Aromaticity 4« + 2 rule

In this method, the orbital symmetry rules are related to the Hiickel aromaticity rule discussed in Chapter 2. Huckel s mle, which states that a cyclic system of electrons is aromatic (hence, stable) when it consists of 4n + 2 electrons, applies of course to molecules in their ground states. In applying the orbital symmetry principle, we are not concerned with ground states, but with transition states. In the present method, we do not examine the molecular orbitals themselves but rather the p orbitals before they overlap to form the MO. Such a set of p orbitals is called a basis set (Fig. 15.5). In investigating the possibility of a concerted reaction, we put the basis sets into the position they would occupy in the transition state. Figure 15.6 shows this for both the... 

Figure 3. GGA and LDA equilibrium structures of cage-Uke (Au ) and amorphous-like (Au ) type for several Au clusters with magic numbers fulfilling the spherical aromaticity rule n=2(L- -l), where L is an integer number (see text).

The Dewar PMO (perturbational MO) method9 avoids calculations by making clever use of alternants. The idea is to divide a molecule formally into two alternant radicals, whose recombination is studied. When the radicals are different, only their NBMOs lie at the same energy (Figure 3.4). Hence their interaction provides almost all of the recombination energy. The other interactions, which are second order in PAB, can then be neglected. We will illustrate the method by deriving the aromaticity rules. 

The so-called aromaticity rules are chosen for comparison, as they provide a beautiful correspondence with the symmetry-based Woodward-Hoffmann rules. A detailed analysis [92] showed the equivalence of the generalized Woodward-Hoffmann selection rules and the aromaticity-based selection rules for pericyclic reactions. Zimmermann [93] and Dewar [94] have made especially important contributions in this field. 

The word aromaticity usually implies that a given molecule is stable, compared to the corresponding open chain hydrocarbon. For a detailed account on aromaticity, see, e.g., Reference [95], The aromaticity rules are based on the Hiickel-Mobius concept. A cyclic polyene is called a Hiickel system if its constituent p orbitals overlap everywhere in phase, i.e., the p orbitals all have the same sign above and below the nodal plane (Figure 7-23). According to HiickeTs rule [96], if such a system has 4n + 2 electrons, the molecule will be aromatic and stable. On the other hand, a Hiickel ring with 4n electrons will be antiaromatic. 

The Dewar aromaticity rule just cited holds if a considered cycle possesses (An -f 2) ji-centres and does not if the number of jx-centres equals An, whence follows. .. 

Dewafr-Huckel aromaticity rule. In a polycyclic alternant hydrocarbon a cycle with (4n + 2) n-centres is aromatic whereas a cycle with An jt-centres is anti-aromatic. 

Anti-Hiickel aromaticity. The aromaticity rules for anti-Hiickel systems are opposite to those for conventional (Hiickel) systems (Table 9). 

Fowler, P. W. Rzepa, H. S. Aromaticity rules for cycles with arbitrary numbers of half-twists, Phys. Chem. Chem. Phys. 2006, 8, 1775-1777. 

The directly bonded C—coupling constants have been used to give a measure of aromaticity in mono- and polycyclic hydrocarbon ring systems.Cyclo-octatetraene reacts with methylene dichloride and methyl-lithium to afford a mixture of syn and anti-9-chlorobicyclo[6,l,0]nona-2,4,6-triene (40 and 41) which, on treatment with a 30% lithium dispersion in tetrahydrofuran, gives cyclonona-tetraenide, which is isolated as the tetraethylammonium salt. The chemical shift and the coupling constant (7i3c-ih = 137 c./sec.) observed for the lithio-salt (42) are indicative of the aromatic character of the ring, in accord with the predictions of Hiickel s Aromaticity rule. 

The Woodward-Hoffmann orbital symmetry rules are not limited in application to the neutral polyene systems that have been discussed up to this point. They also apply to charged systems, just as the Htickel aromaticity rule can be applied to charged ring systems. The conversion of a cyclopropyl cation to an allyl cation is the simplest... 

The above-mentioned Dnp-aromatic rule was extended to anilides of aliphatic Dnp-a-amino acids (Kawai and Nagai, 1977 Nagai, 1979). Anilides of Dnp-L-alanine (35) are regarded as analogs of Dnp-o-phenylalanine (36). The replacement of jS-CH2— and —COOH groups of 36 with —CONH— and —CH3 groups, respectively, gives 35. The CD spectral pattern of 35 is very similar to that of 36. Most measurements were carried out with 4-methoxyaniline derivatives. The CD spectra show a similar pattern between... 

Kawai et al (1978) have thoroughly discussed the chiroptical properties of Dnp derivatives of aromatic a-amino acids and related compounds. In summary, the Dnp-aromatic rule, which was originally found for Dnp derivatives with aromatic side chains, has been extended to compounds of general formulas 37 and 38. Here, R is an alkyl or other group containing no aromatic... 

Kawai et al. (1978) also reported that their earlier interpretation (Kawai and Nagai, 1974 Kawai et ai, 1975b) of the shape of the CD spectra of Dnp derivatives of aromatic amino acids via the exciton coupling of the transition moments of Dnp and the aromatic chromophore was not confirmed by an nmr study. Although this does not change the practical applicability of the Dnp-aromatic rule, it is now believed that the characteristic chiroptical properties of 37 can be rationalized by two probable conformers (39a and 39b). The relative arrangements of the Dnp and aromatic chromophores in... 

A benzene-like intersection exists also for [18]annulene (Scheme 13) that, similarly to benzene, obeys to the Hiickel 4n - - 2 aromaticity rule. In fact, the annulene Si/Sq intersection has a -(CH)3- kink feature, a... 

Nguyen Trong Anh The Use of Aromaticity Rules, Frontier Orbitals and Correlation Diagrams Some Difficulties and Unsolved Problems. In R. Daudel (ed.) Quantum Theory and Chemical Reactions. Reidel, Dordrecht 1980, pp. 177-89. 

Like pyridine and imidazole, pyrrole is an aromatic heterocycle, but it is not nearly as basic as pyridine or imidazole. Pyrrole s lack of base strength can be understood by noticing that the lone pair on the nitrogen atom is in a 2p orbital and is part of the aromatic sextet of electrons. As a consequence, a protonated pyrrole cannot maintain aromaticity because the protonated nitrogen would be sp hybridized and there would be only 4 tt electrons remaining (in violation of two of Hiickel s aromaticity rules). A loss of aromaticity is energetically very costly and severely limits the ability of pyrrole to accept a proton despite its structural similarity to pyridine and imidazole. 

Rappaport SM, Rzepa HS (2008) Intrinsically chiral aromaticity. Rules incorporating linking number, twist, and writhe for higher-twist Mobius annulenes. J Am Chem Soc 130 7613-7619... 

TABLE 4.9 The Same Check for the Present Aromaticity Rules As in Table 4.8 - Yet Here for the Chemical Hardness Based-Aromaticity Scale (Putz, 2010a)... 

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