] this charge transfer leads to filled and empty surface-state bands, mostly localized on the rest atoms and the adatoms, respectively; all partly filled dangling-bond states are then eliminated, and the surface is stable [1]. Experience with the (7x7) structure of Si, however, has shown that many subtler but important effects accompany this main phenomenon [2]. Similar effects should also be present in the Ge(l ll)c(2x8) surface [3,4]. Particularly, scanningtunneling-microscopy (STM) studies find differences in the charge distributions of the two adatoms and the two rest atoms within the c(2x8) unit cell [4]. These differences-reminiscent of those between the faulted and unfaulted halves of the unit cell of Si(ll 0(7x7) [2,5] -suggest the occurrence of structural asymmetries in the c(2x8) cell, also qualitatively indicated by lowenergy electron diffraction (LEED) [6]. The nature of these secondary distortions and asymmetries has not been described so far. Also not understood is the microscopic reason why the surface is in reality c(2x8) and not (2x2) or c(2x4) [12]. As indicated by recent calculations for Si (ill) [13], these difficult problems are now within the reach of modern ab initio methods [14].In this Letter we present first-principles calculations of the structural and electronic properties of Ge(lll)c(2 x8), where the full periodicity of this surface is treated correctly for the first time. Previous theoretical studies have been simplified to an adatom structure with (2x2) periodicity [1,7].We find significant differences in the structures of the (2x2) and c(2x4) subunits of the c(2x8) unit cell, and show that these are consistent with the LEED results in Ref.[6]. The rest atoms have a relative buckling of the order of 0.03 A, and in-plane asymmetries of the order of 0.1 A, while differences are smaller for the adatoms. The (2x2) subunit rest atom,...