The lowest energy transition state for the nondissociative apical/equatorial atom exchange mechanism for three square pyramidal AEX(5) molecular species was calculated (CCSD(T)/pVTZ; B3LYP/pVTZ, aug-cc-pV5Z) to have a hemidirected geometry with C-s symmetry for BrF5, IF5, and XeF5+. In contrast, holodirected C-2v-symmetric transition states for this process were located for the AEX5 square pyramidal molecules CIF5, ICI5, and IBr5. Imaginary frequencies were calculated and examined in a visual/dynamic fashion to gain insight into these fluxional processes. Although both mechanisms exchange one apical for one equatorial atom in each cycle of motion, processes that pass through C 2 v transition states have characteristic features of the well-known Berry pseudorotation and Lever mechanisms while those which pass through transition states of Cs symmetry have features that are a mixture of Berry, Lever, and turnstile-like character. Two periodic trends are observed: as the atomic number on the central atom increases ( same terminal atoms), the barrier for apical/equatorial exchange and the value of the imaginary frequency both decrease. Similarly, as the atomic number of the terminal atoms increase ( same central atom), the barrier for apical/equatorial exchange decreases, as does the computed imaginary frequency.