Pericyclic Reaction Theory

The photochemistry of conjugated polyenes has played a central role in the development of modern molecular photochemistry, due in no small part to its ultimate relevance to the electronic excited state properties of vitamins A and D and the visual pigments, as well as to pericyclic reaction theory. The field is enormous, tremendously diverse, and still very active from both experimental and theoretical perspectives. It is also remarkably complex, primarily because file absorption spectra and excited state behavior of polyene systems are strongly dependent on conformation about the formal single bonds in the polyene chain, which has the main effect of turning on or off various pericyclic reactions whose efficiencies are most strongly affected by conformational factors. 

The Woodward-Hoffmann pericyclic reaction theory has generated substantial interest in the pathways of forbidden reactions and of excited state processes, beginning with a paper by Longuet-Higgins and Abrahamson,54 which appeared simultaneously with Woodward and Hoffmann s first use of orbital correlation diagrams.55 We have noted in Section 11.3, p. 586, that the orbital correlation diagram predicts that if a forbidden process does take place by a concerted pericyclic mechanism,56 and if electrons were to remain in their original orbitals, an... 

The organization of the book is traditional. We have, however, been selective in our choice of topics in order to be able to devote a significant portion J of the book to the pericyclic reaction theory and its applications and to include a chapter on photochemistry. 

Electrophilic Addition to Conjugated Dienes UV-Visible Spectroscopy Pericyclic Reaction Theory... 

The mechanism of olefin metathesis does not involve the classic reactions we have covered—namely, oxidative addition, reductive elimination, (3-hydride elimination, etc. Instead, it simply involves a [2+2] cycloaddition and a [2+2] retrocycloaddition. The [2+2] terminology derives from pericyclic reaction theory, and we will analyze this theory and the orbitals involved in this reaction in Chapter 15. In an organometallic [2+2] cycloaddition, a metal alkylidene (M=CR2) and an olefin react to create a metal lacyclobutane. The metalla-cyclobutane then splits apart in a reverse of the first step, but in a manner that places the alkylidene carbon into the newly formed olefin (Eq. 12.83). Depending upon the organometallic system used, either the alkylidene or the metallacycle can be the resting state of the... 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

For reviews of several concerted reactions within the general theory of pericyclic reactions, see A. R Marchand and R. E. Lehr, eds., Pericyclic Reactions, Vols. I and II, Academic Press, New York, 1977. 

The orbital phase theory includes the importance of orbital symmetry in chanical reactions pointed out by Fukui [11] in 1964 and estabhshed by Woodward and Holiimann [12,13] in 1965 as the stereoselection rule of the pericyclic reactions via cyclic transition states, and the 4n + 2n electron rule for the aromaticity by Hueckel. The pericyclic reactions and the cyclic conjugated molecules have a conunon feature or cychc geometries at the transition states and at the equihbrium structures, respectively. 

Orbitals interact in cyclic manners in cyclic molecules and at cyclic transition structures of chemical reactions. The orbital phase theory is readily seen to contain the Hueckel 4n h- 2 ti electron rule for aromaticity and the Woodward-Hof nann mle for the pericyclic reactions. Both rules have been well documented. Here we review the advances in the cyclic conjugation, which cannot be made either by the Hueckel rule or by the Woodward-Hoffmann rule but only by the orbital phase theory. 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

The first pair of examples we would like to discuss occurs in a field which lends itself naturally to be conquered by theory. Indeed, the past three decades have seen the exploration of mechanistic details of pericyclic reactions as one of the major success stories of computational chemistry. Rooted in qualitative molecular orbital theory, the key concept of... 

Wiest, O., Houk, K. N., 1996, Density Functional Theory Calculations of Pericyclic Reaction Transition Structures Top. Curr. Chem., 182, 1. 

The actual rates of thermally-allowed pericyclic reactions vary vastly, and frontier-orbital theory (14, 15, 16) has proven to be the primary basis for quantitative understanding and correlation of the factors responsible. It is therefore of interest to find the dominant frontier orbital interactions for the group transfer reactions hypothesized to occur. 

Houk, K.N. "Application of Frontier Molecular Orbital Theory to Pericyclic Reactions", in "Pericyclic Reactions", A.P. 

Frontier molecular orbital (FMO) theory 62) has provided new insights into chemical reactivity. This, and the simplicity of its application, has led to its widespread use, particularly in the treatment of pericyclic reactions 63). An FMO treatment depends on the energy of the highest occupied (HOMO) and lowest unoccupied molecular... 

Longuet-Higgins phase-based treatment, three-particle reactive system, 157-168 theoretical background, 43-44 observability, 208 quantum theory, 200 Phase-inverting reactions molecular model, 496-499 phase-change rule, pericyclic reactions, 449-450... 

Density functional theory and MC-SCF calculations have been applied to a number of pericyclic reactions including cycloadditions and electrocyclizations. It has been established that the transition states of thermally allowed electrocyclic reactions are aromatic. Apparently they not only have highly delocalized structures and large resonance stabilizations, but also strongly enhanced magnetic susceptibilities and show appreciable nucleus-independent chemical-shift values. 

Generally, at least in theory, an important aspect of cation-radical polymerization, from a commercial viewpoint, is that either catalysts or monomer cation-radicals can be generated electrochem-ically. Such an approach deserves a special treatment. The scope of cation-radical polymerization appears to be very substantial. A variety of cation-radical pericyclic reaction types can potentially be applied, including cyclobutanation, Diels-Alder addition, and cyclopropanation. The monomers that are most effectively employed in the cation-radical context are diverse and distinct from those that are used in standard polymerization methods (i.e., vinyl monomers). Consequently, the obtained polymers are structurally distinct from those available by conventional methods although the molecular masses observed so far are still modest. Further development in this area would be promising. 

The combination of modem valence bond theory, in its spin-coupled (SC) form, and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wavefunction, is demonstrated to provide quantitative and yet very easy-to-visualize models for the electronic mechanisms of three gas-phase six-electron pericyclic reactions, namely the Diels-Alder reaction between butadiene and ethene, the 1,3-dipolar cycloaddition of fulminic acid to ethyne, and the disrotatory electrocyclic ringopening of cyclohexadiene. 

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. 

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