Although the concerted [3 + 2] mechanism of osmium-catalyzed asymmetric dihydroxylation has been generally accepted, the unusual nonlinear Hammett relationship induced by amine-type ligands remains unexplained. To understand this, we carried out a density functional theory (DFT) study for the osmylation of substituted styrenes by the following: OsO 4 , OsO 4 − pyridine, OsO 4 −4-cyanopyridine, OsO 4 −4-pyrrolidinopyridine, and OsO 4 −quinuclidine. Calculations using the M06 functional successfully reproduce the experimentally observed nonlinear relationships. The transition states exhibit considerable singletdiradical character, which causes the nonlinear Hammett relationship. Regardless of the presence or absence of an amine-type ligand, an electron donation from styrene to OsO 4 is observed, indicating no mechanistic change. Calculations indicate that the electronic interaction between the amine-type ligand and styrene also influences the reaction rate.