Benzenes electronic localization function

Fig. 9 Electronic localization function (ELF) for benzene. Left. ELF = 0.85 iso-surface. Right. ELF = 0.66 iso-surfaces. The right iso-surface is cut on the front side for showing the complex topology the Carbon core basins sharply separate from the scalar ELF field. The aromatic ELF basin is clearly defined. Both in the high or lower ELF value iso-surface, no separation between Sigma and Pi basins can be found, which is a characteristic of delocalized bonds, similar to that shown in Fig. 11. All the molecular plots reporting ELF iso-surfaces or MPD are performed using the Xcrysden program [44]...

S. M. Mattar and S. E. Brewer,/. Phys. Chem., 96,1611 (1992). Geometry Optimization and Computation of the Electronic Structure of Benzene-Vanadium Molecules by the Local-Density-Functional LCAO Method. 

Spin-coupled calculations at the idealized Dm geometry of cyclooctatetraene reveal a description dominated by triplet coupling of pairs of electrons [12], as anticipated earlier. Expressing the total spin function in the Serber basis [29], we find that the mode made up only of triplet-coupled pairs is responsible for 75% of the total. We find that the n orbitals for this antiaromatic system (see Figure 9) adopt localized forms that resemble closely those shown in Figure 4 for benzene, rather than the antipair representation shown for cyclobutadiene in Figure 6. 

Figures are the squares of the coefficients in the state functions expressed as a linear combination of the electronic configurations of the MIM model. G Ground configuration, LE Configuration of the localized excitation, CT Charge transfer configuration. Biu>B2u Eiu The electronic states of benzene...

The second situation referred to above, viz systems containing conjugated double bonds, is perhaps more important to the present discussion. The classical example of such a system is benzene. The molecular orbital treatment regards the six G—G bonds and the six G—H bonds as completely localized molecular orbitals compounded out of carbon sp2 hybrid atomic orbitals and the hydrogen s orbital. So far the treatment is identical with the electron pair theory, discussed in Chapter 4. The G—G bonds will be or bonds formed by the overlap of two sp2 hybrid atomic orbitals, one from each carbon atom and the C—H bonds will also be a bonds formed by the overlap of one sp2 hybrid atomic orbital of carbon with the s atomic orbital of hydrogen. The six carbon 2p atomic orbitals that remain will form completely non-localized molecular orbitals. Thus each 2pt electron will be regarded as existing in the field of six nuclei and will possess a wave function of the form ... 

The dependence of the chemical shifts on the 7t-electron charge density in aromatic molecules has frequently been observed. Karplus and Pople showed that the magnetic shielding (p.p.m. from benzene) of a nucleus (A) in a conjugated molecule is a function of the local charge density, Pa, the free valence, Fa, and the polarity of the C—H bonds, Ah, and is given by the expression—... 

Structure A can easily give up its weakly bound proton and hence function as a Bronsted acid. Structure B possesses electron-accepting properties by virtue of the aluminum atom which contains an empty -orbital. Reversion of the aniline spectrum to that of benzene will occur when the excess electron density distributed to the ring by the amino group becomes localized on the nitrogen atom. Thus proton addition to the amino group in aniline produces the anilinium ion whose... 

Fig 8 4 The extended wave functions of the molecule of benzene must accommodate one electron from each carbon atom, left over after the other three electrons of principal quantum number 2 have been used to form localized bonds... 

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