Aromatic transition state theory

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. 

Another approach to analyzing concerted pericyclic reactions is based on the observation that the forbidden [2+2] cycloaddition involves a cyclic array of four electrons in the transition state, while the allowed [4+2] cycloaddition involves a cyclic array of six electrons. This is a familiar pattern that immediately calls to mind aromaticity, in which the ground states of molecules with four ir electrons in a cycle are destabilized and termed antiaromatic, while molecules with six tt electrons are stabilized and aromatic. Building off an earlier analysis by Evans, Zimmerman developed aromatic transition state theory. Simply put, reactions with a simple cyclic array of 4h + 2 electrons (commonly six) in a pericyclic transition state will be stabilized by aromaticity, making the reactions favorable. Note that the relevant electrons need not be exclusively in it orbitals a mixture of cr and it bonds in a cyclic array is acceptable. 

In order to expand the range of reactions that can be analyzed using aromatic transition state theory, we need to expand our definition of aromaticity. Figure 15.7 shows how to do this. In a conventional cyclic array, we can always arrange for all the constituent orbitals to be in-phase, in which case all neighboring interactions are favorable. This is evident in the lowest-lying tt molecular orbital of any planar, cyclic tt system, and in the first orbital array of Figure 15.7 A. 

The application of aromatic transition state theory to cs cloadditions. 

Once you get used to analyzing cyclic arrays of orbitals, aromatic transition state theory can be a simple and rapid way to analyze pericyclic reactions. As with the other approaches, it is well suited to some types of reactions, but less well suited to others. With practice, you will develop some instincts as to which model to apply to a given reaction. 

This is a very powerful rule, and it is especially useful when there are several components to a pericyclic reaction. With several components it is often difficult to identify the appropriate HOMOs and LUMOs for an FMO analysis, and difficult to quickly write an orbital or state correlation diagram. In such cases, aromatic transition state theory, or the generalized orbital symmetry rule, are the easiest approaches for analyzing the reaction. It is your decision as to which works best for you. 

How do we rationalize this allowed reaction Both FMO and aromatic transition state theory are easy to apply. As shown below, the extra node in the d orbital used in the alkylidene it bond allows the HOMO of the M=Cbond to interact with the UJMOoftheC=C bond constructively. Similarly, the extra node in the d orbital makes the four-electron system Mobius (remember we do not count nodes in the atomic orbitals themselves), and therefore allowed. 

Figure 15.17 B shows the aromatic transition state analysis of these reactions. We draw a picture of an opening pathway with the minimum number of phase changes and examine the number of nodes. The four-electron butadiene-cyclobutene system should follow the Mobius/conrotatory path, and the six-electron hexatriene-cyclohexadiene system should follow the Hiickel/disrotatory path. As such, aromatic transition state theory provides a simple analysis of electrocyclic reactions. The disrotatory motion is always of Hiickel topology, and the conrotatory motion is always of Mobius topology.

We have introduced several different ways to analyze thermal pericyclic reactions. The highly formalized orbital symmetry analyses produce explicit rules, the conclusions of which are summarized in several tables. Other methods, such as FMO and aromatic transition state theories can be applied on a case-by-case basis, although they can be generalized in the same way. The realities are, in day-to-day chemistry, most pericyclic reactions will be familiar types or straightforward extensions of reactions we have covered here. 

Occasionally, though, you will run across a more exotic pericyclic process, and will want to decide if it is allowed. In a complex case, a reaction that is not a simple electrocyclic ringopening or cycloaddition, often the basic orbital symmetry rules or FMO analyses are not easily applied. In contrast, aromatic transition state theory and the generalized orbital symmetry rule are easy to apply to any reaction. With aromatic transition state theory, we simply draw the cyclic array of orbitals, establish whether we have a Mobius or Hiickel topology, and then count electrons. Also, the generalized orbital symmetry rule is easy to apply. We simply break the reaction into two or more components and analyze the number of electrons and the ability of the components to react in a suprafacial or antarafacial manner. 

Use the aromatic transition state theory method to determine whether the reactions given in Exercise 23 are allowed or forbidden as written. 

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 ... 

However, the electronic theory also lays stress upon substitution being a developing process, and by adding to its description of the polarization of aromatic molecules means for describing their polarisa-bility by an approaching reagent, it moves towards a transition state theory of reactivity. These means are the electromeric and inductomeric effects. 

Energy-resolved rate constant measurements near the threshold for diplet methylene formation from ketene have been used to provide confirmation of the fundamental hypothesis of statistical transition state theory (that rates are controlled by the number of energetically accessible vibrational states at the transition state).6 The electronic structure and aromaticity of planar singlet n2-carbenes has been studied by re-election coupling perturbation theory.7 The heats of formation of three ground-state triplet carbenes have been determined by collision-induced dissociation threshold analysis.8 The heats of formation of methylene, vinylcarbene (H2C=CHCH), and phenylcarbene were found to be 92.2 3.7, 93.3 3.4, and 102.8 33.5 kcal mol-1, respectively. 

Figure 6. Logarithmic plot values of LUm/fc versus pressure for the Cope rearrangement of bullvalene (torr at the experimental temperature of 356 K). Experimental values are signified by solid circles. Pressures are the total sample pressure at 356 K. Errors in frUni/fc are reported to 2o. The solid (upper) line represents the values calculated from RRKM theory using the biradicaloid transition state model. The lower line represents calculated rate constants using the aromatic transition-state model. The collision diameter was 3.6 A in both cases.

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