Molecular orbitals Frost circles

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

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. 

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. 

The energy states of the 7c-orbitals can be determined graphically for simple cyclic TC-systems using the scheme developed by Arthur A. Frost and Boris Musu-lin. The polygon is drawn standing on a vertex in a circle, the radius of which, by definition, corresponds to double of the resonance energy 3. One molecular orbital is allocated to each comer of the polygon. The vertical distance from the... 

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). 

The Frost circle allows you to determine quickly the relative energies of the molecular orbitals for any planar, cychc, fully conjugated polyene. Remember. The polygon must be inscribed vertex down. 

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

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). 

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. 

Frost circle (Section 13.6) A device used to find the relative energies of the molecular orbitals of planar, cyclic, fully conjugated molecules. A polygon corresponding to the ring size of the molecule is inscribed in a circle, vertex down. The intersections of the polygon with the circle give the relative positions of the molecular orbitals. 

Molecular orbitals below the midpoint of the cyclic structure are bonding molecular orbitals, those above the midpoint are antibonding molecular orbitals, and any at the midpoint are nonbonding molecular orbitals. This simple scheme is sometimes called a Frost device (or a Frost circle) in honor of Arthur A. Frost, the scientist who devised it. 

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