Molecular system cyclic electron delocalization

The theory of molecular structure based on the topology of molecular charge distribution, developed by Bader and co-workers (83MI2 85ACR9), enables certain features to be revealed that are characteristic of the systems with aromatic cyclic electron delocalization. To describe the structure of a molecule, it is necessary to determine the number and kind of critical points in its electronic charge distribution, i.e., the points where for the gradient vector of the charge density the condition Vp = 0 is fulfilled. 

In spite of the lack of a unique and precise definition, aromaticity is one of the most frequently used concepts in (organic) chemistry. This phenomenon, which is classically associated with a cyclic tt-electron delocalization, results in a stabilization of the molecular system considered. Benzene is the archetype of the phenomenon of aromaticity. Thus, a question of interest is to what extent the amino substituent influences the electron delocalization in the ring. There are several criteria to evaluate the aromaticity, including the geometry-based (HOMA), energy-based (ASE), magnetism-based (NICS) and electronic delocalization (PDI) models. Recent theoretical evaluations65 of these parameters... 

The molecular geometry of cyclic r-electron systems is an important and readily accessible source of Information from which corresponding aromaticity indices may be easily obtained. Unlike other indices, the geometry-based aromaticity indices are applicable to both local and the global r-electron systems. They can even be applied to noncyclic systems, and their values then have an interpretation as measures of r-electron delocalization. 

A cyclic r-conjugated ribbon-like delocalized molecular system where the basis atomic orbitals are organized in a Mobius strip. In contrast to Hiickel systems, where ring orbitals have zero or an even number of phase inversions, Mobius systems are characterized by an odd number of nodes. The electroncounting rule for the stability of Mobius systems is opposite to the Huckel rule 4 -electron Mobius systems have a closed... 

ESR studies have been used extensively to characterize S-N radicals that are persistent in solution at room temperature.32 Typical radicals are cyclic C-N-S systems in which the unpaired electron occupies a delocalized re-orbital. In conjunction with molecular orbital calculations, ESR spectra can provide unique information about the electronic structures of these ring systems. 

Many aromatic compounds have considerable resonance stabilization but do not possess a benzene nucleus, or in the case of a fused polycyclic system, the molecular skeleton contains at least one ring that is not a benzene ring. The cyclopentadienyl anion C5HJ, the cycloheptatrienyl cation C7H+, the aromatic annulenes (except for [6]annulene, which is benzene), azulene, biphenylene and acenaphthylene (see Fig. 14.2.2(b)) are common examples of non-benzenoid aromatic hydrocarbons. The cyclic oxocarbon dianions C Of (n = 3,4,5,6) constitute a class of non-benzenoid aromatic compounds stabilized by two delocalized n electrons. Further details are given in Section 20.4.4. 

Cyclic systems with 4m + 2 carbon atoms are characterized by the aromatic index m. At the lowest level (m = 0) ethylene formally corresponds to a 2-membered ring. The electronic structure shown in Figure 6.1 is consistent with aromatic electron distribution. Benzene (m = 1) is the prototype of properly cyclic aromatics. The molecular o-a-m conserves the sum of atomic angular momenta. The odd couples with the screening function are delocalized around the ring, with zero o-a-m. 

Higher level molecular orbital theory can provide quantitative information about orbital energies and how strongly a molecule holds its electrons. When one compares aromatic and nonaromatic species in this way, it is found that cyclic delocalization causes the TT electrons of benzene to be more strongly bound (more stable) than they would be if restricted to a system with alternating single and double bonds. 

Like 1,3,5-hexatriene, benzene has a six-carbon tt system. The six-carbon tt system in benzene, however, is cyclic. The six p atomic orbitals combine to produce six tt molecular orbitals (Figure 7.12). Three of the MOs are bonding (i/>i, i/>2, and 1/ 3) and three are antibonding (i/>4, i/>5, and i/rg). Benzene s six tt electrons occupy the three lowest-energy MOs (the bonding MOs). The two electrons in i/>i are delocalized over the six carbon atoms. The method used to determine the relative energies of the MOs of compounds with cyclic tt systems is described in Section 15.6. 

---