Orbital Correlation Diagrams

Woodward and Hoffmann's landmark review, "The Conservation of Orbital Symmetry", Academic Press, 1970, provides one of the best introductions to the use of orbital correlation diagrams, and the following discussion is derived from this source. In applying orbital correlation analysis, care must be taken to recognize the pertinent σ and π molecular orbitals and their delocalization as required by the symmetry of the transition state. This must be done for both the bonding and antibonding orbitals, and when necessary for n (nonbonded pair) orbitals. The following principles should be observed:
1. Bonding orbitals undergoing significant change in the reaction, and their antibonding counterparts, should be identified. Normally, these are orbitals associated with the curved arrow description of a reaction.
2. If polyene moieties are involved, all the molecular orbitals of that conjugated system must be used.
3. Ignoring non-participating substituents and heteroatoms, the symmetry elements of the essential molecular skeleton must be identified. All orbitals not clearly symmetric or antisymmetric with respect to these molecular symmetry elements need to be mixed or delocalized until they become so. In this respect, the only important symmetry elements are those that bisect bonds that are made or broken in the reaction. Mixing is usually required for σ orbital analysis.
4. Each bonding and antibonding orbital included in the correlation is assigned one or more symmetry designations, S for symmetric, A for antisymmetric, depending on its fit with each characteristic symmetry element.
5. The molecular orbitals are then arrayed according to their energy (increasing vertically), and location on the reaction coordinate (horizontally). Correlations of reactant and product orbitals are drawn so that orbitals of like symmetry are connected. In making these correlations, lines connecting orbital pairs of opposite symmetry may cross, but lines connecting orbitals of the same symmetry may not.

To illustrate this method of analyzing pericyclic reactions, we shall use a suprafacial cycloaddition reaction. The essential elements of the [4+2] Diels-Alder reaction are shown at the top of the following diagram. As noted in principle 3 above, substituents on the diene and dienophile can be ignored. Consequently, only the three π-electron functions of the reactants need to be considered. Corresponding to these, there are three new bonding orbitals in the product, two σ-orbitals and one π-orbital, and these must also be incorporated in the correlation diagram. The symmetry of all participating orbitals must be evaluated before the diagram is constructed. Two symmetry properties of an isolated double bond were described earlier, and may be applied to the dienophile reactant. For the remaining orbitals a plane perpendicular to the molecular plane is used, as shown in green in the diagram.
The π- molecular orbitals of 1,3-butadiene were also described in an earlier section. Because of the geometrical requirements for cycloaddition, the s-trans conformation used in that example must be changed to the s-cis conformation. To illustrate, the two bonding π-orbitals of the s-cis diene are shown. The new σ-bonds in the product must be evaluated together (mixed), note principle 3 above. Two delocalized σ-bonding orbitals of different symmetry are thus produced.

The essential molecular orbitals for this suprafacial cycloaddition reaction may now be arrayed according to their energy and location on the reaction coordinate. This array will be displayed by clicking on the above diagram. Bonding orbitals are designated either σ or π, and antibonding orbitals by an asterisk. Mixing the σ-bonds leads to two energetically different bonding orbitals (σ₁ & σ₂). Likewise, there are two different antibonding orbitals (σ₃* & σ₄*).An approximate atomic orbital energy level is shown by the horizontal green dashed line, which separates the bonding and antibonding orbitals. A vertical light blue line separates reactant and product orbitals.
Symmetry designations for each orbital are determined relative to the perpendicular symmetry planes shown in the first diagram. Once these symmetries are noted, correlations of reactant and product orbitals may be drawn so that orbitals of like symmetry are connected. By clicking on the diagram a second time, these symmetry assignments and correlation lines will be added to the display. The six electrons that occupy the bonding orbitals of the reactant functions are shown as light blue paired arrows. Since these bonding reactant orbitals correlate with product bonding orbitals, this is considered to be a symmetry-allowed transformation.

It is constructive to compare the allowed [4_s + 2_s] cycloaddition with a [6_s + 2_s] analog. To make this reaction as favorable as possible the double bonds of the hexatriene reactant are placed in a seven membered ring, so that the ends of the conjugated π-electron system are located close together. The appropriate σ and π-orbitals are depicted in the following diagram, and by clicking on the diagram the mirror plane symmetries and correlation lines will be displayed. Clearly, correlation lines from the π₃ and π₄* orbitals of the reactant triene to the π₂ and π₃* orbitals of the product diene cross the bonding/antibonding transition (dotted green line). Consequently, this [6+2] suprafacial thermal cycloaddition is classified as symmetry forbidden.

If the cycloheptatriene is electronically excited by absorption of 260 nm light, one of the electrons in the π₃ bonding orbital is promoted to the π₄* antibonding orbital. Once this happens, as shown by clicking on the diagram a second time, the occupied excited state orbitals correlate with excited state product orbitals, and the photochemical cycloaddition is symmetry allowed.
This discussion of the [6+2] cycloaddition has assumed a suprafacial configuration, e.g. [6_s + 2_s]. The possibility of an alternative antarafacial cycloaddition should also be considered. This is illustrated in the following diagram, and requires a nearly right angle approach of the double bond reactant to the end carbons of a planar triene conformation. The methylene group that closes the seven membered ring must be removed to permit this orientation, as shown by the second equation. A mirror plane no longer provides adequate symmetry characterization of the participating molecular orbitals, so a C₂ rotational axis, two views of which are shown at the bottom of the diagram, is used instead. The alkene single bonds are colored green in these drawings.

A correlation analysis of the orbitals involved in this [6_a + 2_s] cycloaddition will be displayed here by clicking on the diagram. This mode of cycloaddition is seen to be a symmetry allowed thermal process. However, this is not an easily achieved reaction because the necessary coiled conformation of the triene is present in very low concentration. Since the [14+2] cycloaddition noted earlier has a heptaene reactant that is confined in a suitable orientation, the corresponding antarafacial cycloaddition is facilitated, and in fact takes place.

Orbital correlation diagrams for other kinds of pericyclic reactions may be constructed and used for evaluation. The Woodward & Hoffmann review provides examples, as does the excellent Imperial College site. Additional examples will not be supplied here, since the "Frontier Orbital" approach is more easily applied, in the opinion of the author.