which has the largest coefficients on the carbon proximal to the carbonyl group of the carbonyl ylide and on the methyl propiolate terminal alkyne carbon. The reaction with methyl propargyl ether affords one regioisomer resulting from the HOMOdipolarophile-LUMOdipole interaction, which has largest coefficients on the carbon distal to the carbonyl group of the carbonyl ylide and on the methyl propargyl ether terminal alkyne carbon. Regioselectivities of 1,3-dipolar cycloaddition reactions mediated by metal catalysis of diazocarbonyl compounds may also be influenced by the metal through formation of stable metallocarbenes. Stabilization of the metallocarbene, via metal enolate-type interactions, will prevent the formation of carbonyl ylides, resulting in a direct reaction between the metallocarbene dipole and an alkynyl or alkenyl dipolarophile (see image of The dirhodium(II)tetracarboxylate metallocarbene stabilized by πC-Rh→πC=O hyperconjugation.). In this situation, the metal ligands will influence the regioselectivity and stereoselectivity of the 1,3-dipolar cycloaddition reaction. Stereoselectivity and asymmetric induction of the 1,3-dipolar cycloaddition reaction mediated by metal catalysis of diazocarbonyl compounds The stereoselectivity of 1,3-dipolar cycloaddition reactions between carbonyl ylide dipoles and alkenyl dipolarophiles has also been closely examined. For alkynyl dipolarophiles, stereoselectivity is not an issue as relatively planar sp2 carbons are formed, while regioselectivity must be considered (see image of the Products of the 1,3-Dipolar Cycloaddition Reaction Between Carbonyl Ylide Dipoles and Alkenyl or Alkynyl Dipolarophiles). However, for alkenyl dipolarophiles, both regioselectivity and stereoselectivity must be considered as sp3 carbons are generated in the product species. 1,3-dipolar cycloaddition reactions between carbonyl ylide dipoles and alkenyl dipolarophiles can generate diastereomeric products. The exo product is characterized with dipolarophile substituents being cis to the ether bridge of the oxacycle. The endo product is characterized with the dipolarophile substituents being trans to the ether bridge of the oxacycle. Both products can be generated through pericyclic transitions states involving concerted synchronous or concerted asynchronous processes. One early example conferred stereoselectivity in terms of endo and exo products with metal catalysts and Lewis acids. Reactions with just the metal catalyst Rh2(OAc)4 prefer the exo product while reactions with the additional Lewis acid Yb(OTf)3 prefer the endo product. The endo selectivity observed for Lewis acid cycloaddition reactions is attributed to the optimized orbital overlap of the carbonyl π systems between the dipolarophile coordinated by Yb(Otf)3 (LUMO) and the dipole (HOMO). After many investigations, two primary approaches for influencing the stereoselectivity of carbonyl ylide cycloadditions have been developed that exploit the chirality of metal catalysts