Cyclopropane and Cyclopropylcarbinyl— Walsh Orbitals

One of the most challenging molecules for organic electronic structure theory is cyclopropane. It is difficult to understand C-C-C angles of 60° with conventional bonding models. Also, in Section 11.5.14 we examined the unusual reactivity of the cyclopropylcarbinyl cation. Much of the rearrangement chemistry of this cation, as well as its special thermodynamic stability (Chapter 2), can be understood to arise from the uniquely strong donor character of the a bonds in cyclopropane. Here we provide a more detailed description of the bonding in cyclopropane that nicely rationalizes these observations. 

Cyclopropane is very well treated by a combination of group orbitals and the perturbation theory analysis described in this chapter and Chapter 1. First, however, we must consider a new aspect of orbital mixing, the general problem of combining three, equivalent orbitals in a cyclic array. We now have two choices on how to proceed in solving this problem. 

We can perform all the analysis in a manner similar to how the two-orbital mixing problem was addressed (Section 14.2.2). Alternatively, we can use some of the logic we have developed to this point in the chapter, and some of the rules of HMOT, to derive the answer. We choose the latter method here. 

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