In general, the mechanism of organic reactions is believed to undergo the two-electron transfer pathways. However, the one-electron transfer could also exist in some biology and radical chemistry. Copper has surfaced as omnipresent catalysts in organic reactions because of their easily accessible Cu(0), Cu(I), Cu(II), and Cu(III) oxidation states. Thus, the mechanism of the Cu-catalyzed reactions could be quite complex with the change of the oxidation states of the metal centers in different reaction conditions and ligand spheres. Both the one-electron (radical) and two-electron processes could occur for the bond-breakage and bond-formation processes. In addition, the Cu(II), which could act both the promoter and terminal oxidant, capable of promoting a wide range of reactions initiated with the single-electron transfer (SET) process. Molecular oxygen is often used as a sink for the electrons to regenerate the copper(II) or to achieve the higher Cu(III) oxidation state for the two electron reductive elimination.
With the development of new synthetic methods, the need for mechanistic understanding of the reaction details is urgent. Thus, computational chemistry has been proved as the powerful tool to gain mechanistic information of these reactions. In this thesis, we have applied density functional theory (DFT) to perform a comprehensive computational study on the mechanism of the Cu catalyzed or co-catalyzed reactions. In particularly, we pay our attention on the single electron transfer process, together with the reactivity and selectivity. We expect that the study of these diverse processes will bring a better general understanding on the role of copper complexes in homogeneous catalysis.