A 63-atom cluster is employed, in a self-consistent semi-empirical molecular orbital total energy algorithm, to calculate the binding energies of potassium atoms adsorbed on a Si(100) (2*1) reconstructed surface at various possible adsorption sites, namely, sites H, B and C. The authors results strongly suggest that the B site is the most stable one. The results of a half-monolayer coverage calculation show that the double-layered structure of potassium atoms is feasible and in accordance with recent experimental observations. However, the bond length between Si and K, dSi-K, is found to be around 15% lower than the experimental determination. From the Mulliken population analysis, the amount of charge transferred from Si to K atoms varies from 0.01 to 0.32 of the electronic charge at various adsorption sites.