Frost’s circle

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

Show how you could adapt Frost s circle to generate the orbital... 

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. 

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

Use Frost s circle to construct orbital energy diagrams for (a)... 

Frost s circle (Section 11.19) A mnemonic that gives the Hiickel -tr MOs for cyclic conjugated molecules and ions. 

BEBBE5 Use Frost s circle to construct orbital energy diagrams for (a) [lOjannulene and (b) [12]annulene. Is either aromatic according to Huckel s rule ... 

There is an easy way to remember the pattern of MOs for monocyclic systems. Figure 1.11 shows Frost s circle. A polygon corresponding to the ring is inscribed... 

Fig. 1.11. Frost s circle mnenomic for HMOs of cyclic polyenes.

Frost s circle A simple, geometrical approach to approximating the HMO energy levels for planar annulenes. The lowest energy MO has an HMO energy of a+ip. 

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. 

Annulene is a 4n -electron system, and thus, the (neutral) planar form would be expected to exhibit antiaromatic behavior. Indeed, Frost s circle analysis predicts an open-shell species (as with [4]annulene see Figs. 2 and 6). Extensive studies of cyclooctatetraene were performed, and it was established that the neutral state avoids the problem of antiaromaticity by adopting a tub conformation. Both the anion and dianion are known to exist in a planar conformation, the latter being aromatic. This fact is also predicted by simple analysis of the [8]annulene dianion by Frost s circle (see Fig. 6). It is predicted that the planar [8]annulene dianion is a closed-shell system. 

---