MO Theory of Pericyclic Reactions

The formation of alicyclics by electrocyclic and cycloaddition reactions (Section 9.4) proceeds by one-step cyclic transition states having little or no ionic or free-radical character. Such pericyclic (ring closure) reactions are interpreted by the Woodward-Hoffmann rules in the reactions, the new a bonds of the ring are formed from the head-to-head overlap of p orbitals of the unsaturated reactants. 

Reaction occurs when the lowest unoccupied molecular orbital (LUMO) of one reactant overlaps with the highest occupied molecular orbital (HOMO) of the other reactant. If different molecules react, either can furnish the HOMO and the other the LUMO. 

The reaction is possible only when the overlapping lobes of the p orbitals of the LUMO and the HOMO have the same sign (or shading). 

Only the terminal p AO s of the interacting molecular orbitals are considered, as it is their overlap that produces the two new cr bonds to close the ring. 

The bracketed numbers indicate that the cycloaddition involves two species each having two tt electrons. Without ultraviolet light we have the situation indicated in Fig. 9-16(a). Irradiation with uv causes a 7t- tt transition (Fig. 8-3), and now the proper orbital symmetry for overlap prevails [Fig. 9- 6 b)l 

---

A theory of pericyclic reactions stating that the MOs of the reactants must flow smoothly into the MOs of the products without any drastic changes in symmetry. That is, there must be bonding interactions to help stabilize the transition state, (p. 692)... 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offulminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmarm mles [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4—6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

First, pericyclic reactions are defined, and an example of their unusual stereochemical selectivity is presented. A theoretical treatment of pericyclic reactions requires examination of the MOs for the conjugated molecules that participate in these reactions, so MO theory for these compounds is developed next. Then a theoretical explanation for the selectivity and stereochemistry observed in each of the three classes of pericyclic reactions is presented, along with a number of common examples of reactions of each kind. 

For many years, pericyclic reactions were poorly understood and unpredictable. Around 1965, Robert B. Woodward and Roald Hoffmann developed a theory for predicting the results of pericyclic reactions by considering the symmetry of the molecular orbitals of the reactants and products. Their theory, called conservation of orbital symmetry, says that the molecular orbitals of the reactants must flow smoothly into the MOs of the products without any drastic changes in symmetry. In that case, there will be bonding interactions to help stabilize the transition state. Without these bonding interactions in the transition state, the activation energy is much higher, and the concerted... 

Professor Houk and I are coevals and we embarked on our research careers at about the same time. In the beginning of the 1970s, both he and I were independently working on mechanistic aspects of pericyclic reactions, using a combination of experiment, simple perturbational MO theory and semi-empirical MO calculations. My published work in this area was of variable quality whereas Ken s was uniformly... 

We now turn to the ideas, based on MO theory, which have been advanced to explain the patterns of reactivity that all pericyclic reactions show. 

After reading Chapter 14, you might be wondering why we can represent the a bonds in such a simple manner, because fully delocalized MOs without carbon hybridization are the results obtained from sophisticated electronic structure theory. Experience has shown that in pericyclic reactions there is no need to include "spectator bonds", bonds that remain intact throughout the reaction, in the analysis. Remember that orbitals and our notions of bonding are just models. Any model that explains experimental results and can predict them is useful, and the simplest is always the best. Here we show the simplest model that works. We could complicate our model by including the spectator bonds, but the results would be the same. 

In 1952, Fukui published his Frontier MO theorywhich went initially unnoticed. In 1965, Woodward and Hoffmann published their principle of conservation of orbital symmetry, and applied it to all pericyclic chemical reactions. The immense success of these rules" renewed interest in Fukui s approach and together formed a new MO-based framework of thought for chemical reactivity (called, e.g., giant steps forward in chemical theory in Morrison and Boyd, pp. 934, 939, 1201, and 1203). This success of MO theory dealt a severe blow to VB theory. In this area too, despite the early calculations of the Diels-Alder and 2-1-2 cycloaddition reactions by Evans,VB theory missed making an impact, in part at least because of its blind adherence to simple resonance theory. All the subsequent VB derivations of the rules (e.g., by Oosterhoff in Ref. 90) were after the fact and failed to reestablish the status of VB theory. 

---