Frost circles benzene

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 2.28 Relative energies of benzene and cyclooctatetraene molecular orbitals from Frost circles...

We can draw Frost circles (see Section 2.9.3) to show the relative energies of the molecular orbitals for pyridine and pyrrole. The picture for pyridine is essentially the same as for benzene, six jt electrons forming an energetically favourable closed shell (Figure 11.1). For pyrrole, we also get a closed shell, and there is considerable aromatic stabilization over electrons in the six atomic orbitals. 

FIGURE 13.19 The relative energies of the molecular orbitals of benzene derived from a Frost circle. 

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). 

The Frost circle analysis lets us see the relative energies of the molecular orbitals for this system (Rg. 13.27). Notice the degenerate pairs of orbitals. How many electrons must go into the n system In the cation, there is an empty 2p orbital on C(7) and the only n electrons are the six from the three original double bonds. These electrons can fit nicely into the three bonding molecular orbitals of the n system. Note how this system resembles the arrangement of benzene—the occupied degenerate molecular orbitals are fiiU (Fig. 13.27). This ion qualifies as aromatic, and the increased stability relative to other carbocations is dramatic indeed. Notice that the number of atoms involved in the ring— here seven—is independent of the number of n electrons— here... 

Cyclopentadiene is a muci stronger acid than propene. The difference in acidity is enormous. Look carefully at the structure of the cyclopentadienyl anion. Here too, we have a planar, cyclic, and fully conjugated system. The molecular orbitals can be derived from a Frost circle (Fig. 13.29).There are six electrons to put into the molecular orbitals, and, as in the tropylium ion or benzene, they fully occupy the lowest molecular orbital and the set of degenerate bonding molecular orbitals. The cyclopentadienyl anion can be described as aromatic, and for an anion, this species is remarkably stable. Do not fall into the trap of expecting this anion to be as stable as benzene. 

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

FIGURE 11.13 Frost s circle and the tt molecular orbitals of (a) square cyclobutadiene, (b) benzene, and (c) planar cyclooctatetraene. 

Figure 3.48 The Frost-Musulin circle mnemonic (Eq. (3.141)) for HMO orbital energies ej of benzene, n = 6.

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