A Cycloaddition is a pericyclic reaction in which the net result is loss of two pi bonds and gain of two sigma bonds.
Two major topics of cycloaddition reactions are
Cycloadditions are usually described by the backbone size of the participants. This would make the Diels-Alder a (4 + 2) cycloaddition, and the 1,3-dipolar cycloaddition a (3 + 2) cycloaddition. This type of reaction is non-polar addition reaction.
Thermal cycloadditions usually have 4n + 2 pi electrons participating in the starting material. These occur, for reasons of orbital symmetry , in a suprafacial-suprafacial or antarafacial-antarfacial manner (rare). There are a few examples of thermal cycloadditions which have 4n pi electrons; (for example the (2 + 2) cycloaddition), these proceed in a suprafacial-antarafacial sense, such as the dimerisation of ketene, in which the orthognal set of p orbitals allows the reaction to proceed via a crossed transition state.
Cycloadditions in which 4n pi electrons participate can also occur as a result of photochemical activation. Here, one component has an electron promoted from the HOMO (pi bonding) to the LUMO (pi antibonding). Orbital symmetry is then such that the reaction can proceed in a suprafacial-suprafacial manner.