of 1,3-dipoles share four electrons in the π-system over three atoms. The allyl-type is bent whereas the propargyl/allenyl-type is linear in geometry. 1,3-Dipoles containing higher-row elements such as sulfur or phosphorus are also known, but are utilized less routinely. Resonance structures can be drawn to delocalize both negative and positive charges onto any terminus of a 1,3-dipole (see the scheme below). A more accurate method to describe the electronic distribution on a 1,3-dipole is to assign the major resonance contributor based on experimental or theoretical data, such as dipole moment measurements or computations. For example, diazomethane bears the largest negative character at the terminal nitrogen atom, while hydrazoic acid bears the largest negative character at the internal nitrogen atom. Consequently, this ambivalence means that the ends of a 1,3-dipole can be treated as both nucleophilic and electrophilic at the same time. The extent of nucleophilicity and electrophilicity at each end can be evaluated using the frontier molecular orbitals, which can be obtained computationally. In general, the atom that carries the largest orbital coefficient in the HOMO acts as the nucleophile, whereas that in the LUMO acts as the electrophile. The most nucleophilic atom is usually, but not always, the most electron-rich atom. In 1,3-dipolar cycloadditions, identity of the dipole-dipolarophile pair determines whether the HOMO or the LUMO character of the 1,3-dipole will dominate (see discussion on frontier molecular orbitals below). Dipolarophile The most commonly used dipolarophiles are alkenes and alkynes. Heteroatom-containing dipolarophiles such as carbonyls and imines can also undergo 1,3-dipolar cycloaddition. Other examples of dipolarophiles include fullerenes and nanotubes, which can undergo 1,3-dipolar cycloaddition with azomethine ylide in the Prato reaction. Solvent effects 1,3-Dipolar cycloadditions experience very little solvent effect because both the reactants and the transition states are generally non-polar. For example, the rate of reaction between phenyl diazomethane and ethyl acrylate or norbornene (see scheme below) changes only slightly upon varying solvents from cyclohexane to methanol. Lack of solvent effects in 1,3-dipolar cycloaddition is clearly demonstrated in the reaction between enamines and dimethyl diazomalonate (see scheme below). The polar reaction, N-cyclopentenyl pyrrolidine nucleophilic addition to the diazo compound, proceeds 1,500 times faster in polar DMSO than in non-polar decalin. On the other hand, a close analog of this reaction, N-cyclohexenyl pyrrolidine 1,3-dipolar cycloaddition to dimethyl diazomalonate, is sped up only 41-fold in DMSO relative to decalin. Frontier molecular orbital theory 1,3-Dipolar cycloadditions are pericyclic reactions, which obey