4n + 2 systems, and

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. 

Figure 11.14 shows a molecular orbital diagrfflTt for cycloheptatrienyl cation. There are seven tt MOs, three of which are bonding and contain the six tt electrons of the cation. Cycloheptatrienyl cation is a Hiickel (4n + 2) system and is an aromatic ion. 

Obviously, there can be no ring of two carbon atoms though a double bond may be regarded as a degenerate case. However, in analogy to the tropylium ion, a three-membered ring with a double bond and a positive charge on the third atom (the cyclopropenyl cation) is a 4n + 2 system and hence is expected to show aromaticity. The unsubstituted 80 has been prepared,as well as several derivatives, e.g.,... 

A second isomer of [lOJannulene (the cis trans cis cis trans stereoisomer) can have bond angles close to 120° but is destabilized by a close contact between two hydro gens directed toward the interior of the ring To minimize the van der Waals strain between these hydrogens the nng adopts a nonplanar geometry which limits its ability to be stabilized by tt electron delocalization It too has been prepared and is not very stable Similarly the next higher (4n + 2) system [14]annulene is also somewhat desta bilized by van der Waals strain and is nonplanar... 

The thiirene oxide system is of particular interest due to it being simultaneously both a potentially nonbenzenoid aromatic (4n + 2)n and antiaromatic 4nn Hiickel system. 

A particularly attractive group of substrates are the annulenes, since electron transfer allows an interconversion of (4n + 2)n- and (4n)rr-systems, and thus a switch between 7>bond delocalization and rc-bond localization (Mullen, 1984). 

We know that aromatic compounds, polynuclear and heterocyclic compounds follow Huckel s rule in which they have a (4n + 2) system of n electrons and the protons attached to such systems are extremely deshielded due to the circulating sextet of n electrons. As a result, the signals of aromatic protons appear at a very low field than those observed even for benzene. The tau value of benzene is T = 2.63. From this the aromaticity of a compound can be verified. 

Dianions of several of the large ring annulenes have also been prepared.23 The 4n + 2 system [18]annulene, which has outer protons at 8 = +9.3 ppm and inner protons at S = — 3 ppm, is converted by potassium to the dianion, a 4n system with outer protons at S = — 1 ppm and inner protons at S = +29 ppm, the lowest field resonance known for a proton bound to carbon. (The largest known upfield shift, S = — 9 ppm, occurs for the inner protons of an 18 7r electron (4n + 2) monoanion.24)... 

If we analyze the case of hexatriene to cyclohexadiene conversion, the situation is just the reverse. The thermal reaction should be disrotatory and the photochemical reaction conrotatory. The butadiene belongs to (4n)it system and hexadiene to (4n + 2)7 system, and a generalization of the systems may be attempted. 

To summarize thermal supra-supra or antara-antara cycloadditions are allowed for systems having 4n + 2 electrons and supra-antara or antara-supra cycloadditions for systems having 4n electrons. 

NMR). Note the trans-trans-cis double bonds all bond angles can be 120 . [20]annulene presumably could become planar (it isn t quite) but since it is a 4n p electron system rather than a 4n + 2 system, it is not aromatic and the structure shows localized single and double bonds. 

Fig. 20. In comparing the [12]cyclacene 50 with the angular derivative 70, the introduction of [a,c]-fusion may lead to an increase in electronic stability. If each cyclacene is viewed as two independent annulenes, joined by a series of cr-bonds, then 70 represents a situation in which both annulenes — inner and outer rims with 22 and 26 n-electrons, respectively — correspond to Hiickel-type [4n + 2] systems...

J. Whittal, 4n + 2 Systems Fulgides, in H. Durr and H. Bouas-Laurent, Eds., Photochromic Molecules and Systmes, Elsevier, Amsterdam, 1990. 

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. 

There is now no doubt that 4n + 2 systems are aromatic if they can be planar, although 97 and 113 among others, demonstrate that not all such systems are in fact planar enough for aromaticity. The cases of 109 and 111 prove that absolute planarity is not required for aromaticity, but that aromaticity decreases with decreasing planarity. 

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