Htickel 4/ + 2 rule

Benzene is described by molecular orbital theory as a planar, cyclic, conjugated molecule with six it electrons. According to the Htickel rule, a molecule must have 4n + 2 77 electrons, where n - 0, 1, 2, 3, and so on, to be aromatic. Pianar, cyclic, conjugated molecules with other numbers of tt electrons are antiaromatic. 

Aromaticity is associated with cyclic arrays of mobile electrons with favourable symmetries. The mobile electron arrays may be n, o or mixed in character16. The 4n +2/4n Htickel rule provides a quantum mechanical framework which allows one to relate the stability and structure of jr-systcms to their --electron count, and is widely utilized for classifying jr-cyclic systems as aromatic or antiaromatic13. 

Problem 10.10 Use the Htickel rule to indicate whether the following planar species are aromatic or antiaromatic ... 

Hosoya, H., Hosoi, K. and Gutman, I. (1975a). A Topological Index for the Total jt-Electron Energy. Proof of a Generalized Htickel Rule for an Arbitrary Network. Theor.Chim.Acta, 38, 37-47. 

If the ring were sufficiently large that the twist between individual orbitals was small, such a system would not necessarily be less stable than the normal array of atomic orbitals. This same analysis points out that in such an array the Htickel rule is reversed and aromaticity is predicted for the An rr-electron systems. 

The relative stability of the anions derived from cyclopropene and cyclopentadiene by deprotonation is just the reverse of the situation for the cations. Cyclopentadiene is one of the most acidic hydrocarbons known, with a pK of 16.0. The pA s of triphenylcyclopropene and trimethylcyclopropene have been estimated as 50 and 62, respectively, using electrochemical cycles (see Section 6.1). The unsubstimted compound would be expected to fall somewhere between and thus must be about 40 powers of 10 less acidic than cyclopentadiene. MP2/6-311-i-G(2fi(/,2pfi() and B3LYP/6-3ll+G(2df,2pd) calculations indicate a small destabilization of the cyclopropenyl anion, relative to the cyclopropyl anion. Thus the six Tr-electron cyclopentadienide anion is enormously stabilized relative to the four ir-electron cyclopropenide ion, in agreement with the Htickel rule. 

The Htickel rule predicts aromaticity for the six Tr-electron cation derived from cycloheptatriene by hydride abstraction and antiaromaticity for the planar eight TT-electron anion that would be formed by deprotonation. The cation is indeed very stable, with a pA r+ of +4.7. Salts containing the cation can be isolated as a result of a variety of preparative procedures. On the other hand, the pK of cycloheptatriene has been estimated at 36.This value is similar to normal 1,4-dienes and does not indicate strong destabilization. The seven-membered eight Tr-electron anion is probably nonplanar. This would be similar to the situation in the nonplanar eight TT-electron hydrocarbon, cyclooctatetraene. 

The history of carbocations dates back to 1891 when G. Merhng reported that he added bromine to tropylidene (cycloheptatriene) and then heated the product to obtain a crystalline, water-soluble material, C H Br. He did not suggest a structure for it however. Doering and Knox convincingly showed that it was tropylium (cycloheptatrienyhum) bromide (Figure 2.2). This ion is predicted to be aromatic by the Htickel rule. 

Perhaps the most notable difference between S-N and N-O compounds is the existence of a wide range of cyclic compounds for the former. As indicated by the examples illustrated below, these range from four- to ten-membered ring systems and include cations and anions as well as neutral systems (1.14-1.18) (Sections 5.2-5.4). Interestingly, the most stable systems conform to the well known Htickel (4n -1- 2) r-electron rule. By using a simple electron-counting procedure (each S atom contributes two electrons and each N atom provides one electron to the r-system in these planar rings) it can be seen that stable entities include species with n = 1, 2 and 3. 

Based on these results, which ion, if either, appears to be resonance stabilized How does Htickel s rule describe these ions ... 

Housefly, sex attractant of, 255 HPLC, 432 Hiickel, Erich, 523 Htickel 4/j + 2 rule, 523... 

The next example for this rule may be the heterolytic addition of chlorine to the C=C bond. Fig. 4.3b indicates the partial valence-inactive population 60> of the 2pz AO of the /9-carbon in LU, calculated by the extended Htickel method. It is seen that this quantity, (c )2, largely increases according to the approach of the chlorine cation to the carbon atom at which the addition is to take place, so that the reactivity of the /9-position towards the second chlorine atom (anionic species) grows. Also Fig. 4.3a shows the decrease of the LU energy in the direction of the reaction path which has already been mentioned above. 

The investigation of [18]annulene is the oldest of the X-ray annulene studies reported, and it was stated that the hydrogens have not been reliably located. The molecular structure closely resembles that of coronene89. This rules out the possibility of a structure with alternate long and short C—C bonds. The observed spread of CC distances in [14]annulene and in [18]annulene is ca 0.06 A, while that in [16]annulene is twice as large, ca 0.12 A. The annulene molecules therefore have structures that are similar to what is expected on the basis of Htickel s rule. 

The phthalocyanine [1-4] system is structurally derived from the aza-[18]-annulene series, a macrocyclic hetero system comprising 18 conjugated n-electrons. Two well known derivatives of this parent structure, which is commonly referred to as porphine, are the iron(III)complex of hemoglobin and the magnesium complex of chlorophyll. Both satisfy the Htickel and Sondheimer (4n + 2)- electron rule and thus form planar aromatic systems. 

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

In 1931, Erich Htickel postulated that monocyclic (single ring) planar compounds that contained carbon atoms with unhybridized atomic p orbitals would possess a closed bond shell of delocalized n electrons if the number of n electrons in the molecule fit a value of 4 + 2 where n equaled any whole number. Because a closed bond shell of n electrons defines an aromatic system, you can use Hiickel s Rule to predict the aromaticity of a compound. For example, the benzene molecule, which has 3 n bonds or 6 n electrons, is aromatic. 

In 1930, when Htickel first derived his rule, he considered only aromatic annulenes. Antiaromatic and nonaromatic systems are extensions introduced by later authors, in particular by Dewar. 

Cyclooctatetraene is [8]annulene, with eight pi electrons (four double bonds) in the classical structure. It is a (41V) system, with N = 2. If Htickel s rule were applied to cyclooctatetraene, it would predict antiaromaticity. However, cyclooctatetraene is a stable hydrocarbon with a boiling point of 153 °C. It does not show the high reactivity associated with antiaromaticity, yet it is not aromatic either. Its reactions are typical of alkenes. 

Cyclooctatetraene would be antiaromatic if Htickel s rule applied, so the conjugation of its double bonds is energetically unfavorable. Remember that Htickel s rule applies to a compound only if there is a continuous ring of overlapping p orbitals, usually in a planar system. Cyclooctatetraene is more flexible than cyclobutadiene, and it assumes a nonplanar tub conformation that avoids most of the overlap between adjacent pi bonds. Hiickel s rule simply does not apply. 

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