The B3LYP density functional studies on the mechanism of the S(N)2-substitution reaction of methyl halides and epoxides with lithium organocuprates(I), (CH3)(2)CuLi . LiCl and [(CH3)(2)CuLi](2), revealed the energetics and the geometries of important transition states and intermediates along the reaction pathway, In the absence of solvent coordination on the copper atom, the reaction takes place in a single step through rate determining cleavage of the C-X bond (X = leaving group) involving nucleophilic participation of the CH3-Cu bond composed of the copper 3d(z)(2) orbital and carbon 2s+2p orbitals. Consideration of solvent polarity and coordination of an explicit (CH3)(2)O molecule to a lithium atom in the cuprate cluster lowers the activation energy to <20 kcal/mol, which is a reasonable value for the reaction taking place below 0 degrees C. Solvation of the copper atom does not change much the geometry or the energy of the transition state, but modifies the pathway afterward. The origin of the "trans-diaxial opening of cyclohexene oxide" has been ascribed to the inverted stereochemistry of the electrophilic carbon atom in the rate-determining step of the reaction, Coordination of BF3 lowers the activation energy of the nucleophilic ring opening of epoxide as much as to 9.2 kcal/mol. The origin of the acceleration of epoxide ring opening by BF3 is attributed to the cooperative activation of borane and lithium atoms on the epoxide oxygen atom.