The Huckel Rule

The relative energies of cyclohexene, 1,3-cyclohexadiene, 1,3,5-cyclohexatriene, and benzene and their heats of hydrogenation to form cyclohexane in kj mole .  

What is responsible for the unusual stability and unique reactivity of benzene  

The ring must contain only sp -hybridized atoms that can form a delocalized system of n molecular orbitals. 

The number ofjt electrons in the delocalized n system must equal 4n + 2, where n is an integer. 

The 4 + 2 rule was proposed by Erich Hiickel and is known as the Hiickel rule. The Hiickel rule predicts that cyclic n systems having 2 ( = 0), 6 ( = 1), 10 ( = 2), and 14 ( = 3) 7t electrons will be unusually stable that is, they will be aromatic. 

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. 

A planar, cyclic system of unsaturated atoms containing (4/j + 2) n-electrons will be aromatic, where n is a positive integer or zero. It will possess extra stabilization. Some slight deviation from planarity is allowed. A similar system but containing 4 i n-electrons will be anti-aromatic. Not only will it lack aromatic stabilization, but the closed loop of n-electrons will result in additional destabilization with respect to that anticipated. 

These ideas are predicted by calculation and are confirmed by experiment. 

The presence ot electrons in anti txrnding o-bilals is uestabilLrmg Orbitals that tall on Ihe energy reference lino are called ixjritXMidtng oibttais. me presence ot electrons m these orbitals has no influence on the total Donning 

This rule is now an important criterion for aromaticity. Those systems that contain An n-electrons are unstable and are referred to as antiaromatic compounds. 

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Annulene, [22]annulene, and [24]annulene have all been reported. The NMR spectrum of [22]annulene is consistent with regarding the molecule as aromatic, whereas those of the [20] and [24] analogs are not. In each case, there is some uncertainty as to the preferred conformation in solution, and the NMR spectra are temperature-dependent. Although the properties of these molecules have not been studied as completely as those of the smaller systems, they are consistent with the predictions of the Huckel rule. 

PATr+ of about 0-2. Several methods for generating the phenalenyl cation have been developed.Because the center carbon is part of the conjugated system, the Huckel rule, which applies only to monocyclic conjugated systems, cannot be applied to just the peripheral conjugation. The nature of the phenalenyl system is considered further in Problem 12 at the end of this chapter. 

The Huckel rule is strictly applicable only to monocyclic compounds, but the genera] concept of aromaticity can be extended beyond simple monocyclic compounds to include polycyclic aromatic compounds. Naphthalene, with two... 

Q Which of the following heterocycles conform to the Huckel rule (4h +2) for aromaticity (i) furan (ii) l//-azepine (iii) pyrylium perchlorate [chlorate(VIl)] ... 

Anions of small heterocyclics are little known. They seem to be involved in some elimination reactions of oxetan-2-ones (80JA3620). Anions of large heterocycles often resemble their acyclic counterparts. However, anion formation can adjust the number of electrons in suitable systems so as to make a system conform to the Huckel rule, and render it aromatic if flat geometry can be attained. Examples are found in Chapter 5.20. Anion formation in selected large heterocycles can also initiate transannular reactions (see also Section 5.02.7 below). 

Suprafacial or Huckel transition state in a pericyclic reaction is associated with a plane of symmetry and is particularly favourable if the number of cyclically conjugated Tr-electrons in the transition state equals [4n - - 2] (the Huckel rule, where = 0,1, 2,...). 

The Huckel rule is strictly applicable only to monocyclic compounds, but the general concept of aromaticity can be extended beyond simple mono-cyclic compounds to include polycyclic aromatic compounds. Naphthalene, with two benzene-like rings fused together, anthracene, 1,2-benz-pyrene, and coronene are all well-known compounds, BenzoLa]pyrene is particularly interesting because it is one of the cancer-causing substances that has been isolated from tobacco smoke. 

Benzene is described by molecular orbital theory as a planar, cyclic, conjugated molecule with six it electrons. According to the Huckel rule, a molecule must have 4 + 2 it electrons, where n = 0,1, 2, 3, and so on, to be aromatic. Planar, cyclic, conjugated molecules with other numbers of ir electrons are antiaroraatic. 

This includes heteroannulenes, which comply with the HUCKEL rule, i.e. which possess An + 2) -electrons delocalized over the ring. The most important group of these compounds derives from [6]annulene (benzene). They are known as heteroarenes, e.g. furan, thiophene, pyrrole, pyridine, and the pyrylium and thiinium ions. As regards stability and reactivity, they can be compared to the corresponding benzenoid compounds [1]. 

Figure 7. Illustration of the Huckel rule for the fulvene and heptafulvene derivatives. (Reprinted with permission from ref 65. Copyright 1995 Slovak Academy of Sciences.)...

The compound [18]-annulene is large enough to be planar and obeys the HUckel rule (4n + 2 = 18, with n=4). It is a brownish red fairly stable reactive solid. NMR evidence shows that it has aromatic character. The an-nulene with n= 7, [30]-annulene, can also exist in a planar form but is highly unstable. See also pseudoaromatic. 

The next higher annulene, cyclooctatetraene, is readily determined to be nonaromatic. The bond lengths around the ring alternate as expected for a polyene, and thermochemical data provide no evidence of special thermodynamic stability. Neither is the molecule antiaromatic. It is readily isolated and has the chemical behavior of a polyene. The molecule has a tub shape,and therefore is not a planar system of the type to which the Huckel rule applies. 

Larger annulenes permit the incorporation of irons double bonds into the rings hence, isomeric annulenes warrant consideration beginning with the cyclodecapen-taenes. [10]Annulene should, by the Huckel rule, possess aromatic stabilization if it were planar. All the isomeric cyclodecapentaenes suffer serious strain that prevents the planar geometry from being adopted. The trans,cis,trans,cis,cis-isomer, which has minimal angle strain, suffers a severe nonbonded repulsion between the two internal hydrogens ... 

That this nonaromaticity is a consequence of nonplanarity, not of a breakdown of the Huckel rule, can be demonstrated by study of a 10-7r-electron ring in which the steric problems associated with the cyclodeca-l,3,5,7,9-pentaenes are avoided. Compound 4 avoids these steric problems with only slight loss of planarity in the... 

The Huckel rule would predict nonaromaticity for [16]annulene. The compound has been synthesized and thoroughly characterized. The bond lengths show significant alteration (C=C, 1.34 A C-C, 1.46 A), and the molecule is significantly less planar than [14]annulene. These structural data are consistent with regarding [16]annulene as being nonaromatic. 

As with cyclooctatetraene, then, [10]annulene does not exist in a planar form and the Huckel rule cannot be applied. 

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