Electron density distribution, by the

This chapter is based on the VSEPR and LCP models described in Chapters 4 and 5 and on the analysis of electron density distributions by the AIM theory discussed in Chapters 6 and 7. As we have seen, AIM gives us a method for obtaining the properties of atoms in molecules. Throughout the history of chemistry, as we have discussed in earlier chapters, most attention has been focused on the bonds rather than on the atoms in a molecule. In this chapter we will see how we can relate the properties of bonds, such as length and strength, to the quantities we can obtain from AIM. 

For localized orbitals the development of the polarization in tinre b very fast, and the corresponding response frequencies lie in the optical range. In isotropk nonpolar materials, the short-time (high-frequet>cy, unrelaxed) polarization is due to deformation of the electron density distribution by the external electrk field. The unrelaxed permittivity is related to the refractive index of light (n) as e. s n In nonisotropk nulerials c and fl arc tensors. 

The 327-670 GHz EPR spectra of canthaxanthin radical cation were resolved into two principal components of the g-tensor (Konovalova et al. 1999). Spectral simulations indicated this to be the result of g-anisotropy where gn=2.0032 and gi=2.0023. This type of g-tensor is consistent with the theory for polyacene rc-radical cations (Stone 1964), which states that the difference gxx gyy decreases with increasing chain length. When gxx-gyy approaches zero, the g-tensor becomes cylindrically symmetrical with gxx=gyy=g and gzz=gn. The cylindrical symmetry for the all-trans carotenoids is not surprising because these molecules are long straight chain polyenes. This also demonstrates that the symmetrical unresolved EPR line at 9 GHz is due to a carotenoid Jt-radical cation with electron density distributed throughout the whole chain of double bonds as predicted by RHF-INDO/SP molecular orbital calculations. The lack of temperature... 

As this abbreviated review has indicated there is no universally accepted interpretation of Cl shifts in iron compounds, and most of the empirical correlations that have been found are limited to either one spin state, or to one or two valence states. In most cases it is clear that the failure to find extended agreement between data and theory is because the theory has been forced to a limit where its approximations are no longer valid. Probably the main reason for the limited success of empirical correlations—e.g., the Cl shift with the nepheleuxetic and spectrochemical series or with electronegativity differences—is that the Cl shift depends on electron density distributions while the other quantities by-and-large depend on, or are measures of, electronic energy level differences. Since there is usually no simple relationship between the two quantities, the limited agreement is not surprising. It is clear that the... 

In the framework of AIM theory, which well be used extensively to describe dihydrogen bonds, the situation above corresponds to the electron density distribution in the H2 molecule, where the pc parameter takes the very large value 1.857 au and the Laplacian, V pc, is strongly negative ( —34.15 au). These data have been obtained by ab initio calculations at the MP2/6-31G level [4],... 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

One of the most obvious examples is strong deshielding of the a-protons in the series pyridine (8 8.29 ppm), phosphabenzene (8.61), arsabenzene (9.68), stibabenzene (10.94), and bismabenzene (13.25), although other data unambiguously point to a falling off of the aromaticity in this sequence. Here the contribution by crAringcurr is mostly obscured by local effects connecting with nonuniform distribution of the electron density and by the anisotropy of the heavier heteroatoms. 

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