Quantum mechanical ab initio calculations at the MP2/6-311++G** level of theory have been used to predict the binding energies and geometries of benzene-BX3 and ethenc-BX3 (X= H, F, Cl) complexes. Single point calculations at a much higher level of correlation (MP4) and larger basis sets (6-311++G(2df,p) + diffuse(d,p)) have also been carried out. The calculations reveal interesting trends in their binding energies and geometries. The binding energies indicate that all of them are weakly bound van der Waals complexes with the exception of the C2H4-BH3 complex. While complexes involving BF3 are the weakest (binding energies) in cases of both ethene and benzene, there is a reversal in the relative order of the binding energies as one moves from ethene to benzene. Thus C6H6-BCl3 is more tightly bound than C6H6-BH3 The geometry exhibited by the lowest energy conformer in cases of complexes involving benzene is different from those involving ethene. In contrast to most weak van der Waals interactions involving benzene, H-pi, and aromatic-aromatic, the boron atom lies directly over one of the benzene carbons. This observation has been explained by comparing the geometries obtained in complexes involving both benzene and ethene. More importantly, there is strong evidence of an unusual increase in the nucleophilicity of one of the benzene carbons in the lowest energy conformer of systems involving benzene, which implies that Lewis acid-aromatic ring interactions have an important role in electrophilic aromatic substitution reactions.