The 4n 2 Rule

Huckel was the first to show by the molecular orbital theory that the monocyclic conjugated polyenes have filled stable shells of ir electrons when the number of such electrons was 4n + 2, where n is a positive integer. When 

2 rule for aromatic character. It has been used with considerable success in a priori predictions of stable cyclopropen— ium and tropylium cations. It also explains why no one has yet been able to prepare anionic salts of cyclopropene and cycloheptatriene analogous to the stable anionic salts of cy— clopentadiene. 

Sketch out qualitatively the energy levels and electronic configurations that would be expected for planar cyclob ctatetraene. 

Stable cyclooctatetraene exists in the tub conformation (p. 21). Use the LCAO method (and group theory) to determine the energy levels of nonplanar cyclob cta— tetraene on the basis of assignment of full p for ir overlap across the double bonds and 0. 25p for overlap across the single bonds of the tub structure. 

THE APPLICATION of the LCAO method to other elements than carbon is straightforward as long as absolute comparisons are not required. The calculations of the electronic states of tetraazacyclobutadiene and hexaazabenzene would be exactly the same for carbon, provided the extra unshared electron pairs are regarded as being strictly localized and a and p are assigned values appropriate for nitrogen. 

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The oxygen m furan has two unshared electron pairs (Figure 11 16c) One pair is like the pair m pyrrole occupying a p orbital and contributing two electrons to complete the SIX TT electron requirement for aromatic stabilization The other electron pair m furan IS an extra pair not needed to satisfy the 4n + 2 rule for aromaticity and occupies an sp hybridized orbital like the unshared pair m pyridine The bonding m thiophene is similar to that of furan... 

Section 11 23 Huckel s rule can be extended to heterocyclic aromatic compounds Unshared electron pairs of the heteroatom may be used as tt electrons as necessary to satisfy the 4n + 2 rule... 

According to the Hiickel criteria for aromaticity, a molecule must be cyclic, conjugated (that is, be nearly planar and have ap orbital on each carbon) and have 4n + 2 tt electrons. Nothing in this definition says that the number of p orbitals and the number of nr elections in those orbitals must be the same. In fact, they can he different. The 4n + 2 rule is broadly applicable to many kinds of molecules and ions, not just to neutral hydrocarbons. For example, both the cydopentadienyl anion and the cycloheptatrienyl cation are aromatic. 

According to Hiiekel s rule, turcasarin should not be aromatic, but even if the macrocycle should fulfill the (4n +2) rule for aromatic systems the lack of planarity due to the loop conformation would prevent aromatic stabilization. In fact, the existence of the loop conformation in which the whole macrocycle is twisted was demonstrated by X-ray structure analysis and NMR investigations. 

This last requirement is an important characteristic of all aromatic systems. It s known as Hilckel s rule, or the 4n + 2 rule. To apply this rule, begin by assigning 4n + 2 = number of 7 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 Hilckel number), so the last requirement to be classified as an aromatic is satisfied. Figure 6-7 contains several aromatic species with n = 1. 

These predictions indeed are borne out by many experiments, some of which we will discuss later. That the 4n + 2 rule does not apply to noncyclic systems in the same way will be seen by working Exercise 21-18d and 21-18e. 

On the basis of this result and the 4n + 2 rule, work out a mechanism for the reaction and then use this mechanism to predict what product will be formed from the Cope rearrangement of 3,4-dimethyl-1,5-hexadiene. Show your reasoning. 

We have mentioned already (Section 22-3C) the large differences in nmr chemical shifts between the inside and outside hydrogens of [18]annulene —a substance which with 18 tt electrons should be aromatic by the 4n + 2 rule. These differences are observed only at low temperatures. The proton nmr spectrum of [18]annulene at room temperature is a single resonance, which indicates that the inside (Ha) and outside (Hb) hydrogens are equilibrating rapidly. This can take place only if cis-trans interconversion occurs about the double bonds (marked c and t) ... 

This model was not cast in the terms usually used by organic chemists, and thus its adoption required considerable time. However, it led in an obvious way to the 4n+2 rule for aromaticity which has been a mainstay of organic chemists interested in the subject. It led to the prediction that the following ions would be stabilized in a fashion similar to that for benzene. 

Valence bond theory, in the terms defined by Pauling, is not able to account for the 4n+2 rule, and the properties of cyclobutadiene and cyclooctatetraene. It has been suggested that the problem with these molecules is the strain associated with the bond angles in the planar structures.10 However, this was shown to be incorrect by the observation that the addition of two electrons to cyclooctatetraene leads to the planar dianion. It is only recently that it has been recognized that cyclic permutations must be included in order to properly treat cyclic systems via valence bond theory.11 One of Pauling s few failures in structural theory is his nonrecognition of the problems associated with the 4n molecules. 

Example 7.7. Cyclo-addition reactions and the 4n + 2 rule. The predictive power of the Woodward-Hoffmann principle becomes apparent, for example, with the application to cyclo-addition reactions [32,35,36]. Consider first the dimerization of ethene to cyclobutane ... 

Both pyracyclene (133) (which because of strain is stable only in solution) and dipleiadiene (134) are paratropic, as shown by NMR spectra. These molecules might have been expected to behave like naphthalenes with outer bridges, but the outer n frameworks (12 and 16 electrons, respectively) constitute antiaromatic systems with an extra central double bond. With respect to 133, the 4n + 2 rule predicts pyracylene to be aromatic if it is regarded as a 10-7i-electron naphthalene unit connected to two 2-7t-electron etheno systems, but antiaromatic if it is viewed as a 12-7t-electron cyclododecahexaene periphery perturbed by an internal cross-linked etheno unit. Recent studies have concluded on energetic grounds that 133 is a borderline case, in terms of aromaticity-antiaromaticity charac-... 

Applications of the SHM are discussed in great detail in several books [21] here we wiU deal only with those applications which are needed to appreciate the utility of the method and to smooth the way for the discussion of certain topics (like bond orders and atomic charges) in later chapters. We will discuss the nodal properties of the MOs stability as indicated by energy levels and aromaticity (the 4n + 2 rule) resonance energies and bond orders and atomic charges. 

Thus the stabilization energy calculation agrees with the deduction from the disposition of filled MOs (i.e. with the 4n + 2 rule) that the cyclobutadiene dication should be stabilized by electron delocalization, which is in some agreement with experiment [45], More sophisticated calculations indicate that cyclic 4n systems like cyclobutadiene (where planar cyclooctatetraene, for example, is buckled by steric factors and is simply an ordinary polyene) are actually destabilized by n electronic effects their resonance energy is not just zero, as predicted by the SHM, but less than zero. Such systems are antiaromatic [17,46],... 

The Seg ion has the remarkable structure illustrated in Figure 3 (13). Although a planar monocyclic structure with 14 tt electrons would fit the 4n + 2 Rule, such a structure is ruled out by the requirement that the selenium bond angles be around 95°. The only planar structure even with bond angles as high as 105° is the following, in which two of the atoms are almost on top of each other. 

Removal of two electrons from S4N4 would yield the species S4N42, which as yet has not been identified but which may be the stable sulfur-nitrogen cationic species which forms when S4N4 is dissolved in anhydrous sulfuric acid (19), This species would be isoelectronic with the cyclo-octatetraenide ion CgHg and, because of adherence to the 4n + 2 Rule,... 

Using theoretical data, Huckel formulated the 4n + 2 rule which states that exceptional resonance stability is to be expected with ir electron systems containing 4n + 2 electrons in planar, cyclic structures, where n is an integer. This applies to a continuous series of p orbitals which are capable of effective overlapping. For example, benzene has 6, or 4(1) +2 (with n=l), if electrons. Therefore, according to Huckel s rule, benzene is aromatic and is stabilized by resonance. 

An aromatic compound is a cyclic structure that contains continuous tt electron clouds above and below the plane of the molecule. The ir clouds must also contain a total of kn+2 tt electrons, where n can be any integer. This requirement is called the 4n+2 rule or Huckel s rule and is derived from quantum mechanics. Thus, to determine whether any given compound is aromatic, first inspect the structure to see if it is cyclic and planar. Then detennine the number ofTf electrons and see if all these satisfy Kuckel s rule. 

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