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The adsorption of sodium on the Ge(0 0 1)(2 x 1) surface at the coverage (Theta) of 0.5 and 1 ML has been investigated by using ab initio total energy calculations. It was found that at Theta = 0.5 ML T3 and T4 sites are nearly degenerate and Na adatoms preferred to adsorb at T3 and T4 sites. This finding agrees well with Meyerheim et al.'s experimental results, but does not support theoretical investigations of Spiess et al., who found HH site was the most stable. For 1 ML coverage the most stable configurations are a combination of the HH and T3 or T4 sites. Work function and dipole moment analysis showed that upon Na adsorption on Ge(0 0 1)(2 x 1) and Si(0 0 1)(2 x 1) surface the dipole-dipole repulsion is small and no depolarization effect occurs as the coverage increases from 0.5 to I ML. (c) 2005 Elsevier B.V. All rights reserved.