Hiickel s rule

Heterocyclics with seven and more ring members display an enormous variety of shapes. Bond lengths are often close to those of open chain counterparts, but bond angles can be greatly different. Aromaticity is possible where the conditions of planarity and Hiickel s rule are met, but the majority of fully unsaturated large heterocycles are not aromatic (see below). 

The tropylium and the cyclopropenyl cations are stabilized aromatic systems. These ions are arumatic according to Hiickel s rule, with the cyclopropeniiun ion having two n electrons and the tropyliiun ion six (see Section 9.3). Both ring systems are planar and possess cyclic conjugation, as is required for aromaticity. 

Table 9.1. Hiickel s Rule Relationships for Charged Species...

One of molecular- orbital theories early successes came in 1931 when Erich Hiickel discovered an interesting pattern in the tt orbital energy levels of benzene, cyclobutadiene, and cyclooctatetraene. By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar- geometries, Hiickel found that whether a hydrocar bon of this type was aromatic depended on its number of tt electrons. He set forth what we now call Hiickel s rule ... 

Hiickel proposed his theory before ideas of antiaiomaticity emerged. We can fflnplify his generalization by noting that among the hydrocarbons covered by Hiickel s rule, those with (4n) tt electrons not only are not aromatic, they are antiaromatic. 

Benzene, cyclobutadiene, and cyclooctatetraene provide clear- examples of Hiickel s rule. Benzene, with six tt electrons is a (4n + 2) system and is predicted to be aromatic by the rule. Square cyclobutadiene and planar- cyclooctatetraene are 4n systems with four and eight tt electrons, respectively, and are antiarornatic. 

In the next section we ll explore Hiickel s rule for values of n greater than 1 to see how it can be extended beyond cyclobutadiene, benzene, and cyclooctatetraene. 

Most of the synthetic work directed toward the higher annulenes was caiiied out by Franz Sondheimer and his students, first at Israel s Weizmann Institute and later at the University of London. Sondheimer s research systematically explored the chemistry of these hydrocarbons and provided experimental verification of Hiickel s rule. 

Hiickel s rule is now taken to apply to planar-, monocyclic, completely conjugated systems generally, not just to neutral hydrocarbons. 

Section 11.19 An additional requiiement for aromaticity is that the number of tt electrons in conjugated, planar, monocyclic species must be equal to An + 2, where n is an integer. This is called Hiickel s rule. Benzene, with six TT electrons, satisfies Hiickel s rule for n =. Square cyclobutadiene (four TT electrons) and planar- cyclooctatetraene (eight tt electrons) do not. Both are examples of systems with An tt electrons and are antiaromatic. 

Hiickel s rule (Section 11.19) Completely conjugated planar monocyclic hydrocarbons possess special stability when... 

Hiickel s rule states that planar cyclic 71 systems involving 4n+2 electrons will be unusually stable ( aromatic ), while cyclic 7i systems with 4n electrons will be unstable ( antiaromatic ). 

Hiickel s rule tells us that eyelooetatetraene (CgHs) should be quite unlike benzene (C Hf,). 

Porphyrin systems therefore obey Hiickel s rule in having An + 2 n = A) TT-electrons in a planar, cyclic, conjugated array. Both major tautomeric forms have delocalization pathways with opposite N-Hs (trails tautomers), as shown in 71a 71b. It is already known (76AHCS1) that tautomers with inner hydrogens adjacent (cis tautomers) are much less stable, playing an important role only in the mechanism of proton transfer in porphyrins and phthalocyanines. 

Chlorocyclopropene. on treatment with AgBF4, gives a precipitate of AgCl and a stable solution of a product that shows a single HNMR absorption at 11.04 8. What is a likely structure for the product, and what is its relation to Hiickel s rule ... 

Draw an energy diagram for the three molecular orbitals of the cyclopropenyl system (C l I3). How ate these three molecular orbitals occupied in the cyclopropenyl anion, cation, and radical Which of the three substances is aromatic according to Hiickel s rule ... 

Thiepin, as a seven-membered conjugated system with sulfur as heteroatom, is a member of the 8 7t-electron heteroannulenes which are antiaroinatic according to Hiickel s rule. In contrast to oxepin, thiepin is not stable at room temperature and no valence isomerism with an arene sulfide has been observed. Stable thiepins are obtained only when two bulky substituents, e.g. /ert-butyl, are introduced into positions 2 and 7. In benzothiepins the annellation effect of the aromatic rings contributes decisively to the stability of these compounds stability increases with an increasing number of fused benzene rings. 

Although [34]octaphyrin 80 fulfills Hiickel s rule, the II NMR spectrum indicates by the high-field shift of the methine protons that the system is nonaromatic. The X-ray structure analysis demonstrates clearly the reason for the lack of aromatic stabilization, namely the nonplanar loop conformation in which the whole macrocycle is twisted similarly to the [32]octaphyrin structure and which is also found for [36]octaphyrin and [40]decaphyrin structures (vide infra). 

The most obvious compound in which to look for a closed loop of four electrons is cyclobutadiene (52). Hiickel s rule predicts no aromatic character here, since 4 is not a number of the form 4 + 2. There is a long history of attempts to prepare this... 

It is strong evidence for Hiickel s rule that 59 and 60 are not aromatic while the cyclopropenyl cation (55) and the cyclopentadienyl anion (39) are, since simple resonance theory predicts no difference between 59 and 55 or 60 and 39 (the same number of equivalent canonical forms can be drawn for 59 as for 55 and for 60 as for 39). 

There are three geometrically possible isomers of [lOJannulene the all-cis (71), the mono-trans (72), and the cis-trans-cis-cis-trans (54). If Hiickel s rule applies, they should be planar. But it is far from obvious that the molecules would adopt a planar... 

In the 1930 s HiickeP proposed, on the basis of molecular-orbital calculations, a theoretical criterion for aromaticity of cyclic polyenes, known as Hiickers rule, which states that cyclic polyenes should be aromatic if, and only if, they contain 4n- -2 Jt-electrons. At that time only two of such cyclic polyenes were known benzene and cyclo-pentadienyl anion, each having six rc-electrons and satisfying Huckel s rule. Since then, the validity of Hiickel s rule had not been challenged... 

Though these substances are not monocyclic like benzene—and Hiickel s rule should not, strictly, apply to them—the introduction of the transannular bond, that makes them bi- and tricyclic, respectively, seems to cause relatively little perturbation, so far as delocalisation of the n electrons over the cyclic group of ten or fourteen carbon atoms is concerned. 

Results from X-ray studies of three annulenes are presented In Table 8. According to Hiickel s rule [14]annulene (14-ANN) and [18]annulene (18-ANN) should be aromatic and most probably planar molecules, while [16]annulene (16-ANN), as a [4n]annulene, should be antiaromatic. The [14]annulene molecule is nonplanar, with a structure that approaches C2h symmetry. The cause of the nonplanarity is the steric overcrowding in the center of the molecule. While the spread of the individual bond lengths implies possible significant differences, there is no significant pattern to the values obtained. 

In general, linear 7r-electron systems with Z1r = 2N electrons at the lowest energy levels have closed-shell singlet states while cyclic systems reach closed shell structures only when ZT = 4N + 2. Cyclic 7r-electron systems with Zn 4N + 2 will therefore exhibit multiplet ground states according to Hund s rules, and should be chemically reactive because of the unpaired electrons. Hiickel s rule that predicts pronounced stability for so-called aromatic ring systems with 4jV + 2 7r-electrons is based on this shell structure. The comparison with cyclic systems further predicts that ring closure of linear 7r-electron systems should be exothermic by an amount... 

A rule for helping to predict if a monocyclic planar system of delocalized tt electrons will exhibit aromatic character. The ring system will be aromatic if the number of delocalized tt electrons equals 4n -h 2 where nisa positive integer or zero. For example, the ring system in phenylalanine obeys Hiickel s rule. See Aromaticity... 

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