Hiickel’s 4n + 2 rule

See Fig. 20-1. The four C s and the heteroatom Z use ip -hybridized atomic orbitals to form the a bonds. When Z is O or S, one of the unshared pairs of e s is in an sp HO. Each C has a p orbital with one electron and the heteroatom Z has a p orbital with two electrons. These five p orbitals are parallel to each other and overlap side-by-side to give a cyclic rr system with six p electrons. These compounds are aromatic because six electrons fit Hiickel s 4n + 2 rule, which is extended to include heteroatoms. 

To fill the MOs, the six electrons are added, two to an orbital, beginning with the lowest energy orbital. As a result, the six electrons completely fill the bonding MOs, leaving the antibonding MOs empty. This is what gives benzene and other aromatic compounds their special stability and this is why six 7t electrons satisfies Hiickel s 4n + 2 rule. 

This is not a strict definition of aromaticity it is actually very difficult to define aromaticity precisely, but all aromatic systems obey Hiickel s (4n + 2) rule. 

Hiickel s 4n +2 rule successfully predicts the stability of hydrogen rings. 

While Hiickel s 4n + 2 rule applies only to monocyclic systems, HMO theory is applicable to many other systems. HMO calculations of fiised-ring systems are carried out in much the same way as for monocyclic species and provide energy levels and atomic coefficients for the systems. The incorporation of heteroatoms is also possible. Because of the underlying assumption of orthogonality of the c and n systems of electrons, HMO theory is restricted to planar molecules. 

Feixas F, Matito E, Sola M, Poater J (2008) Analysis of Hitckel s [4n + 2] rule through electronic delocalization measures. J Phys Chem A 112 13231-13238 Feixas F, Matito E, Sola M, Poater J (2010) Patterns of Jt-electron delocalization in aromatic and antiaromatic organic compounds in the light of the Hiickel s 4n + 2 rule. Phys Chem Chem Phys 12 7126-7137... 

Seven equivalent VB structures can be written for the tropylium cation so only one seventh of the positive charge is expected to be on each carbon. Because the cation has six tt electrons, it is expected from Hiickel s (4n + 2)7r-electron rule to be unusually stable for a carbocation. 

On the basis of Hiickel s (4n +2) ir- electron rule, all of these systems can be expected to be aromatic in nature. They do indeed exhibit varying degrees of aromatic stabilization depending on the nature and position of the heteroatom. They cannot all be represented by conventional classical structures. Structures (la)-(lc) can be represented by classical covalent bonded structures whereas those of the (Id) type form the nonclassical structures in the sense that they can be drawn only as charge-separated systems or biradicals in systems wherein X/Y are sulfur or selenium atoms, of-orbital participation in bonding is conceivable, leading to tetravalent sulfur or selenium. 

Benzene is the smallest member of the class of aromatic cyclic polyenes following Hiickel s (4 + 2) rule. Most of the 4n ir systems are relatively reactive anti- or nonaromatic species. Hiickel s rule also extends to aromatic charged systems, such as the cyclopentadienyl anion, cycloheptatrienyl cation, and cyclooctatetraene dianion. 

As another example, the tropylium ion [3 ], which is stabilized by virtue of the 67t electrons spread over a heptagonal sp hybridized carbon framework [Hiickel s (4n 4- 2)v rule with = 1], is also unstable in the gas phase. Its formation from toluene or the benzyl cation has been a long-standing problem in organic mass spectrometry, and the reaction mechanism and energetics have recently been exhaustively discussed (Lif-shitz, 1994). It was, however, isolated as the bromide salt by Doering and Knox (1954, 1957), and was the first non-benzenoid aromatic carbocation. 

Do a Hiickel calculation on the conjugated four-carbon ring cyclobutadiene. Calculate the tt-electron delocalization energy. Comment on the applicablity of Hiickel s 4N -b 2 rule for aromaticity. 

It is important to examine aromaticity in its wider concept at this point. There are many compounds and systems besides benzene that are aromatic. They possess common features in addition to planarity and aromatic stability. MO calculations carried out by Hiickel in the 1930s showed that aromatic character is associated with planar cyclic molecules that contained 2, 6, 10, 14 (and so on) n-electrons. This series of numbers is represented by the term 4n + 2, where n is an integer, and gave rise to Huckel s An + 2 rule that refers to the number of n-electrons in the p-orbital system. In the case of benzene, n— 1, and thus the system contains six n-electrons that are distributed in MOs as shown above. 

This last requirement is an important characteristic of all aromatic systems. It s known as Huckel s rule, or the 4n + 2 rule. To apply this rule, begin by assigning 4n + 2 = number of -electrons in a cyclic system. Next, solve for n, and if n is an integer (a whole number), the system is aromatic. In the case of benzene, 4n + 2 = 6, so n = 1. One is an integer (a Hiickel number), so the last requirement to be classified as an aromatic is satisfied. Figure 6-7 contains several aromatic species with n = 1. 

Let s look at some examples to see how the Hiickel 4n + 2 rule work... 

Hiickel s rule (presented in Section 21.1) states that for planar, monocyclic hydrocarbons containing completely conjugated sp hybridized atoms, the presence of(4n + 2) K-electrons leads to aromaticity ( n is an integer in the series 0, 1, 2, 3, etc.). This rule is associated with particularly stable molecules. Acyclic molecules with a continuous array of sp hybridized carbon atoms are known as polyenes. For aromaticity, there must be a ring, so cyclic polyenes are required. If the number of 71-electrons does not equal 4n + 2, then aromaticity does not exist and the system is rather unstable (this is sometimes called an antiaromatic system). If HiickeVs rule (or the 4n + 2 rule, as it is called) is used, the presence of 2, 6, 10, 14, 18, etc. K-electrons in a ring where every atom is Sff hybridized is characteristic of an aromatic compound. Benzene clearly fits this rule and so does compound 111, which has 14 71-electrons. 

The famous Hiickel 4n + 2 rule [19], which explained the unusual stability of mono-cyclic systems, is widely and well known. In contrast, Clar s rule on the great stability of benzenoid systems having 6n % electrons, which is much broader as it applies to polycyclic conjugate systems, appears not to be so widely known. According to... 

To understand this particular research, we need to pay special attention to the Kekule structure for pyrene (Fig. 14.17). The total number of tt electrons in pyrene is 16 (8 double bonds = 16 77 electrons). Sixteen is a non-Hiickel number, but Hiickel s rule is intended to be applied only to monocyclic compounds and pyrene is clearly tetracyclic. If we disregard the internal double bond of pyrene, however, and look only at the periphery, we see that the periphery is a planar ring with 14 tt electrons. The periphery is, in fact, very much like that of [14]annulene. Fourteen is a Hiickel number (4n + 2, where n = 3), and one might then predict that the periphery of pyrene would be aromatic by itself, in the absence of the internal double bond. 

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