We wish to develop a notation that will permit us to state a generalized selection rule summarizing the conclusions of the pericyclic theory.
Local Symmetry and Interaction Topology
We have taken care to emphasize in the discussion that the important symmetry is the local symmetry of the part of the molecule actually involved in the reaction. We have already given in Section 11.1 a justification for this course; another example is appropriate here, now that we have gained an appreciation of the role of orbital symmetry in pericyclic reactions. In Equation below,
the substitution of a methyl for one hydrogen on the diene 11 destroys the symmetry. Now a mirror plane reflection (for disrotatory closure) or twofold rotation axis (for conrotatory closure) is no longer a symmetry operation. No symmetry element remains to provide a distinction among different orbitals.22 Yet we know fromthe success of ? electron and localized bonding pictures of molecules that the methyl group should have at most a secondary influence. It is clearly the topology of the interactions among the basis orbital functions that should determine the course of the reaction. The inherent symmetry of this topology, shorn of minor disturbances by substituents or by distortion, is the symmetry with which we need be concerned. The examples we have used to illustrate the ideas of orbital symmetry control serve a useful function because they allow us to visualize that inherent symmetry in terms of the molecule as a whole. But we can as well abstract the essential features of the pattern of orbital interaction by discarding altogether the molecular framework and keeping only the pericyclic reacting orbitals. This argument justifies the Woodward and Hoffmann stipulation (p. 586) that a pericyclic process must be reduced to its highest inherent symmetry for analysis.
Interaction Diagrams
In order to develop this idea further, we adopt an approach similar to that of DewarZ3 and introduce the orbital interaction diagram as a topological notation for paths of interaction amongst basis orbitals in pericyclic processes. We depict an orbital system by a schematic drawing of the basis orbitals, and use a short curved line to indicate interaction between two orbitals. When we wish to
distinguish interactions present in starting materials from those in products, we use dotted lines for the former and solid lines for the latter; we call such a picture a directed orbital interaction diagram, or, more briefly, a directed diagram. When the distinction is unimportant, solid lines serve throughout and the result is the orbital interaction diagram or, more simply, the interaction diagram. A closed loop of interconnected orbitals then symbolizes the pericyclic process. By way of example, Structure 12 shows the ethylene .rr bond in this convention; 13 would be hexaInteraction Diagrams In order to develop this idea further, we adopt an approach similar to that of DewarZ3 and introduce the orbital interaction diagram as a topological notation for
paths of interaction amongst basis orbitals in pericyclic processes. We depict an orbital system by a schematic drawing of the basis orbitals, and use a short curved line to indicate interaction between two orbitals. When we wish to distinguish interactions present in starting materials from those in products, we use dotted lines for the former and solid lines for the latter; we call such a picture a directed orbital interaction diagram, or, more briefly, a directed diagram. When the distinction is unimportant, solid lines serve throughout and the result is the orbital interaction diagram or, more simply, the interaction diagram. A closed loop of interconnected orbitals then symbolizes the pericyclic process. By way of example, Structure 12 shows the ethylene .rr bond in this convention; 13 would be hexatriene; 14 a a bond between two centemZ4 We note first that the arrangement of orbitals and their orientations are unimportant; we assume that we have examined
the structures of reactant and product and have determined which basis orbitals to use and what the significant interactions are; thenceforth we need maintain only the topology intact. Thus 15 and 16 are entirely equivalent to 14;
