The geometries of AF(6)E molecules, which may have either an O-h or a C-3v geometry, have been studied by means of the electron localization function. Our results show that when the molecule has a C-3v geometry, there is a valence-shell monosynaptic V( A) basin corresponding to the presence of a lone pair in the valence shell of the central atom A. The population of this basin is, however, extensively delocalized so that the electron density has a core-valence basin character, which is consistent with an earlier suggestion of a weakly active lone pair that gives a C-3v distorted octahedral molecule rather than the valence-shell electron-pair repulsion predicted pentagonal-pyramid geometry. In contrast, the molecules with O-h geometry do not have a monosynaptic valence-shell basin, but they have a larger core. These results provide confirmation of a previous suggestion that in AX(6)E ( X = Cl, Br, I) molecules with the O-h geometry the ligands X are sufficiently closely packed around the central atom A so as to leave no space in the valence shell for the lone pair E, which remains part of the core. Among the corresponding fluorides, only BrF6- has the O-h geometry, while the others have the C-3v geometry because there is sufficient space in the valence shell to accommodate the lone pair, the presence of which distorts the O-h geometry to C-3v. The energies of the O-h and C-3v geometries have been shown to be very similar so the observed geometries are a consequence of a very fine balance between ligand-ligand repulsions and the energy gained by the expansion of the two nonbonding electrons into the valence shell.