Frost circles

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

Show how you could adapt Frosts circle to generate the ] oribital energy level diagram shown in Figure 11 14 for cycloheptatrienyl cation j... 

Frosts circle (Section 11 19) A mnemonic that gives the Huckel TT MOs for cyclic conjugated molecules and 10ns Functional class nomenclature (Section 4 2) Type of lUPAC nomenclature in which compounds are named according to functional group families The last word in the name... 

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. 

An inscribed polygon is also called a Frost circle. 

Inscribed polygon method (Section 17.10) A method to predict the relative energies of cyclic, completely conjugated compounds to determine which molecular orbitals are filled or empty. The inscribed polygon is also called a Frost circle. 

Fig. 35. Frost circle mnemonics for Huckel and Mobius energy levels illustrated with those for three and four membered rings...

Frost circles showirrg the number and relative energies of the 77 MOs for planar, fuUy conjugated four-, five-, and sfa<-membered rings. 

Figure 21.6 shows Frost circles describing the MOs of monocyclic, planar, and fully conjugated four-, five-, and sbc-membered rings. This apparently coincidental method works because it reproduces geometrically the mathematical solutions to the wave equation. 

Construct a Frost circle for a planar seven-membered ring with one 2p orbital on each atom of the ring and show the relative energies of its seven tt molecular orbitals. Which are bonding MOs, which are antibonding, and which are nonbonding ... 

Refer to the Frost circle shown in Figure 21.6 for a planar, fully conjugated five-membered ring. The six ir electrons occupy the itj, and tTj molecular orbitals,... 

Refer to the Frost circle constructed in the answer to Example 21.1. In the ground-state electron configuration of the cycloheptatrienyl cation, the six tt electrons occupy the 77, 772, 3 molecular orbitals, all of which are bonding. 

To predict the pattern of molecular orbitals found on a molecular orbital energy diagram, it is helpful to use the inscribed polygon method (Frost circles). 

Frost circle (Section 21.2A) A graphic method for determining the relative energies of ir MOs for planar, fuUy conjugated, monocyclic compounds. 

If we accept that Frost circles accurately predict the relative energy levels of the MOs in a conjugated ring system, then we can use Frost circles to gain a better understanding of the... 

Frost circles for different-size ring systems. 

Previously, we used MO theory and Frost circles to explain the requirement for a Hiickel number of Tt electrons. Let s now take a closer look at the Frost circle of a five-membered ring (Figure 18.12). A five-membered ring will be aromatic if it contains six Tt electrons (a Hiickel number). In order... 

The Frost circle for a five-membered ring system. 

Now let s explore the Frost circle of a seven-membered ring (Figure 18.13). Once again, exactly six ir electrons are necessary to achieve aromaticity. 

Frost circles accurately predict the relative energy levels of the MOs in a conjugated ring system. 

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