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." The resulting reaction is a cyclization reaction. Many but not all cycloadditions are 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 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.A more recent, IUPAC-preferred notation 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, the 1,3-dipolar cycloaddition is [4 + 2].