The surface reconstruction, 3 x 2, induced by Yb adsorption on a Ge (Si)(111) surface has been studied using first principles density-functional calculation within the generalized gradient approximation. The two different possible adsorption sites have been considered: (i) H(3) (this site is directly above a fourth-layer Ge (Si) atom) and (ii) T(4) (directly above a second-layer Ge (Si) atom). We have found that the total energies corresponding to these binding sites are nearly the same, indeed for the Yb/Ge (Si)(111)-(3 x 2) structure the T(4) model is slightly energetic by about 0.01 (0.08) eV/unitcell compared with the H(3) model. In particular or the Ge sublayer, the energy difference is small, and therefore it is possible that the T(4), H(3), or T(4)H(3) (half of the adatoms occupy the T(4) adsorption site and the rest of the adatoms are located at the H(3) site) binding sites can coexist with REM/Ge(111)-(3 x 2). In contrast to the proposed model, we have not determined any buckling in the Ge = Ge double bond. The electronic band structures of the surfaces and the corresponding natures of their orbitals have also been calculated. Our results for both substrates are seen to be in agreement with the recent experimental data, especially that of the Yb/Si(111)-(3 x 2) surface. (C) 2010 Elsevier B.V. All rights reserved.