In organic chemistry, a cycloaddition is a 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 and thus pericyclic. Nonconcerted cycloadditions are not pericyclic. 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: where the variables are the numbers of linear atoms in each reactant. The product is a cycle of size . 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. 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. Thermal cycloadditions and their stereochemistry Thermal cycloadditions are those cycloadditions where the reactants are in the ground electronic state. They usually have (4n + 2) π electrons participating in the starting material, for some integer n. These reactions occur for reasons of orbital symmetry in a suprafacial-suprafacial (syn/syn stereochemistry) in most cases. Very few examples of antarafacial-antarafacial (anti/anti stereochemistry) reactions have also been reported. There are a few examples of thermal cycloadditions which have 4n π electrons (for example the [2 + 2]-cycloaddition). These proceed in a suprafacial-antarafacial sense (syn/anti stereochemistry), such as the cycloaddition reactions of ketene and allene derivatives, in which the orthogonal set of p orbitals allows the reaction to proceed via a crossed transition state, although the analysis of these reactions as [π2s + π2a] is controversial. Strained alkenes like trans-cycloheptene derivatives have also been reported to react in an antarafacial manner in [2 + 2]-cycloaddition reactions. Doering (in a personal communication to Woodward) discovered that heptafulvalene and tetracyanoethylene can react in a suprafacial-antarafacial [14 + 2]-cycloaddition. This result was later confirmed and