The topomerization mechanisms of the SF4 and SCl2F2 sulfuranes, as well as their higher (SeF4. TeF4) and isoelectronic analogues (PF4-, AsF4-, SbF4-, SbCl4-. ClF4+, BrF4+, BrCl2F2+, and IF4+), have been computed at B3LYP/6-31+G* and at B3LYP/6-311+G*. All species have trigonal bipyramidal (TBP) Ct, ground states. In such four-coordinated molecules, Berry rotation exchanges both axial with two equatorial ligands simultaneously while the alternative "lever" mechanism exchanges only one axial ligand with one equatorial ligand. While the barrier for the lever exchange in SF4 (18.8 kcal mol(-1)) is much higher than that for the Berry process (8.1 kcal mol(-1)), both mechanisms are needed for complete ligand exchange. The FaxFax and FeqFeq isomers of SF2Cl2 have nearly the same energy and readily interconvert by BPR with a barrier of 7.6 kcal mol(-1). The enantiomerization of the FaxFeq chiral isomer can occur by either the Berry process (transition state barrier 8.3 kcal mol(-1)) or the "lever" mechanism via either of two C, transition states, based on the TBP geometry: Cl-ax <----> Cl-eq or F-ax <----> F-eq exchanges with barriers of 6.3 and 15.7 kcal mol(-1), respectively. Full scrambling of all ligand sites is possible only by inclusion of the lever mechanism. Planar, "tetrahedral", and triplet forms are much higher in energy. The TBP C-3v structures Of AX(4) either have two imaginary frequencies (NIMAG = 2) for the X = F, Cl species or are minima (NIMAG = 0) for the X = Sr, I compounds. These "effective monkey saddle points" have degenerate modes with two small frequencies, imaginary or real. Although a strictly defined "monkey saddle" (with degenerate frequencies exactly zero) is not allowed, the flat C-3v symmetry region serves as a "transition state" for trifurcation of the pathways. The BPR mechanism also is preferred over the alternative lever process in the topomerization of the selenurane SeF4 (barriers 5.9 vs 12.1 kcal mol(-1)). the tellurane TeF4 (2.1 vs 6.4), and the interhalogen cations ClF4+ (2.5 vs 14.8), BrF4+ (4.7 vs 11.3), BrF2Cl2+ (14.6 vs 17.4), and IF4+ (1.4 vs 6.0), as well as for the series PF4- (7.0 vs 9.0), AsF4- (9.3 vs 17.2), and SbF4-(3.8 vs 5.3 kcal mol(-1)). all computed at B3LYP/6-311+G* with the inclusion of quasirelativistic pseudopotentials for Te, I, and Sb. The heavier halogens increasingly favor the lever process, where the barrier (2.6 kcal mol(-1)) pertaining to the effective monkey saddle point (G, minimum for SbCl4-) is less than that for the Berry process (8.2 kcal mol(-1)).