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A '''cycloaddition''' is a [[pericyclic]] [[chemical reaction]], in which "two or more unsaturated molecules (or parts of the same molecule) combine with the formation of a cyclic adduct in which there is a net reduction of the bond multiplicity."<ref name=goldbook>{{cite web|last=International Union of Pure and Applied Chemistry (IUPAC)|title=Cycloaddition|url=http://goldbook.iupac.org/C01496.html|accessdate=26 February 2014}}</ref> The resulting reaction is a [[cyclization]] reaction. Many but not all cycloadditions are [[Concerted reaction|concerted]]. As a class of [[addition reaction]], cycloadditions permit carbon–carbon bond formation without the use of a [[nucleophile]] or [[electrophile]].
 
Cycloadditions can be described using two systems of notation. An older but still common notation is based on the size of linear arrangements of atoms in the reactants. It uses [[parentheses]]: (''i'' + ''j'' + …) where the variables are the numbers of linear atoms in each reactant. The product is a cycle of size (''i'' + ''j'' + …). In this system, the standard [[Diels-Alder reaction]] is a (4 + 2)-cycloaddition, the [[1,3-dipolar cycloaddition]] is a (3 + 2)-cycloaddition and [[cyclopropanation]] of a carbene with an alkene a (2 + 1)-cycloaddition.<ref name=goldbook />
 
A more recent, IUPAC-preferred notation, first introduced by Woodward and Hoffmann, uses [[square brackets]] to indicate the number of ''electrons'', rather than carbon atoms, involved in the formation of the product. In the [''i'' + ''j'' + …] notation, the standard Diels-Alder reaction is a [4 + 2]-cycloaddition, while the 1,3-dipolar cycloaddition is also a [4 + 2]-cycloaddition.<ref name=goldbook />
 
==Thermal cycloadditions and their stereochemistry==
Thermal cycloadditions are those cycloadditions where the reactants are in the ground electronic state. They usually have (4''n'' + 2) π electrons participating in the starting material, for some integer n. These reactions occur for reasons of [[orbital symmetry]] in a [[suprafacial]]-suprafacial or [[antarafacial]]-antarafacial manner (rare). There are a few examples of thermal cycloadditions which have 4''n'' π electrons (for example the [2 + 2] -cycloaddition). These proceed in a suprafacial-antarafacial sense, such as the dimerisation of [[ketene]], in which the [[orthogonal]] set of [[p orbital]]s allows the reaction to proceed via a crossed [[transition state]].
 
==Photochemical cycloadditions and their stereochemistry==