4. Theoretical Explanation.

The original explanation of Woodward and Hoffmann involved generating a so called "orbital "correlation diagram" for the reaction under consideration, and then carrying out the reaction in such a manner that the symmetries of the reactant and product orbitals matched exactly. Such an approach, whilst theoretically rigorous, is not readily applicable to the majority of more complex reactions. Two much simpler methods have been outlined, the first of which will be expanded in more detail, whilst the second will only be described briefly;

In a practical sense, the first of these is the most easily remembered and applied. Although it may not seem obvious, this rule is actually derived from the original Woodward-Hoffmann approach.

Conservation of Orbital Symmetry.

Let us first define the symmetry properties of a 1s and a 2p orbital with respect to a plane of symmetry or an axis of symmetry as shown below;

One can take this one step further by considering the symmetry properties of molecular orbitals formed by the overlap of two or more atomic orbitals;

MOs formed from two overlapping sigma orbitals:


MOs formed from two overlapping p orbitals (sigma bonds):


MOs formed from two parallel overlapping p orbitals (p bonds):


We can now use these basic orbitals to construct the relevant molecular orbitals for two interconverting molecules, cyclobutene and butadiene, with the purpose of following how these two sets of orbitals change when one molecule is converted into the other. Note particularly that we need only construct the MOs explicitly involved in the reaction; most of the sigma framework remains unchanged and no orbitals derived from this need to be considered:





In order to interconvert cyclobutene and butadiene, the four MOs labelled Y1, Y2, Y3, Y4 must be converted into Ys, Yp, Yp*, Ys*. There are two stereochemically distinct ways in which this might be accomplished; conrotation;


disrotation;


This enables a correlation diagram for the reaction to be constructed, according to the following rules: no two orbitals of the same symmetry can cross during the reaction, whilst orbitals of different symmetry can cross. The favoured pathway is the one which results in a product of the same electronic excitation as the reactant. A pathway which results in the product in a higher electronic state than the reactant is said to be "forbidden".


Whilst this rule is normally followed fairly well for ground states, it can be overturned when for example steric or geometrical strain in the "allowed" pathway promotes the "forbidden" route. The situation is actually more complex for photochemical reactions, and much recent evidence suggests that the Woodward-Hoffmann rules are not always followed see note 1. These correlation diagrams can be generalised for any electrocyclic reaction with appropriate symmetry. However, correlation diagrams are less readily applied for reactions with no symmetry. Dewar and Zimmerman independently noticed that the 'topological' properties of these correlation diagrams are very similar to those obtained using eg Huckel theory for aromatic molecules. For example, the diagram for the electrocyclic conversion of hexatriene to cyclohexadiene is remarkably similar at the transition state to the ground state orbitals of benzene;


Transition State Aromaticity.

The suprafacial mode orbital correlation diagram for hexatriene can be generalised by reference to benzene. The benzene molecule has the same 'suprafacial' topology, by which we mean that the p electron density in benzene is continuous along the top or bottom face of the molecule. If the transition state for the pericyclic reaction has the same topology, it is said to resemble 'HUCKEL' topology, after E. Huckel who first indicated why a molecule such as benzene should be especially stable.

Thus a 'suprafacial' or 'Huckel' transition state in a pericyclic reaction is particularly favourable if the number of cyclically conjugated p electrons in the transition state equals 4n+2 (the Huckel rule, where n = 0, 1, 2 etc).

Huckel was also able to show that if a cyclic conjugated p system is irradiated with light so that it goes into the first 'excited' electronic state, it is especially stable if the number of cyclically conjugated electrons equals 4n Hence photochemically activated pericyclic reactions will proceed suprafacially via a Huckel transition state if the electron count corresponds to 4n. The antarafacial mode described above has no counterpart in a stable aromatic molecule, as benzene did for the suprafacial mode. An antarafacial mode could be formed by taking benzene and giving the p system a 180š twist. If this is done, the resultant 'twisted' benzene has been termed 'Mobius Benzene'.


Here the electron density continuity passes through the plane of the molecule, from the top face through to the bottom face. Such a MOBIUS system it turns out is especially stable if it contains 4n electrons (or 4n+2 if photochemically excited). These four conditions are most easily summarised as follows;

The Frontier Orbital Method (The following is optional and is intended for use in tutorials). This involves using the principles of quantum mechanics to generate the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) for the reactant(s). The formation of the new sigma bond must occur by appropriate overlap of the nodes of these orbitals. If only one sigma bond is forming, as in an electrocyclic reaction, then only the overlap of the HOMO of the reactant is considered. Such overlap can occur in one of two fundamental ways; The suprafacial mode involves each component of the new sigma bond being formed from the SAME face of the reactant p system.

The antarafacial mode involves a 'twisting' of the orbitals so that the two components of the new s bond come from OPPOSITE faces of the reactant p system. If two or more sigma bonds form during the reaction, as in cycloaddition reactions, then the overlap of the HOMO of one reactant with the LUMO of the second reactant must be considered. For simple systems, the form of the HOMO and LUMO is not difficult to remember. For more complex systems, explicit calculations have to be carried out and the Frontier Orbital method becomes more difficult to apply. The advantage of the "FMO" method is that it can be expressed quantitatively in terms of the magnitude of the coefficients involved, and can hence be used to predict regioselectivity etc.

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