Ab initio calculations (B3LYP/Lanl2DZ level of theory) were performed in this study to determine all the structural and catalytic zinc parameters required in order to study MMPs and their complexes with hydroxamate inhibitors by means of the AMBER force field. The parameters thus obtained were used in order to study the docking of some known MMPi (Batimastat, CGS 27023A and Prinomastat) and our previously described inhibitor a which had shown an inhibitory activity for MMP-1, and -2, with the aim of explaining the different selectivity. On this basis the two enantiomers (R)-b and (S)-b were designed and synthesized, as more potent MMP-2 inhibitors than our previously described inhibitor a. Between these two enantiomers the eutomer (R)-b proved to be 24.7 times and 15.3 times more potent than CGS 27023A and the parent compound a on MMP-2, maintaining a higher index of MMP-2/MMP-1 selectivity compared with CGS 27023A and the more potent inhibitor Prinomastat. The hydroxamate (R)-b can be considered as a progenitor of a new class of biphenylsulfonamido-based inhibitors that differ from compound a in the presence of an alkyl side chain on the C alpha atom, and show different potency and selectivity profiles on the two MMPs considered.