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 π 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 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 orbitals allows the reaction to proceed via a crossed transition state.
Cycloadditions in which 4n π electrons participate can also occur as a result of photochemical activation. Here, one component has an electron promoted from the HOMO (π bonding) to the LUMO (π* antibonding). Orbital symmetry is then such that the reaction can proceed in a suprafacial-suprafacial manner. One example is the photochemical dimerization of cinnamic acid  :
Note that not all photochemical (2+2) cyclizations are cycloadditions; some are known to operate by radical mechanisms.
Some cycloadditions instead of π bonds operate through strained cyclopropane rings; as these have significant π character. For example, an analog for the diels-alder reaction is the quadricyclane-DMAD reaction:
In the (i+j+...) cycloaddition notation i and j refer to the number of atoms involved in the cycloaddition. In this notation a Diels-Alder reaction is a (4+2)cycloaddition and a 1,3-dipolar addition such as the first step in ozonolysis is a (3+2)cycloaddition. The IUPAC preferred notation however, with [i+j+...] takes electrons into account and not atoms. In this notation the DA reaction and the dipolar reaction both become a [4+2]cycloaddition. The reaction between norbornadiene and an activated alkyne is a [2+2+2]cycloaddition.
Types of cycloaddition
Two major cycloaddition reactions are :
Cycloadditions often have metal-catalyzed and stepwise radical analogs, however these are not strictly speaking pericyclic reactions. When in a cycloaddition charged or radical intermediates are involved or when the cycloaddition result is obtained in a series of reaction steps they are sometimes called formal cycloadditions to make the distinction with true pericyclic cycloadditions.
- IUPAC Gold Book definition
- An Exploration of a Photochemical Pericyclic Reaction Using NMR Data Sara M. Hein Journal of Chemical Education Vol. 83 No. 6 June 940 2006
- The two trans alkenes react head-to-tail and the isolated isomer is called truxillic acid
- Stereoselective Intermolecular Formal [3+3] Cycloaddition Reaction of Cyclic Enamines and Enones Mohammad Movassaghi, Prof. Dr. *, Bin Chen, Dr. Angew. Chem. Int. Ed. 2007, 46, 565 –568 doi:10.1002/anie.200603302