Hiickel 4/ + 2 rule

Hiickel s MO work [4] in this area of course stands preeminent. But it has been much elaborated first, as regards the possibility of a Mobius cycle (with one P 0) whence [39,41] the electron-count conditions for stability and reactivity are interchanged, as indicated in Table 1 following second, as regards the interpretation of Huckel rule as a basis for the Woodward-Hoffmann rules (at least for electrocyclic reactions) and third, as regards the rules applicability [39] to cycles even when embedded in more extensive n-networks. 

Mobius cycle open shell closed shell 

The relevant VB-theoretic work seems less well known, with a first important result being with the work of Fischer Murrell [42 ], which however is focused on the ionic case with the electron- and site-count being different. Basically they note a correspondence between the VB many-body basis states with net charges moved around and the AO basis of the 1 -electron MO-model with electrons moved around. 

The VB work of Oosterhoff et al [43] is relevant also to the neutral case but makes use of the non-orthogonalized VB model. Epiotis [44] also deals with the general case, possibly utilizing anti-orthogonalized AOs. Basically these workers note (beyond the exchange permutations) the importance of the cyclic permutations around the cycle, such as typically are discarded in the lowest order derivations to the Pauling-Wheland VB model. The inclusion of such terms is crucial most especially for 4-cycles - and such corrected models for quantitative work are available [33]. 

Indeed this is a theorem for the simple VB model [49] as well as the half-filled Hubbard model [50]. A related type of result applies [51] for Ji-network species decorated with carbene groups. Such results enable one to easily imagine various possibilities for high-spin species, as early noted by Ovchinnikov [52]. 

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Anions of small heterocyclics are little known. They seem to be involved in some elimination reactions of oxetan-2-ones (80JA3620). Anions of large heterocycles often resemble their acyclic counterparts. However, anion formation can adjust the number of electrons in suitable systems so as to make a system conform to the Hiickel rule, and render it aromatic if flat geometry can be attained. Examples are found in Chapter 5.20. Anion formation in selected large heterocycles can also initiate transannular reactions (see also Section 5.02.7 below). 

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

The term annulene was coined to refer to the completely conjugated monocyclic polyenes. The synthesis of annulenes has been extended well beyond the first two members of the series [4]annulene (cyclobutadiene) and [6]annulene (benzene). The generality of the Hiickel rule can be tested by considering the properties of members of the annulene series. 

Aimulene offers a particularly significant test of the Hiickel rule. The internal cavity in [18]annulene is large enough to minimize steric interactions between the internal hydrogens in a geometry that is free of angle strain. Most MO calculations find the delocalized structure to be more stable than the polyene. ... 

The Hiickel rule predicts aromaticity for the six-7c-electron cation derived from cycloheptatriene by hydride abstraction and antiaromaticity for the planar eight-rc-electron anion that would be formed by deprotonation. The cation is indeed very stable, with a P Cr+ of -1-4.7. ° Salts containing the cation can be isolated as a product of a variety of preparative procedures. On the other hand, the pK of cycloheptatriene has been estimated at 36. ° This value is similar to those of normal 1,4-dienes and does not indicate strong destabilization. Thus, the seven-membered eight-rc-electron anion is probably nonplanar. This would be similar to the situation in the nonplanar eight-rc-electron hydrocarbon, cyclooctatetraene. 

In agreement with the Hiickel rule those annulenes and dehydroannulenes which contain (4 n + 2) 77 electrons and a reasonably planar carbon skeleton appear to be aromatic. Aromaticity in annulenes is usually equated with positive resonance energy and the absence of bond alternation. The most direct method of measuring bond alternation is by single crystal X-ray diffraction. Unfortunately this method has been applied in only a few cases. 

Both cases with n = 0 and n = 1 in the Hiickel rule of 4n+2 jr-electrons can be achieved for four-member ed heterocyclic rings. However, the stability of the resulting system is low in either case, owing to ring strain, the adjacency of two X- or Z-type atoms, or the mesoaromatic character when such heteroatoms are not adjacent, as in 1,3-diborete. 

Hirsch and co-workers calculated NICS values for tetrahedral clusters of N, P, As, Sb, and Bi, as well as for the corresponding tetra-anions composed of Si, Ge, Sn, or Pb atoms, finding diatropic values for 2,n(n 1) jr-systems.296a b It was postulated by Hirsch, Schleyer, and their co-workers that for icosahedral fullerenes and their hetero-analogues the Hiickel rule, involving 4/2+2 //-electrons, should be replaced by the 2(/2+l)2 electron rule.296... 

The graph-theoretical 4N + 2 Hiickel rule analogy with the aromaticity of two-dimensional polygons requires that N = 0 in all the three-dimensional deltahedra. The Jemmis-Schleyer interstitial electron rule [55], originally introduced for nido half-sandwich species, also relates the 4N + 2 Hiickel rule to the delocalized deltahedra directly In this treatment, N is typically 1. 

Hirsch s rule has more limited applicability than the Hiickel rule. However, the 2(n +1)2 concept has been used very successfully to interpret relative fullerene stabilities [66], and to suggest new systems, including neutral and charged non-fullerene carbon [67] and homoaromatic cages [68]. All these species have large NICS values in their centers and satisfy other criteria of aromaticity. 

Williams [1] has given an excellent review on Early Carboranes and Their Structural Legacy and he defines carboranes as follows Carboranes are mixed hydrides of carbon and boron in which atoms of both elements feature in the electron-deficient polyhedral molecular skeleton . According to the electron counting rules [2] for closo- (2n + 2 SE), nido- (2n + 4 SE) and arachno-clusters (2n + 6 SE SE = skeletal electrons, n = number of framework atoms) and the An + 2 n electron Hiickel rule, small compounds with skeletal carbon and boron atoms may have an electron count for carboranes and for aromatics (see Chapters 1.1.2 and 1.1.3). 

Problem 10.7 Cyclooctatetraene (CgH ), unlike benzene, is not aromatic it decolorizes both dil. aq. KMnO and Brj in CCI4. Its experimentally determined heat of combustion is -4581 kJ/mol. (a) Use the Hiickel rule to account for the differences in chemical properties of CgHg from those of benzene, (b) Use thermochemical data af Problem 10.4 to calculate the resonance energy, (c) Why is this compound not antiaromatic (d) Styrene, CgH5CH==CH2, with heat of combustion —4393 kJ/mol, is an isomer of cyclooctatetraene. Is styrene aromatic ... 

The solubility properties suggest that these compounds are salts. The stability of the organic ions formed indicates that they conform to the Hiickel rule and are aromatic. 

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

In principle, recently published19 rules for writing structural formulas have been adhered to in the present review with the one exception that a full circle in the cycle is used to denote not only a 7r-electron sextet but any number of 7r-electrons consistent with the Hiickel rule in general. 

In accord with the Hiickel rule of 4/t + 2 electrons, both cyciobutadiene and cyclooctatetraene (cot) are nonaromatic. Cyclooctatetraene contains alternating bond lengths and has a tub-shaped conformation ... 

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