Transition state pericyclic, theory

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 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. 

In 1969 R.B. Woodward and R. Hoffmann developed a general theory of concerted reactions which proceed through a cyclic transition state process which they turned pericyclic. They used the concept of orbital symmetry to predict which types of cyclic transition state are energetically feasible. 

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. 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

Dewar s perturbation molecular orbital (PMO) method analyzes the interactions that take place on assembling p orbitals in various ways into chains and rings.44 It is similar to the methods we have used in Section 10.4 in considering aromaticity, but lends itself better to a semiquantitative treatment. We shall nevertheless be concerned here only with the qualitative aspects of the theory as it applies to pericyclic transition states. 

This review has provided an overview of the studies of pericyclic reaction transition states using density functional theory methods up to the middle of 1995. Since the parent systems for most of the pericyclic reaction classes have been studied, a first assessment of DFT methods for the calculation of pericyclic transition structures can be made. 

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... 

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)... 

Although Otto Diels and Kurt Alder won the 1950 Nobel Prize in Chemistry for the Diels-Alder reaction, almost 20 years later R. Hoffmann and R. B. Woodward gave the explanation of this reaction. They published a classical textbook, The Conservation of Orbital Symmetry. K. Fukui (the co-recipient with R. Hoffmann of the 1981 Nobel Prize in Chemistry) gave the Frontier molecular orbital (FMO) theory, which also explains pericyclic reactions. Both theories allow us to predict the conditions under which a pericyclic reaction will occur and what the stereochemical outcome will be. Between these two fundamental approaches to pericyclic reactions, the FMO approach is simpler because it is based on a pictorial approach. Another method similar to the FMO approach of analyzing pericyclic reactions is the transition state aromaticity approach. 

Chapter 8 covers extensively pericyclic reactions and also includes the aromatic transition state theory. Most of the examples are taken from latest literature and are useful for postgraduate and research students. 

More recently, molecular orbital theory has provided a basis for explaining many other aspects of chemical reactivity besides the allowedness or otherwise of pericyclic reactions. The new work is based on the perturbation treatment of molecular orbital theory, introduced by Coulson and Longuet-Higgins,2 and is most familiar to organic chemists as the frontier orbital theory of Fukui.3 Earlier molecular orbital theories of reactivity concentrated on the product-like character of transition states the concept of localization energy in aromatic substitution is a well-known example. The perturbation theory concentrates instead on the other side of the reaction coordinate. It looks at how the interaction of the molecular orbitals of the starting materials influences the transition state. Both influences on the transition state are obviously important, and it is therefore important to know about both of them, not just the one, if we want a better understanding of transition states, and hence of chemical reactivity. 

This chapter is an introduction to qualitative molecular orbital theory and pericyclic reactions. Pericyclic reactions have cyclic transition states and electron flow paths that appear to go around in a loop. The regiochemistry and stereochemistry of these reactions are usually predictable by HOMO-LUMO interactions, so to understand them we need to understand molecular orbital theory, at least on a qualitative basis. 

One question that needs to be addressed is why are the activation volumes of pericyclic cycloadditions smaller (more negative) than those of the corresponding stepwise reactions involving diradical intermediates In the past it was assumed that the simultaneous formation of two new n bonds in a pericyclic [4 - - 2] cycloaddition leads to a larger contraction of volume than the formation of one bond in the stepwise process. The interpretation presented [28] is limited by the scope of Eyring transition state theory where the activation volume is related to the transition state volume, as mentioned above, and does not incorporate dynamic effects related to pressure-induced changes in viscosity [41]. An extensive discussion of reaction rates in highly viscous solvents can be found in Chapter 3. 

One of the main reasons is probably related to the small rate constant increase in the low pressure range (0-300 MPa) even for fairly pressure-dependent reactions such as pericyclic cycloadditions. The kinetic effect is derived from the relationship of Evans and Polanyi in the transition state theory as ... 

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