In organic chemistry, a pericyclic reaction is the type of organic reaction wherein the transition state of the molecule has a cyclic geometry, the reaction progresses in a concerted fashion, and the bond orbitals involved in the reaction overlap in a continuous cycle at the transition state. Pericyclic reactions stand in contrast to linear reactions, encompassing most organic transformations and proceeding through an acyclic transition state, on the one hand and coarctate reactions, which proceed through a doubly cyclic, concerted transition state on the other hand. Pericyclic reactions are usually rearrangement or addition reactions. The major classes of pericyclic reactions are given in the table below (the three most important classes are shown in bold). Ene reactions and cheletropic reactions are often classed as group transfer reactions and cycloadditions/cycloeliminations, respectively, while dyotropic reactions and group transfer reactions (if ene reactions are excluded) are rarely encountered. In general, these are considered to be equilibrium processes, although it is possible to push the reaction in one direction by designing a reaction by which the product is at a significantly lower energy level; this is due to a unimolecular interpretation of Le Chatelier's principle. There is thus a set of "retro" pericyclic reactions. Mechanism of pericyclic reaction By definition, pericyclic reactions proceed through a concerted mechanism involving a single, cyclic transition state. Because of this, prior to a systematic understanding of pericyclic processes through the principle of orbital symmetry conservation, they were facetiously referred to as 'no-mechanism reactions'. However, reactions for which pericyclic mechanisms can be drawn often have related stepwise mechanisms proceeding through radical or dipolar intermediates that are also viable. Some classes of pericyclic reactions, such as the [2+2] ketene cycloaddition reactions, can be 'controversial' because their mechanism is sometimes not definitively known to be concerted (or may depend on the reactive system). Moreover, pericyclic reactions also often have metal-catalyzed analogs, although usually these are also not technically pericyclic, since they proceed via metal-stabilized intermediates, and therefore are not concerted. Despite these caveats, the theoretical understanding of pericyclic reactions is probably among the most sophisticated and well-developed in all of organic chemistry. The understanding of how orbitals interact in the course of a pericyclic process has led to the Woodward–Hoffmann rules, a simple set of criteria to predict whether a pericyclic mechanism for a reaction is likely or favorable. For instance, these rules predict that the [4+2] cycloaddition of butadiene and