Even though recent developments in electronic structure calculations based on density functional theory (DFT) allow us to use them for more and more realistic systems, they still remain unsuited for comprehensive studies of complex transition metal compounds involving intricate structural and chemical effects. In that case, the tight-binding approximation (TBA) is a good compromise to get reliable results with only a minimal set of parameters, provided that clear rules enable a proper self-consistent treatment of charge transfers between inequivalent sites. Thus, in the case of the Co-Au system, DFT calculations demonstrate that a local neutrality rule is obeyed per orbital and per chemical species. Shifting the atomic levels accordingly in TBA calculations is then sufficient to accurately determine the local densities of states whatever the chemical configuration. In addition, this also allows us to justify the derivation from TBA of pairwise ordering pair interactions and to determine them self-consistently.