Understanding the bonding in complexes X:BH3−nFn and X:BH3−nCln, for X=N2, HCN, LiCN, H2CNH, NF3, NH3 with n=0–3, is a challenging task. The trends in calculated binding energies cannot be explained in terms of any of the usual indexes, including π donation from the halogen lone pairs to the p(π) empty orbital on B, deformation energies, charge capacities, or LUMO energies, which are normally invoked to explain the higher Lewis acidity of BCl3 relative to BF3. The results of the high-level G3B3 ab initio calculations reported in this study suggest that the interaction energies of these complexes are determined by a combination of at least three factors. These include the decrease in the electron-accepting ability of B as a result of π donation by the halogen atom, the increase in the electron-acceptor capacity of B due to deformation of the acid, and the large increase in the deformation energy of the acid with increasing halogen substitution. The dominant effects are those derived from the electronic effects of acid deformation. Deformation not only has direct energetic consequences, which are reflected in the large differences between dissociation (D0) and interaction (Eint) energies, but also leads to an enhancement of the intrinsic acidities of BH3−nFn and BH3−nCln moieties by lowering the LUMO energies to very different extents, consistent with the frontier orbital model of chemical reactivity. Although this lowering depends on both the number and the nature of the halogen substituents, binding energies do not systematically increase or decrease as the number of halogen atoms increases.