Delocalization index

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). 

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... 

In order to compare the global hardness as an all-metal aromaticity descriptor, we determine other quantities employed to evaluate aromaticity. The delocalization index (DI, 8 in Equation i)35,36 is derived from Bader s atoms-in-molecules (AIM) theory37 from the exchange-correlation density matrix (Txc) ... 

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 degree of jt-delocalization between atoms A and B was quantified in the framework of the —> AIM theory, by the delocalization index DIab, which is defined as ]Poater, Fradera et al., 2003a, 2003b Poater, Garcia-Cruz et al., 2004 Krygowski, Ejsmont et al., 2004]... 

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. 

Para-Delocalization Index delocalization degree indices (0 Delocalization Index)... 

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. 

Another computational study of aromaticity was based on -center delocalization indexes ( -DIs) and led to the conclusion that the order of stability within a series of position isomers (here 1,2,3-, 1,2,4-, and 1,3,5-triazine) is not controlled by aromaticity. The least stable isomer was found to be the most aromatic one (relative energies in kcal mol , 6-DIs in parentheses) within that series 1,2,3-triazine 1 (44.0, 2.75), 1,2,4-triazine (27.3, 2.47), and 1,3,5-triazine (0.0, 2.32) for comparison benzene 2.67 <2006T12204> compare Section 9.01.2.8. 

Second, the substituent effect on the stabiHty and the aromaticity of substituted aza analogs of naphthalene should be considered. Different mono- and disubstituted derivatives of aza- and diazanaphthalenes (with F, Cl, OH, OCH3, and CN substituents) have been studied theoretically (2010JPOC(23)440, 2011CTC(963)263). Electronic (para-delocalization index (PDl), ATI, and FLU), magnetic (NICS), and structural (HOMA) aromaticity indices have been used to describe the local Tt-electron delocalization. It has been pointed out that the decrease of the aromaticity of dia-zanaphthalene can be compensated by the introduction of an... 

Bultinck, P Rafat, M Ponec, R., van Gheluwe, B Carbo-Dorca, R and Popelier, P. (2006) Electron delocalization and aromaticity in linear polyacenes atoms in molecules multicenter delocalization index. The Journal of Physical Chemistry A, 110, 7642—7648. 

Shghtly earher than the appearance of NICS, attempts to construct numerical characteristics of the electron delocalization based on Bader s quantum theory of atoms in molecules (QTAIM) (1990MI) or electron localization function (ELF) (1990JCP5397) had begun. The most important for aromaticity description are electron sharing indices. For example, the delocalization index (DI) provides a value 6(A,B) which is the number of electrons delocalized or shared between atoms A and B. The next useful aromaticity... 

A). Hydrogen atoms of the PCP ligand are omitted for clarity, (b) Fragment of molecular graph of the system. Electron density at the (3,-1) bond critical point and bond order (as a delocalization index [21], in bold italic) are reported for W-H H-Ni and C-H H-Ni contacts. Color codes -bond critical points, -ring critical points. 

Table 9.21 presents the following localization indices the MnUiken popnlation of LWF (9.46) Qo dne to the oxygen atom and corresponding contribntions from 2s and 2p-oxygen functions. The atomic delocalization index of LWF... 

Empirical and Semiempirical Calculations. Castillo et al. proposed a new empirical approach for the evaluation of fluorine fluorine SSCCs, /(F, F), in aromatic compounds. The correlations between /(F, F), the delocalization index calculated from the theory of atoms in molecules (AIM)/ and the fluorine-fluorine internuclear separation, i/pF. were investigated. They obtained the following empirical equation for /(F, F) ... 

It has been shown by Castillo et that both the intermolecular distance and the delocalization index yield strong correlations with the experimental /pF... 

Wang Y-G, Wiberg KB, Werstiuk NH (2007) Correlation effects in EOM-CCSD for the excited states evaluated by AIM localization index (LI) and delocalization index (DI). J Phys Chem 111 3592-3601... 

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