ethylene under thermal conditions is likely a pericyclic process, while the [2+2] cycloaddition of two ethylene molecules is not. These are consistent with experimental data, supporting an ordered, concerted transition state for the former and a multistep radical process for the latter. Several equivalent approaches, outlined below, lead to the same predictions. The aromatic transition state theory assumes that the minimum energy transition state for a pericyclic process is aromatic, with the choice of reaction topology determined by the number of electrons involved. For reactions involving (4n + 2)-electron systems (2, 6, 10, ... electrons; odd number of electron pairs), Hückel topology transition states are proposed, in which the reactive portion of the reacting molecule or molecules have orbitals interacting in a continuous cycle with an even number of nodes. In 4n-electron systems (4, 8, 12, ... electrons; even number of electron pairs) Möbius topology transition states are proposed, in which the reacting molecules have orbitals interacting in a twisted continuous cycle with an odd number of nodes. The corresponding (4n + 2)-electron Möbius and 4n-electron Hückel transition states are antiaromatic and are thus strongly disfavored. Aromatic transition state theory results in a particularly simply statement of the generalized Woodward–Hoffmann rules: A pericyclic reaction involving an odd number of electron pairs will proceed through a Hückel transition state (even number of antarafacial components in Woodward–Hoffmann terminology), while a pericyclic reaction involving an even number of electron pairs will proceed through a Möbius transition state (odd number of antarafacial components). Equivalently, pericyclic reactions have been analyzed with correlation diagrams, which track the evolution of the molecular orbitals (known as 'correlating' the molecular orbitals) of the reacting molecules as they progress from reactants to products via a transition state, based on their symmetry properties. Reactions are favorable ('allowed') if the ground state of the reactants correlate with the ground state of the products, while they are unfavorable ('forbidden') if the ground state of the reactants correlate with an excited state of the products. This idea is known as the conservation of orbital symmetry. Consideration of the interactions of the highest occupied and lowest unoccupied molecular orbitals (frontier orbital analysis) is another approach to analyzing the transition state of a pericyclic reaction. Arrow-pushing for pericyclic reactions The arrow-pushing convention for pericyclic reactions has a somewhat different meaning compared to polar (and radical) reactions. For pericyclic reactions, there is often no obvious movement of