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Woodward Hoffmann Rules

The Woodward-Hoffmann rules, are a set of rules in organic chemistry that predict the barrier heights of pericyclic reactions based on the conservation of orbital symmetry. The theory was devised by Robert Burns Woodward and Roald Hoffmann in 1969. Roald Hoffmann was awarded the Nobel prize in chemistry in 1981. The Woodward-Hoffmann rules provide an approach to explain differences between thermal and photochemical electrocyclic reactions by considering the orbital symmetry. These rules can be applied to concerted reactions involving π orbitals, electro-cyclic reactions, cycloadditions, sigmatropic and group transfer reactions. They can not be applied to reactions proceeding through a radical mechanism and reactive intermediates. Concerted reactions involving π orbitals take place readily when the orbital symmetry is maintained during the reaction process. With this, "Orbital symmetry is conserved in concerted reactions".[1]


 Figure 1: Parallel approach of two ethylene molecules and energy levels of the orbitals.[1]

 Figure 1 shows the parallel maximum approach of two ethylene molecules with four π orbitals during reaction. The four π orbitals will be transformed into four σ orbitals of cyclobutane. In the reaction of two ethylene molecules there are existing three mirror planes 1, 2 and 3 for the initial and final states (see Figure 1). In the correlation diagram π orbitals, symmetric to mirror planes 1 and 2, are noted by SS. Orbitals, that are antisymmetric to the mirror planes, are abbreviated as AA and orbitals, that are symmetric to mirror plane 1 but antisymmetric to mirror plane 2, are noted as SA and vice versa (see Figures 2 and 1). The symmetry behavior for symmetry-oriented orbital correlation diagrams for the initial state and final state as well as the symmetry behavior for mirror planes 1 and 2 are shown in Figure 2.


Figure 2: Complete correlation diagram for the formation of cyclobutane from two molecules of ethylene.[1]

 The reaction is impossible from the two ground-state ethylene molecules in a concerted reaction while maintaining the orbital symmetry. Hence, the reaction can only take place to give ground-state cyclobutane through a transition state by activation of the molecules. The required energy corresponds to the activation energy. Photochemical excitation of an electron from a π orbital to the lowest anti-bonding orbital leads to a more favorable overall energy balance. Reaction of the ground state are forbidden by symmetry. Despite this, reactions of the excited state are symmetry allowed. With these considerations, the [2+2]-cycloadditions are thermally prohibited and photochemically allowed (allowed in excited state), [4+2]-cycloadditions (Diels-Alder Reaction) are thermally allowed and photochemically prohibited (allowed in ground state). The general rules for this type of reaction system can be derived by the number of π orbitals involved in the reaction. The number of π orbitals are given as m and n. The selection rules for [m+n] cycloadditions are shown in Table 1. A suprafacail process is a process where the changing bonds lie on the same face. Consequently, for antrafacial the formed or broken bonds lie on different faces (see Figure 3).

Table 1: Selection rules for [m+n] cycloadditions.[1]woodwardhoffmannT1



Figure 3: Orientations of suprafacial and antrafacial processes.[1]


  1. WOODWARD, R. B.; HOFFMANN, R.: The Conservation of Orbital Symmetrya, Angewandte Chemie International Edition in English, 1969-November, 8 (11), 781–853, DOI:10.1002/anie.196907811.


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