- The ionization potential of small metal and dielectric spheres is considered in different frameworks: classical, semiclassical, and quantum mechanical density functional approach. Classical calculations give conflicting results, and the generally accepted result for the ionization potential of a metal sphere of radius R: WI(R)=bulk work function+(3/8)q2/R is shown to be wrong, resulting from the classical image potential too close to the metal surface. Using appropriate cutoff to the image potential, the result WI(R)=bulk work function+(1/2)q2/R (previously obtained from solvation energy considerations) is recovered. Experimental results on relatively large particles are in agreement with the latter result. For very small clusters, deviations of experimental results from this classical behavior are shown by a density functional calculation to arise from quantum mechanical effects. These are first the spilloff of the electronic wave functions beyond the cluster edge and secondly from exchange and correlation contributions.