This article describes BP86/SV(P) (DFT) calcns. on a representative set of weakly coordinating anions (WCAs) of type [M(L)n]-, their parent neutral Lewis acids M(L)n-1 and their ate complexes with fluoride, i.e., [FM(L)n]n-1 (M = B, L = F, OTeF5, C6H5, C6F5, C6H3(CF3)2, CF3; M = P, As, Sb, L = F, OTeF5; M = Al, L = OC(CF3)3). Compds. with fluoride bridges, i.e., SbnF5n and [SbnF5n +1]- (n = 2, 3, 4), Al2(L)5F and [(L)3Al-F-Al(L)3]- (L = OC(CF3)3), (F4C6{1,2-B(L)2}2), [F4C6{1,2-B(L)2}2F]-, [F4C6{1,2-B(L)2}2OMe]- (L = C6F5) were also calcd. Based on these BP86/SV(P) and auxiliary MP2/TZVPP, G2, and CBS-Q calcns. the relative stabilities and coordinating abilities of these WCAs were established with regard to the fluoride ion affinities (FIA) of the parent Lewis acids, the ligand affinity (LA) of the WCAs, the decompn. of a given WCA in the presence of a hard (H+, proton decompn. PD) and a soft electrophile (Cu+, copper decompn. CuD), the position of the HOMO, the HOMO-LUMO gap, and population analyses of the anions providing partial charges for all atoms. To obtain data that is more reliable, the assessed quantities were calcd. through isodesmic reactions. If parts of the calcns. could not be done isodesmically, higher levels such as MP2/TZVPP, G2, and CBS-Q were used to obtain reliable values for these reactions. Although the obtained results can not be taken as abs., the relative ordering of the stabilities of all WCAs will undoubtedly be correct, since a single methodol. was chosen for the investigation. To include media effects the decompn. reactions of a subset of 14 WCAs with the SiMe3+ and [Cp2ZrMe]+ ions were also calcd. in PhCl and 1,2-F2C6H4 (COSMO solvation model). We found that in most cases gas-phase calcns. and soln. calcns. give comparable results for the stability of the anion. Applications of the LA and FIA that allow one to decide, on thermodn. grounds, which WCA or Lewis acid is the most suitable for a given problem are sketched. [on SciFinder (R)]