The B3LYP density functional studies on the dirhodium tetracarboxylate-catalyzed C-H bond activation/C-C bond formation reaction of a diazo compound with an alkane revealed the energetics and the geometry of important intermediates and transition states in the catalytic cycle. The reaction is initiated by complexation between the rhodium catalyst and the diazo compound. Driven by the back-donation from the Rh 4d(xz) orbital to the C-N sigma*-orbital, nitrogen extrusion takes place to afford a rhodium-carbene complex. The carbene carbon of the complex is strongly electrophilic because of its vacant 2p orbital. The C-H activation/C-C formation proceeds in a single step through a three-centered hydride transfer-like transition state with a small activation energy. Only one of the two rhodium atoms works as a carbene binding site throughout the reaction, and the other rhodium atom assists the C-H insertion reaction. The second Rh atom acts as a mobile ligand for the first one to enhance the electrophilicity of the carbene moiety and to facilitate the cleavage of the rhodium-carbon bond. The calculations reproduce experimental data including the activation enthalpy of the nitrogen extrusion, the kinetic isotope effect of the C-H insertion, and the reactivity order of the C-H bond.