extended by Erden and Kaufmann, who reported the suprafacial-antarafacial cycloaddition of heptafulvalene with N-phenyltriazolinedione. Photochemical cycloadditions and their stereochemistry Cycloadditions in which 4n π electrons participate can also occur via 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. An example is the DeMayo reaction. Another example is shown below, the photochemical dimerization of cinnamic acid. The two trans alkenes react head-to-tail, and the isolated isomers are called truxillic acids. Supramolecular effects can influence these cycloadditions. The cycloaddition of trans-1,2-bis(4-pyridyl)ethene is directed by resorcinol in the solid-state in 100% yield. 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 Diels-Alder reactions The Diels-Alder reaction is perhaps the most important and commonly taught cycloaddition reaction. Formally it is a [4+2] cycloaddition reaction and exists in a huge range of forms, including the inverse electron-demand Diels–Alder reaction, Hexadehydro Diels-Alder reaction and the related alkyne trimerisation. The reaction can also be run in reverse in the retro-Diels–Alder reaction. Reactions involving heteroatoms are known; including the aza-Diels–Alder and Imine Diels–Alder reaction. Huisgen cycloadditions The Huisgen cycloaddition reaction is a (2+3)cycloaddition. Nitrone-olefin cycloaddition The Nitrone-olefin cycloaddition is a (3+2)cycloaddition. Cheletropic reactions Cheletropic reactions are a subclass of cycloadditions. The key distinguishing feature of cheletropic reactions is that on one of the reagents, both new bonds are being made to the same atom. The classic example is the reaction of sulfur dioxide with a diene. Other Other cycloaddition reactions exist: [4+3] cycloadditions, [6+4] cycloadditions, [2 + 2] photocycloadditions, metal-centered cycloaddition and [4+4] photocycloadditions Formal cycloadditions 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