Quantum mechanical ab initio calculations with complete geometry optimization using relativistic effective core potentials for osmium are reported for the postulated intermediates of the base-catalyzed addition reaction of OsO4 (1) with olefins, using NH3 and ethylene as model compounds. The energy of the HOMO of 1 is substantially raised upon complexation with NH3. The four-membered cyclic species 3 suggested by Sharpless as an intermediate for the addition reaction is predicted to be a minimum on the potential energy hypersurface. Structure 3 is calculated to be 30.5 kcal mol(-1) (QCISD(T) + ZPE) higher in energy than the five-membered cyclic isomer 2. Both isomers are strongly stabilized by complexation with ammonia. The Os-NH3 binding energy is significantly higher in 2(NH3) and 3(NH3) than in 1(NH3), which explains the acceleration of the addition reaction in the presence of a base. The formation of 2(NH3) from 1(NH3) and ethylene is exothermic, while the formation of 3(NH3) is calculated to be slightly endothermic by about 5-10 kcal mol(-1). The energy calculations suggest that 3(NH3) is initially formed in a [2 + 2] concerted reaction with a nucleophilic and an electrophilic phase, followed by isomerization to 2(NH3). The complexes 1(2NH(3)) and 2(2NH(3)), which have two ammonia ligands, are also calculated as energy minimum structures. The asymmetric five-membered cyclic isomer 2a(2NH(3)), with one axial and one equatorial ammonia group, which is suggested by Corey as the initial reaction product, is another minimum on the potential energy surface. Structure 2a(2NH(3)) is predicted to be 24.2 kcal mol(-1) less stable than the isomer 2(2NH(3)). The calculations also indicate tile formation of dimeric structures as possible intermediates. Complex 1(NH3) may form the dimer 5(2NH(3)) with four idential Os-O bonds. The addition of two molecules of ethylene to 5(2NH(3)) yields the complex 4(2NH(3)). The geometry-optimized intermediates of the second reaction cycle with low enantioselectivity postulated by Sharpless are discussed. The comparison of the theoretically predicted geometries with the experimental structures show good agreement.