Sigmatropic reactions Frontier Orbital analysis

A frontier orbital analysis of the ene reaction is shown in Fig. 8.62. It displays many features of the [3,3]-sigmatropic shift. Thus, the hydrogen atom transfer from an allylic site to a double bond is seen to be symmetry allowed with respect to the HOMO of an... 

An alternative analysis of sigmatropic reactions involves drawing the basis set atomic orbitals and classifying the resulting system as Htickel or Mobius in character. When this classification has been done, the electrons involved in the process are counted to determine if the TS is aromatic or antiaromatic. The conclusions reached are the same as for the frontier orbital approach. The suprafacial 1,3-shift of hydrogen is forbidden but the suprafacial 1,5-shift is allowed. Analysis of a 1,7-shift of hydrogen shows that the antarafacial shift is allowed. This analysis is illustrated in Figure 10.31. These conclusions based on orbital symmetry considerations are supported by HF/6-31G calculations, which conclude that 1,5-shifts should be suprafacial, whereas... 

Write the frontier molecular orbital analysis for a [3,3]-sigmatropic shift in the analogous fashion as presented in the chapter except that you are using a geometry that would lead to a boatlike conformation for the transition state. As a hint, you should find that the reaction is allowed. However, why would this geometry be less favorable ... 

The orbital symmetry study of sigmatropic reactions will help us to understand the stereochemistry of these reactions. An FMO analysis of this process indicates the interaction between the frontier orbitals of the n system and orbitals of the migrating atom or atoms. Let us consider the simplest case of 1,3-sigmatropic shift of hydrogen. In this case, n system is an allyl radical and the migrating atom is hydrogen. Their frontier orbitals are allyl i2 and hydrogen Is for thermal reaction... 

For the analysis of sigmatropic rearrangements, the correlation diagrams are not relevant since it is only the transition state and not the reactants or products that may possess molecular symmetry elements. However, these reactions can be analyzed satisfactorily by using frontier molecular orbital (FMO) and perturbation molecular orbital (PMO) methods. 

As discussed during the previous frontier molecular orbital theory analysis of [3,3]-sigmatropic shifts, a chairlike transition state is allowed for these reactions. As you will show in Problem 20.48, a boatlike transition state is also allowed by frontier molecular orbital theory. However, chair conformations are more favorable than boat conformations for six-membered cyclic rings (look back at Section 2.5A). This preference influences the stereochemistry of these shifts, as we now show with an example. 

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