Frost circles cyclobutadiene

A useful mnemonic device for quickly setting down the HMOs for cyclic systems is Frosts circle.If a regular polygon of n sides is inscribed in a circle of diameter 4/3 with one comer at the lowest point, the points at which the comers of the polygon touch the circle define the energy levels. The energy levels obtained for benzene and cyclobutadiene with Frost s circle are shown in Fig. 1.12. 

FIGURE 13.20 The relative energies of the molecular orbitals of cyclobutadiene derived from a Frost circle. Electrons have been added to this construct after the energies of the orbitals have been determined. 

Cyclooctatetraene is another example of a An molecule. But here we find neither the special stability of benzene, nor the special instability of cyclobutadiene. The molecule behaves like four separated, normal alkenes. Let s first examine planar cyclooctatetraene.The Frost circle again determines the relative positions of the molecular orbitals (Fig. 13.22). 

FIGURE 11 13 Frost s circle and the TT molecular orbitals of (a) square cyclobutadiene (b) ben zene and (c) planar cyclooctatetraene... 

Fig. 1.12. Energy level diagrams for cyclobutadiene and benzene, illustrating the application of Frost s circle.

The instability of [4]annulene (a neutral 4n n-electron annulene) can be gleaned from either Frost s Circle or HMO theory. As shown in Fig. 2. the former predicts an open-shell triplet, implicating instability. The latter reports no gain in energy (0 P) relative to its acyclic analogue, butadiene. Experimental evidence shows that cyclobutadiene IS. in fact, a closed shell species, with alternate single and double bonds. Regardless, as predicted. [4]annulene proved to be an unstable compound. 

---