Woodward Hoffmann Rules

The Woodward-Hoffmann (W-H) rules are qualitative statements regarding relative activation energies for two possible modes of reaction, which may have different stere-ochemical outcomes.18 For simple systems, the rules may be derived from a conservation of orbital symmetry, but they may also be generalized by an FMO treatment with conservation of bonding. Let us illustrate the Woodward-Hoffmann rules with a couple of examples, the preference of the 4 + 2 over the 2 + 2 product for the reaction of butadiene with ethylene, and the ring-closure of butadiene to cyclobutene.

A face-to-face reaction of two n-orbitals to form a cyclobutane involves the formation of two new C—C o-bonds. The reaction may be imagined to occur under the preservation of symmetry, in this case C2v, i.e. concerted (one-step, no intermediates) and synchronous (both bonds are formed at the same rate).

Figure 15.11 Reaction of two ethylenes to form cyclobutane under C2v symmetry

Both the reactant and product orbitals may be classified according to their behaviour with respect to the two mirror planes present, being either Symmetric (no change of sign) or Antisymmetric (change of sign). The energetic ordering of the orbitals follows from a straightforward consideration of the bonding/antibonding properties. Since orbitals of different symmetries cannot mix, conservation of orbital symmetry establishes the correlation between the reactant and product sides.

The orbital correlation diagram shown in Figure 15.12 indicates that an initial electron configuration of (n1 + n2)2(n1 - n2)2 (ground state for the reactant) will end up as a doubly excited configuration (o1 + o2)2(o*1 + o*2)2 for the cyclobutane product. This by itself indicates that the reaction should be substantially uphill in terms of energy. It may be put on a more sound theoretical footing by looking at the state correlation diagram in Figure 15.13.

Woodward Hoffmann Correlation Diagram

The ground state wave function for the whole system (all four active and the remaining core and valence electrons) is symmetric with respect to both mirror planes, while the first excited state is antisymmetric. The intended correlation is indicated with dashed lines, the lowest energy configuration for the reactant correlates with a doubly excited configuration of the product, and vice versa. Since these configurations have the same symmetry (SS), an avoided crossing is introduced, leading to a significant barrier for the reaction. The presence of a reaction barrier due to symmetry conservation for the orbitals makes this a Woodward-Hoffmann forbidden reaction. The

Figure 15.13 State correlation diagram for cyclobutane formation

Figure 15.13 State correlation diagram for cyclobutane formation reaction for the excited state, however, does not encounter a barrier and is therefore denoted an allowed reaction.

The same conclusion may be reached directly from a consideration of the frontier orbitals. Formation of two new o-bonds requires interaction of the HOMO of one fragment with the LUMO on the other. When the interaction is between orbital lobes on the same side (Suprafacial) of each fragment (2s + 2s), this leads to the picture shown in Figure 15.14.

Figure 15.14 2s + 2s HOMO-LUMO interaction leading to two new o-bonds

It is clearly seen that the HOMO-LUMO interaction leads to the formation of one bonding and one antibonding orbital, i.e. this is not a favourable interaction. The FMO approach also suggests that the 2 + 2 reaction may be possible if it could occur with bond formation on opposite sides (Antarafacial) for one of the fragments.

Although the 2s + 2a reaction is Woodward-Hoffmann allowed, it is sterically so hindered that thermal 2 + 2 reactions in general are not observed. Photochemical 2 + 2 reactions, however, are well known.19

The 4s + 2s reaction of a diene with a double bond can in a concerted and synchronous reaction be envisioned to occur with the preservation of Cs symmetry. The corresponding orbital correlation diagram is shown in Figure 15.17. In this case the orbital correlation diagram shows that the lowest energy electron configuration in the reactant, (n1)2(n2)2(n3)2, correlates directly with the lowest energy

Figure 15.15 2s + 2a HOMO-LUMO interaction leading to two new o-bonds
Figure 15.16 Reaction of butadiene and ethylene to form cyclohexene under Cs symmetry

electron configuration in the product, (o1)2(o2)2(n1)2. This is also shown by the corresponding state correlation diagram, Figure 15.18.

In this case, there is no energetic barrier due to unfavourable orbital correlation, although other factors lead to an activation energy larger than zero. The direct correlation of ground state configurations for the reactant and product indicates a (relatively) easy reaction, and is an allowed reaction. The lowest excited state for the reactant, however, does not correlate with the lowest excited product state, and the photochemical reaction is consequently forbidden.

The FMO approach again indicates that the 4s + 2s interaction should lead directly to formation of two new bonding o-bonds, i.e. this is an allowed reaction.

The preference for a concerted 4s + 2s reaction is experimentally supported by observations that show that the stereochemistry of the diene and dieneophile is carried over to the product, for example a trans,trans-1,4-disubstituted diene results in the two substituents ending up in a cis configuration in the cyclohexene product.20

The ring-closure of a diene to a cyclobutene can occur with rotation of the two termini in the same (Conrotatory) or opposite (Disrotatory) directions. For suitably substituted compounds, these two reaction modes lead to products with different stereochemistry.

The disrotatory path has Cs symmetry during the whole reaction, while the conrotatory mode preserve C2 symmetry. The orbital correlation diagrams for the two possible paths are shown as Figures 15.21 and 15.22.

It is seen that only the conrotatory path directly connects the reactant and product ground state configurations. Taking into account also the excited states leads to the state correlation diagram in Figure 15.23.

The conrotatory path is Woodward-Hoffmann allowed for a thermal reaction, while the corresponding photochemical reaction is predicted to occur in a disrotatory fashion.

Figure 15.17 Orbital correlation diagram for cyclohexene formation

Figure 15.18 State correlation diagram for cyclohexene formation

Figure 15.19 4s + 2s HOMO-LUMO interaction leading to two new o-bonds
Figure 15.20 Two possible modes of closing a diene to cyclobutene
Butadiene Cyclobutene Diagram
Figure 15.21 Orbital correlation diagram for the disrotatory ring-closure of butadiene
Conrotatory Motion Butadiene
Figure 15.22 Orbital correlation diagram for the conrotatory ring-closure of butadiene

Disrotatory

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