Quantitative electron delocalization

Table IV lists the redox potentials of conjugated ferrocene oligomers (mainly dimers with a single bridge). Potential values are denoted against different reference electrodes as given in the references. The values can be primarily compared using the relationship mentioned in the footnote of the table, although care should be taken with some errors derived from junction potentials which depend on experimental conditions. There have been several reports on the quantitative estimation of structural factors affecting internuclear electron delocalization.

A quantitative study on local aromaticity based on n-center electron delocalization indices, wheren is the number of atoms in the ring, was performed on benzo[c]furan and benzo[b]furan. 

Coordination of metal ions often has a dramatic effect on the n delocalization in porphyrins and porphyrinoids. It has particularly conspicuous influence on the electronic spectra of metalloporphyrins, which show a dependence on the identity of the metal ion, axial ligation, oxidation level, and spin state. In regular porphyrins, metal coordination reduces the number of observed Q bands from four to two, reflecting the higher symmetry of the chromophore relative to the free base. However, detailed quantitative information on the Jt-electron delocalization is more easily accessible from other physical methods. 

In the MO theory, the most reliable approach for the study of reaction pathways perhaps is CASSCF [12, 13], but multi-VBSCF is essentially at the same level with CASSCF [14]. Since a VB wave function can be expanded into the combination of numerous Slater determinants that are used to define configurations in the MO theory, the VB theory provides a very compact, accurate description for chemical reactions. While both MO and VB theories have their own advantages as well as disadvantages, in our opinions, there are some areas where the VB theory is particularly superior to the MO theory 1) the refinement of molecular mechanics force field 2) the development of empirical or semi-empirical VB approaches 3) the impact of intermolecular charge transfer or intramolecular electron delocalization on the structure and properties 4) the validation of classical chemical theories and concepts at the quantitative level 5) the elucidation of chemical reactions and excited states intuitively. 

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). 

A quantitative measure of electron delocalization in a planar, cyclic molecule may be obtained by comparing the measured out-of-plane magnetizability component or magnetic anisotropy with the value predicted for a hypothetical structure in which the electron distribution is completely localized. The difference between the observed and calculated values, Ayani and is the estimate of the extent of electron delocalization and of the relative... 

The majority of our discussion revolved around the definition of aromaticity. Schleyer argues that aromaticity can be defined perfectly well. It is the manifestation of cyclic electron delocalization which is expressed in various ways. The problem with aromaticity comes in its quantitative definition. How big is... 

An energy difference for the isodesmic reaction [Eq. (28)] indicates a quantitative measure of the extent of electron delocalization (6-31G ) (62). The energy difference for the C, structure of the silacyclopentadienide anion is only 2.2 kcal/mol, which is much smaller than 73.4 kcal/mol for the carbon analog, a planar cyclopentadienide anion (C2 ). On the basis of these calculations, it is concluded that the ground-state structure of the silacyclopentadienide anion has only ca. 3% of the resonance stabilization exhibited by the cyclopentadienide anion. However, the previous calculation (3-21G//STO-2G) on the 2 planar structure shows that the resonance energy is 23 kcal/mol, which means ca. 25% as aromatic as the carbon analog (65). 

Structural data available from experimental [22a] as well as theoretical [22c, 41] studies demonstrate that diphosphirenium salts 2 P also benefit from a certain amount of aromatic stabilization. However, the resonance energy of o4-phosphorus-containing systems is smaller. From a quantitative point of view, the electron delocalization in phosphirenium salts C has been calculated to be half that of the corresponding phosphirenylium salts H [42]. 

Use of Electron Spin Resonance Techniques. Electron spin resonance (ESR) studies have been used to examine both activity of antioxidants " and their location within the Uposome . Studies of antioxidant radicals via ESR provide data on the electron delocalization within the antioxidant, which can be correlated with antioxidant activity, although not always with very good agreement with inhibition studies . Spin traps have been themselves examined as potential antioxidants, and have been used to attempt to trap peroxyl species for study . However, trapped peroxyl species are not very stable and carbon-centered radicals have been preferentially trapped, even though in some studies other techniques (e.g. malondialdehyde/thiobarbituric acid, MDA/TEARS-technique) indicate the presence of peroxide species in the sample . Eremy s salt ((K+S03 )2N0 ) has been used in micellar systems to determine rate constants quantitatively for the antioxidants a-Toc and ascorbic acid and their derivatives, because it reacts with them in a way similar to peroxyl radicals and can be used as a spin probe in stop-flow ESR studies . ESR has also been used to monitor the loss of dPPH and galvinoxyl signal intensity... 

Giuffreda, M.G., Bruschi, M. and Liithi, H.P. (2004) Electron delocalization in linearly m-conjugated systems a concept for quantitative analysis. Chem. Eur. J., 10, 5671-5680. 

Since these local group susceptibility values are derived under the explicit assumption that all electron motions are localized, the difference between the observed magnetic susceptibility and that calculated from local group values should provide a quantitative measure of electron delocalization and perhaps aromaticity.19 There are also a variety of other applications for the local susceptibilities given in Table 8. For instance, molecular values can be measured in a number of small molecules by molecular beam techniques.1 In many of these molecules an accurate measurement of the susceptibility anisotropy is difficult. Magnetic susceptibilities calculated by the methods of this paper can thus be combined with g values obtained by other methods to extract quad-rupole moments. Alternatively, calculated susceptibility anisotropies... 

Only the Cs structure is a minimum on the 101 potential surface. The planar C2v structure is the transition state for pyramidal inversion between equivalent Cs structures, the inversion barrier being 16.2 kcalmol- 1 259 Note the large differences in the geometries of the C2v and Cs structures, in particular the much longer C-Si bond and the butadiene-like geometry of the carbon skeleton in the Cs structure. The fact that 101 is not planar indicates that electron delocalization is weak and relatively unimportant. A quantitative measure of the extent of electron delocalization in the Cs 101 is given by isodesmic equation 32. 

The difference between the dipole moments of the aromatic compound and the corresponding tetrahydro derivative is called the mesomeric moment and represents a measure of the -electron delocalization. The mesomeric dipole moment is directed, in all the congener systems, from the heteroatom toward the ring. The values obtained (furan 1.03 D, thiophene 1.35 D, selenophene 1.29 D, tellurophene 1.17 D) are in excellent quantitative agreement with other aromaticity indices based on structural and magnetic properties12 (see discussion in Section II,C). 

Considerable effort has been devoted to the determination of rate and equilibrium constants for benzene derivatives with meta- and pnrn-trifluoro-methyl substituents in a search for an exalted substituent effect which would provide evidence for special electron delocalization. Resonance interactions are generally detectable by such procedures. To illustrate, two sigma constants Op-NOi p-N(h with values of 0.78 and 1.24, respectively are necessary to describe the behavior of the nitro group quantitatively by the Hammett equation... 

D-MEDNEs Three-dimensional Markovian electron delocalization negentropies 3D-QSAR Three-dimensional quantitative structure activity relationship ADME Allied toxicological physicochemical and absorption Disposition... 

Yamamoto, T., Kaneno, D., Tomoda, S. (2008). The origin of cis effect in 1,2-dihaloethenes the quantitative comparison of electron delocalizations and steric exchange repulsions. Bulletin of the Chemical Society of Japan, 81,... 

Magnetic properties further support it-acidity. Quantitatively, g values reflect 7i-effects because deviations from g (the fi-ee electron value) arise from unquenched orbital angular momentum (fi-om circulation of the t2g electrons). Delocalization of d electrons into n levels on the ligand diminishes the unquenched orbital angular momentum (as measured by k, the orbital reduction factor), and thereby Ag. For example, in copper(II) complexes of thioether ligands, g values deviate from 2 by little compared to those of harder ligands such as OH 2 or NH3 [22]. 

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