The MP2/6-31G (*) //HF/6-31G (*) level study on (H2O)(20)H+ clusters suggests that the edge-shared prismic structure is more stable than a fused cubic or a dodecahedral cluster by similar to 7 and 22 kcal/mol, respectively. Only the dodecahedral cavity is large enough to enclose an H3O+ ion, and the hydronium ion originally placed in cavity either moves as a whole or loses its H+ ion to the surface during optimization and forms species like H5O2+, H7O3+ and H9O4+ ions on the surface. Based on HOH angular distortions and associated energy requirements we postulate that the edge-shared prismic or fused cubic clusters are not likely to form.