the Dewar-Zimmerman rules and the Woodward–Hoffmann rules. In the Dewar-Zimmerman treatment, the reaction proceeds through a 5-center, zero-node, 6-electron Huckel transition state for this particular molecular orbital diagram. However, each orbital can be randomly assigned a sign to arrive at the same result. In the Woodward–Hoffmann treatment, frontier molecular orbitals (FMO) of the 1,3-dipole and the dipolarophile overlap in the symmetry-allowed π4s + π2s manner. Such orbital overlap can be achieved in three ways: type I, II and III. The dominant pathway is the one which possesses the smallest HOMO-LUMO energy gap. Type I The dipole has a high-lying HOMO which overlaps with LUMO of the dipolarophile. A dipole of this class is referred to as a HOMO-controlled dipole or a nucleophilic dipole, which includes azomethine ylide, carbonyl ylide, nitrile ylide, azomethine imine, carbonyl imine and diazoalkane. These dipoles add to electrophilic alkenes readily. Electron-withdrawing groups (EWG) on the dipolarophile would accelerate the reaction by lowering the LUMO, while electron-donating groups (EDG) would decelerate the reaction by raising the HOMO. For example, the reactivity scale of diazomethane against a series of dipolarophiles is shown in the scheme below. Diazomethane reacts with the electron-poor ethyl acrylate more than a million times faster than the electron rich butyl vinyl ether. This type resembles the normal-electron-demand Diels-Alder reaction, in which the diene HOMO combines with the dienophile LUMO. Type II HOMO of the dipole can pair with LUMO of the dipolarophile; alternatively, HOMO of the dipolarophile can pair with LUMO of the dipole. This two-way interaction arises because the energy gap in either direction is similar. A dipole of this class is referred to as a HOMO-LUMO-controlled dipole or an ambiphilic dipole, which includes nitrile imide, nitrone, carbonyl oxide, nitrile oxide, and azide. Any substituent on the dipolarophile would accelerate the reaction by lowering the energy gap between the two interacting orbitals; i.e., an EWG would lower the LUMO while an EDG would raise the HOMO. For example, azides react with various electron-rich and electron-poor dipolarophile with similar reactivities (see reactivity scale below). Type III The dipole has a low-lying LUMO which overlaps with HOMO of the dipolarophile (indicated by red dashed lines in the diagram). A dipole of this class is referred to as a LUMO-controlled dipole or an electrophilic dipole, which includes nitrous oxide and ozone. EWGs on the dipolarophile decelerate the reaction, while EDGs accelerate the reaction. For example, ozone