EN
The generalization of the Budd-Vannimenus theorem for jellium model of metal surface, when the positive background is described by a non-negative function, is given. Using the displacement electron density profile method and the generalized Budd-Vannimenus theorem it is shown that work function expressions given on the basis of Koopmans theorem and by Monnier et al. are equivalent both for a clean metal and for a metal covered by a metallic adlayer.