Ab initio calculations at MP2/6-31G*, B3LYP/6-3lG*, and B3LYP/6-311+G** levels indicate relatively high potential barriers for the intramolecular rearrangement of B9H92- via the single DSD (diamond-square-diamond) or the double DSD mechanism, 28.4 and 21.3 kcal/mol, respectively. However, its open face-protonated form, B9H10- (2b) is highly fluctional. Two other minima, 2a (C-2 nu) and 2c (C-3 nu) have energies 1.1 and 9.7 kcal/mol higher than 2b. Facile rotation of the BH2 group in 2a is coupled with reversible opening of the boron cage from the close to a nido form. Structure 2c, with a face-bound proton, is a very shallow minimum along the degenerate rearrangement pathway of 2b. None of the optimized structures of B9H10- give calculated B-11 chemical shifts corresponding to experiment; the NMR assignments and interpretation need to be refined. Members of the BnHn+1- series (n = 6-8, 10, and 12) have both common as well as specific features. All BnHn+1- species are fluxional, due to rapid proton migration. The additional hydrogen H* rotates over the whole boron octahedron in B6H7- and over one side of the bipyramid in B7H8-. In B10H11-, the "extra" hydrogen H* migrates around the faces of a "polar region" near the apical borons more readily than from pole to the other; as in B9H10-, H* migration in B8H9- is accompanied by a skeletal rearrangement. The proton affinities (PA) in the BnHn2- series decrease with increasing size, since the Coulomb repulsion in the dianions becomes smaller and the coordination number at the protonation sites increases.