Stacking fault formation is at the origin of nanostructuration phenomena at close-packed like in the case of the famous Au(111) herrigbone reconstruction. The balance energy between FCC stacking and HCP stacking is conditionning also the structural homogeneity of an epitaxial growing deposit on such surfaces. In this context we apply a sp-d tight binding model to study the evolution of the stacking fault energy at (111) surfaces of metals. We show in this way the relative importance of sp-d hybridation both in the formation of defects at the surface of metals and in reconstruction phenomena as a function of band filling especially for the end of transition series. In our work, we also use a method of DFT, precisely the SIESTA method, which is based on orbital atomic localized, which allows us to compare sp-d tight binding model with a more accurate values. Finally, we compare our results with atomistic simulations. It is concluded that although atomistic calculations are powerful tools to investigate relaxation mechanisms at surfaces, a higher degree of accuracy on electronic structure could be necessary to quantify the energy of some defects at surfaces like FCC stacking and HCP stacking. In particular long range interactions associated to less localized sp electrons are clearly playing a non negligible role in reconstruction phenomena for metals like platinum and gold. 

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