Carbenes are desperate to find another pair of electrons with which to complete their valence shell of electrons. In this respect they are like carbocations. They are electrophilic but uncharged, which has consequences for the type of nucleophiles carbenes choose to react with. Carbenes attack nucleophiles by taking electrons from their HOMO, and for carbenes any HOMO will do, such as a lone pair, a C=C double bond, or even a C-H bond. These can be considered as insertion reactions. Click the links below to view different examples of insertion reactions:
Type of nucleophile
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Method of insertion
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P. de Frémont, N. Marion and S. P. Nolan, Coord. Chem. Rev., 2009, 253, 862–892.