The reaction of carbene insertion into the C−H bond of indole catalyzed by the Rh 2 (HCO 2 ) 4 complex has been investigated in detail through DFT calculations. Results indicate that the indole can proceed via a nucleophilic attack at the carbene first to generate a carbonium ylide intermediate followed by a [1,4]-proton transfer to give a free enol. In this case, the final C−H insertion product can be obtained through the self-catalyzed [1,3]-proton shift of enol. Alternatively, the nucleophilic attack can also involve the concerted formations of C−O and C−C bonds to produce an oxocarbonium ylide intermediate. The subsequent [1,2]-proton shift catalyzed by a molecule of enol is also energetically feasible to give the C−H insertion product. It indicates the coexistence of two distinct pathways for the C−H insertion reaction of indole. However, the ratio between them can be regulated by the substituents on both carbenoid and indole. For instance, the enol pathway is always dominant for the phenyl-substituted carbenoid. However, the ratio of the two pathways becomes comparable for the ethylsubstituted carbenoid. The reason is mainly associated with the flexibility of the RhC bond of the carbenoid, which plays an important role in determining the approach of indole to the carbenoid. This finding is also useful to understand the reaction mechanisms for the related [3 + 2] annulation and the three-component reactions of indole.

The insertion of a carbenoid into an N−H bond of an amine cooperatively catalyzed by a dirhodium catalyst and a spiro chiral phosphoric acid has been investigated in detail using density functional theory methods. Calculations indicate that the reaction begins with the nucleophilic amine attacking at the carbenoid, forming a metal-associated ammonium ylide first followed by a rapid proton transfer to afford a metal-associated enamine intermediate. Subsequently, the enamine intermediate dissociates from the metal and yield a more stable sevenmembered-ring conformation via an intramolecular hydrogen-bond exchange. Formation of the enamine intermediate requires an overall barrier of 5.7 kcal/mol and is exergonic by 5.1 kcal/mol. Calculations demonstrated that, although the conversion of the achiral enamine into the N−H insertion product can be facilitated efficiently by the dirhodium catalyst through a two-step process, it can be compressed to a large extent. This is due to the more competitive decomposition of the diazoacetate catalyzed by the dirhodium catalyst, which can give a carbenoid for the next catalytic cycle. Meanwhile, formation of the carbenoid is considerably exergonic, which can promote the direct [1,3]-proton shift of enamine. However, in the presence of the spiro chiral phosphoric acid, the asymmetric proton induction of enamine is greatly favored, requiring an activation free energy of 6.0 kcal/mol to afford the major R product. This agrees well with the experimental observation.