investigated the mechanism to expand the scope of synthetic molecules with respect to regio- and stereo-selectivity. However, due to the high turn over frequencies of these reactions, the intermediates and mechanism remains elusive. The generally accepted mechanism, developed by characterization of stable ruthenium-carbenoid complexes and rhodium metallocarbenes, involves an initial formation of a metal-carbenoid complex from the diazo compound. Elimination of nitrogen gas then affords a metallocarbene. An intramolecular nucleophilic attack by the carbonyl oxygen regenerates the metal catalyst and forms the carbonyl ylide. The carbonyl ylide can then react with an alkene or alkyne, such as dimethyl acetylenedicarboxylate (DMAD) to generate the oxacycle. However, it is uncertain whether the metallocarbene intermediate generates the carbonyl ylide. In some cases, metallocarbenes can also react directly with dipolarophiles. In these cases, the metallocarbene, such as the dirhodium(II)tetracarboxylate carbene, is stabilized through hyperconjugative metal enolate-type interactions. Subsequent 1,3-dipolar cycloaddition reaction occurs through a transient metal-complexed carbonyl ylide. Therefore, a persistent metallocarbene can influence the stereoselectivity and regioselectivity of the 1,3-dipolar cycloaddition reaction based on the stereochemistry and size of the metal ligands. The mechanism of the 1,3-dipolar cycloaddition reaction between the carbonyl ylide dipole and alkynyl or alkenyl dipolarophiles has been extensively investigated with respect to regioselectivity and stereoselectivity. As symmetric dipolarophiles have one orientation for cycloaddition, only one regioisomer, but multiple stereoisomers can be obtained. On the contrary, unsymmetric dipolarophiles can have multiple regioisomers and stereoisomers. These regioisomers and stereoisomers may be predicted based on frontier molecular orbital (FMO) theory, steric interactions, and stereoelectronic interactions. Regioselectivity of the 1,3-dipolar cycloaddition reaction mediated by metal catalysis of diazocarbonyl compounds Regioselectivity of 1,3-dipolar cycloaddition reactions between carbonyl ylide dipoles and alkynyl or alkenyl dipolarophiles is essential for generating molecules with defined regiochemistry. FMO theory and analysis of the HOMO-LUMO energy gaps between the dipole and dipolarophile can rationalize and predict the regioselectivity of experimental outcomes. The HOMOs and LUMOs can belong to either the dipole or dipolarophile, for which HOMOdipole-LUMOdipolarophile or HOMOdipolarophile-LUMOdipole interactions can exist. Overlap of the orbitals with the largest coefficients can ultimately rationalize and predict results. The archetypal regioselectivity of the 1,3-dipolar cycloaddition reaction mediated by carbonyl ylide dipoles has been examined by Padwa and coworkers. Using a Rh2(OAc)4 catalyst in benzene, diazodione underwent a 1,3-dipolar cycloaddition reaction with methyl propiolate and methyl propargyl ether. The reaction with methyl propiolate affords two regioisomers with the major resulting from the HOMOdipole-LUMOdipolarophile interaction,