4m+ 2 rule

It is of interest to examine the aromaticity of the next possible monocyclic aromatic system, Ci0H8. The decagon with f order C-C bonds is shown in Figure 6.6(d) with superimposed o-a-m unit circles. As these circles do not intersect, delocalization of o-a-m is highly unlikely. Experimentally the compound is found to be non-aromatic, cyclodecapentaene. Whereas the effective C-C-C aromatic angle increases with carbon number there is no possibility of monocyclic aromatics beyond benzene. Cyclo-octatetraene (COT) (Figure 6.6(c)) is eliminated by the 4m+2 rule. 

Benzene satisfies the Am + 2 rule. Ilie cyclopentadienyl radical "CsHs is one electron short of satisfying (16.52) the cyclopentadienyl anion C5H5 satisfies the 4m + 2 rule the cation C5H5 is predicted to have a triplet ground state and be highly reactive. These predictions are borne out C5H 5 is found to be considerably more stable than either QH or CsHs. Similarly, C7H7 should be more stable than 07117 or C7H7, as is verified experimentally for example, the salt C H Br" is readily prepared. 

The 4m + 2 rule is sometimes applied to polycyclic systems however, the pattern (16.49) of HMO levels holds only for a monocyclic system, and use of the 4m + 2 rule for polycyclic systems is not justified. 

Tlie 4m + 2 rule actually does not depend on the Huckel assumptions (16.18) to (16.21). The C H tt MOs (16.51) were derived solely by symmetry considerations and are the correct SCF minimal-basis-set tt MOs. With k = 0, we have an MO with all plus signs in front of the AOs. Clearly this MO has a lower energy than any of the others. For the remaining MOs, the pair with k=j and k = nc j ate complex conjugates of each other and must have the same energy. (Since H is Hermitian, we have... 

It should be remembered that the Hiickel rule involving 4m- -2 7t-electrons (with n — 0, 1, 2,...) is necessary but insufficient, because other factors may interfere with the extent of delocalization. The most obvious ones are the existence of a closed shell of filled bonding electrons, the absence of occupied anti-bonding levels and the absence of non-bonding levels. As a consequence, no classically aromatic three-membered ring with a re-electron sextet is possible. As will be discussed in the section devoted to four-membered rings, steric strain is an important factor. 

Benzene is described by molecular orbital theory as a planar, cyclic, con jugatea molecule with six tt electrons. According to the Hiickel rule, a molecule must have 4m 2 7T electrons, where n = 0, 1, 2, 3, and so on, to be aromatic. Planar, cyclic, conjugated molecules with other numbers of tt electrons are antiaromatic. 

The rule, which is due to Hiickel 35>, states that only annulenes of (4m + 2)-type are stable and those of (4w)-type are not. 

This is Hiickel s famous 4m -I- 2 rule, which ascribes exda stability to monocyclic conjugated systems that satisfy (17.46). With 4m + 1 or 4m - 1 rr electrons, the compound is a free radical. With 4m tt electrons, there are two electrons in a shell that can hold four electrons, and Hund s rule predicts a triplet (diradical) ground state. 

C4H4 is predicted by the 4m -l- 2 rule to have a triplet ground state. Cyclobutadiene, C4H4, first synthesized in 1965, is a highly reactive compound that dimerizes at temperatures... 

Planar, cyclic, fully conjugated molecules containing 4m -I- 2 7t electrons are especially stable and are called aromatic. The 4m -h 2 rule works because such molecules have a set of filled degenerate molecular orbitals, in a sense a closed shell. 

Table 20.2 summarizes all An and 4m + 2 reactions. Other 4m processes will follow the rules for the 2 + 2 dimerization of a pair of alkenes, and 4m + 2 processes will resemble the 4 + 2 cycloaddition we know as the Diels-Alder reaction. Perhaps you can see the relationship to aromatidty (4m + 2) that plays a role in this analysis. The transition state for these cycloaddition reactions is cyclic and will be allowed only in the cases where the number of electrons makes the transition state aromatic, 4m + 2 electrons for thermal processes and 4m for photochemical reactions. 

The general rule for all pericyclic reactions was formulated by Woodward and Hoffmann ([3], p. 169). A ground-state pericyclic change is symmetry allowed if the total number of (An + 2)s and (4m)a components is odd. 

Post-irradiation reduction of cerium (IV) in concentrated sodium nitrate solutions was previously reported by Pikaev, Glazunov, and Yakubovich (20) in pulsed electron irradiations of 0.8IV sulfuric acid containing 0.5M sodium nitrate and 2 X 10"4M cerium (IV). They attributed the post-irradiation reaction to intermediate formation of pernitric acid, originally suggested by Allen (1) as an intermediate in the radiolysis of nitric acid solutions. Furthermore, they ruled out nitrous acid since it has been shown previously that the non-radiolytic reaction between cerium (IV) and nitrous acid goes to completion very quickly under the same conditions. However, they presented no evidence to refute the... 

In antiaromatic annulene ions with 4m 1 or 4 2 atoms the two degenerate MOs have atoms in common. Consequently, because these MOs are nondisjoint, at the geometry of highest symmetry the triplet is calculated to lie well below the singlet in energy. Thus, as predicted by Hund s rule, many antiaromatic annulene ions (e.g., cyclopentadienyl cation and hexachlorobenzene dication) have been found experimentally to have triplet ground states. 

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