Density functional calculations have been carried out to model the dimeric mechanism of the Sharpless epoxidation. A hexacoordinated system Ti(O-CH2-CH2-O)(O-O-Me) (O-CH2-CH=CH2)(H2O) (10) was first studied in detail. Transition structures were fully optimized with the nonlocal density functional approximation (BLYP) and the 3-21G basis set. Energies were further calculated with the HW3 basis set (equivalent to the 6-31G* basis set). The calculated activation energy is close to those observed experimentally. The titanium center in each transition structure has a distorted octahedral geometry. The Ti-O-O unit has a perfect eta(2) structure. The Ti-O-O approaches the C=C in a spiro fashion with the two C- - -O bonds forming to similar extents. There is a significant conformational preference for the peroxy alkoxy group to be away from the bridging oxygen. The allylic alcohol substrate strongly favors a conformation with the allylic C-O bond gauche to the Ti-O-water bond if the oxidant is tert-butyl peroxide. This conformational preference vanishes if the oxidant is methyl hydroperoxide. The tartrate ester groups were modeled with formyl groups and were found to favor equatorial conformation instead of axial conformation in the transition structure. A modified Sharpless dimeric model is developed which uniquely explains the importance of the bulky peroxide and ligand structure to the stereochemistry of the Sharpless epoxidation.