Atomization energies at 0 K and enthalpies of formation at 0 and 298 K are predicted for the BH(4-n)X(n)(-) and the BH(3-n)X(n)F(-) compounds for (X = F, Cl, Br, I, NH(2), OH, and SH) from coupled cluster theory (CCSD(T)) calculations with correlation-consistent basis sets and with an effective core potential on I. To achieve near chemical accuracy (+/-1.0 kcal/mol), additional corrections were added to the complete basis set binding energies. The hydride, fluoride, and X(-) affinities of the BH(3-n)X(n) compounds were predicted. Although the hydride and fluoride affinities differ somewhat in their magnitudes, they show very similar trends and are both suitable for judging the Lewis acidities of compounds. The only significant differences in their acidity strength orders are found for the boranes substituted with the strongly electron withdrawing and back-donating fluorine and hydroxyl ligands. The highest H(-) and F(-) affinities are found for BI(3) and the lowest ones for B(NH(2))(3). Within the boron trihalide series, the Lewis acidity increases monotonically with increasing atomic weight of the halogen, that is, BI(3) is a considerably stronger Lewis acid than BF(3). For the X(-) affinities in the BX(3), HBX(2), and H(2)BX series, the fluorides show the highest values, whereas the amino and mercapto compounds show the lowest ones. Hydride and fluoride affinities of the BH(3-n)X(n) compounds exhibit linear correlations with the proton affinity of X(-) for most X ligands. Reasons for the correlation are discussed. A detailed analysis of the individual contributions to the Lewis acidities of these substituted boranes shows that the dominant effect in the magnitude of the acidity is the strength of the BX(3)(-)-F bond. The main contributor to the relative differences in the Lewis acidities of BX(3) for X, a halogen, is the electron affinity of BX(3) with a secondary contribution from the distortion energy from planar to pyramidal BX(3). The B-F bond dissociation energy of X(3)B-F(-) and the distortion energy from pyramidal to tetrahedral BX(3)(-) are of less importance in determining the relative acidities. Because the electron affinity of BX(3) is strongly influenced by the charge density in the empty p(z) lowest unoccupied molecular orbital of boron, the amount of pi-back-donation from the halogen to boron is crucial and explains why the Lewis acidity of BF(3) is significantly lower than those of BX(3) with X = Cl, Br, and I.