Electron delocalization index

Magnetic susceptibility anisotropy has been used to estimate relative aromaticities of some azines <1977JOC897>. If the extent of -electron delocalization for benzene is taken as 1.0, the corresponding values for azines are pyridine 0.7, pyridazine 0.7, pyrimidine 0.5, and 1,3,5-triazine 0.3. Another quantitative magnetic index is the exaltation of the total magnetic susceptibility (A). All aromatic systems reveal large A values, whereas for nonaromatic compounds A is close to zero and it is assumed that aromaticity increases with A. For six-membered monocycles the following values of A have been reported (in units of cm3 mol-1 x —106) benzene (17.9), pyridine (18.3), pyridazine (8.7), pyrimidine (18.2), pyrazine (12.7), l-ethyl-2-pyridone (13.0), and 1,3,5-triazine (19.0). 

Flygare et al. advocated the utilization of diamagnetic anisotropy, Xaniso> atid the susceptibility component perpendicular to the ring plane, x%% <1974CRV653, 1971JA5591>. However, it has been pointed out that electron delocalization influences only the out-of-plane component of the susceptibility and that the local and nonlocal contributions to Xaniso must be differentiated and only the latter can constitute aromaticity indexes <1973JA7961, 1974TL2885>. 

An interesting comparison between several aromaticity indices (harmonic oscillator model, nucleus-independent chemical shift, para-delocalization index, aromatic fluctuation index, multicenter indices, atoms-in-molecules theoretical indices and graph-theoretical indices) concluded that the most reliable ones are based on electron delocalization (08JCC1543). 

In the same way as the a, -separation has been performed, one can proceed to a cr, rr-separation.52 This separation has been used to evaluate the aromaticity of organic molecules and clusters. An index of aromaticity was proposed using a scale based on the bifurcation analysis of the ELF constructed from the separated densities. In principle, the total ELF has no information about tt and cr bonds, it depends only on the total density. Hence, the ELF does not show clear differences between both kinds of bonds. However, the topological analysis over separated densities, ones formed by the rr-orbitals and the other ones formed by the cr-orbitals, yields the necessary information.52 Of course, this is possible only for the molecules which present the cr, tt symmetries, i.e. planar molecules. The bifurcation analysis of the news ELFW and ELFCT can be interpreted as a measure of the interaction among the different basins and chemically, as a measure of electron delocalization.45 In this way, the tt and a aromaticity for the set of planar molecules described in the Scheme 1 has been characterized.52... 

The [la,3s] sigmatropic shift of the fluorine atom in the 3-fluorpropene system has been also previously discussed in detail. The transition state has been thoroughly characterized in terms of a ion-pair structure with a charge separation of 0.6e, and the changes in the bonding characteristics along the intrinsic reaction coordinate reaction (IRC) path (see Schemes 5a and 5b) were described in terms of the ELF basin properties, i.e. electron populations, variance and delocalization indexes.84... 

The electronic nature of the 3c-2e bonding of the 2-norbomyl cation and its 2,2-difluoro-substituted derivative (144) has been studied by Esteves and coworkers (B3LYP/6-311-I-I-G level). " The delocalization index (DI) and the C(l)-C(6) and C(l)-C(2) bond lengths (DI = 0.5 and 1.895 A, respectively, for each bond) clearly show the delocalized 3c-2e bonding. Data for the... 

The Grabowski index, Arp, describes rr-electron delocalization as a consequence of the intramolecular H-bond formation. To define Arp parameter the geometry of the so-called open conformation is needed—the situation when the intramolecular H-bond does not exist and this system is a reference state. Figure 6 presents the dependence of HOMA on resonance parameter Arp on HOMA. 

Moreover, the mean of all DI of poro-related carbons in a given six-membered ring, called Para-Delocalization Index (PDI), has been defined as an aromaticity criterion based on electron delocalization. This index is closely related to NICS and HOMA indices the higher the PDI indices the higher the absolute value of NICS and the higher the HOMA values, thus reflecting greater aromaticity. 

Poater, J., Eradera, X., Duran, M. and Sola, M. (2003b) The delocalization index as an electronic aromaticity criterion application to a series of planar polycyclic aromatic hydrocarbons. Chem. Eur. /., 9, 400 06. 

Zahradnlk et al.160 have combined a set of parameters which may be regarded as aromaticity indices into the stability index. The approach is more comprehensive than that of Balaban, but as the authors point out it is obviously difficult to assess the relative importance of the selected indices. Those included are the specific delocalization energy DE,P34 (Section II, A,3,a) related to the extent of -electron delocalization, Aq the difference between the maximum and minimum ir-electron density in the molecule (related to the reactivity toward nucleophilic and electrophilic reagents see the preceding section), the free valence F (related to radical reactivity) and the radical super-delocalizability ST (related to radical reactivity, oxidizability, and reducibility). 

Chermahini et al. (2007JMST(822)33) also studied substituent effects on the aromaticity (expressed by HOMA and NICS indices) of anionic and protonated forms of C5-X tetrazole derivatives (with X = NH2, OH, OMe, SMes, H, Me, F, Cl, BH2, CF3, CN, NO, and NO2). They have shown that the stability order of protonated forms is related to the nature of the substituent. For electron-withdrawing substituents, the stability follows the sequence 1,3-H > 1,4-H > 2,3-H > 1,2-H, but in the case of electron-donating groups the order of the stabihty changes to 1,4-H > 1,3-H > 1,2-H > 2,3-H. NICS(O) values suggest that the anionic forms of tetrazoles are less aromatic than IH- tautomers, whereas the obtained NICS(l) and HOMA values indicate that the aromaticity of anionic forms lies between those found for IH- and 2H- tautomeric forms. In the case of protonated tetrazole derivatives, the most aromatic are the 2,3-H forms, whereas 1,4-H tautomers are the least aromatic. Based on the HOMA index analysis the authors concluded that the aromaticity of protonated systems can be related to the nature of the substituent. However, a closer look on their results suggests that the Tt-electron delocalization of all the studied protonated systems hardly depends on the nature of the substituent at the position C5. 

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