Electronic, deformation polarization density

Figure 2 Electron-density contours for chemisorption. Upper row contours of constant electron density in (any) plane normal to the metal surface containing the ad-atom nucleus (indicated by -f). The metal is to the left of the solid vertical line. Center row deformation charge density. The polarization of the core region, shown for Li, has been deleted for Si and Cl because of its complexity. Bottom row The bare-metal electron-density profile, shown to establish the distance scale. (From Ref. 38.)...

In the Kohn-Sham Hamiltonian, the SVWN exchange-correlation functional was used. Equation 4.12 was applied to calculate the electron density of folate, dihydrofolate, and NADPH (reduced nicotinamide adenine dinucleotide phosphate) bound to the enzyme— dihydrofolate reductase. For each investigated molecule, the electron density was compared with that of the isolated molecule (i.e., with VcKt = 0). A very strong polarizing effect of the enzyme electric field was seen. The largest deformations of the bound molecule s electron density were localized. The calculations for folate and dihydrofolate helped to rationalize the role of some ionizable groups in the catalytic activity of this enzyme. The results are,... 

As mentioned in [Section 24.1], and as already demonstrated in Equation 24.39, the Fukui functions as well as the chemical hardness of an isolated system can be properly defined without invoking any change in its electron number. We define a new Fukui function called polarization Fukui function, which very much resembles the original formulation of the Fukui function but with a different physical interpretation. Because of space limitation, only a brief presentation is given here. More details will appear in a forthcoming work [33]. One assumes a potential variation <5wext(r), which induces a deformation of the density 8p(r). A normalized polarization Fukui function is defined by... 

For the C02 Cjo cluster, the translational frequencies e = 54 cm-1 and a [ = 122 cm-1 are smaller than for C2H2 C7o both these vibrations are coupled to the deformation vibrations of the guest and the cage. According to the Mulliken population analysis, there is some electron density redistribution and an increase of polarity of the both M-X bonds in the encapsulated guests, as compared to the free molecules BeF2 and CO2 (induced polarization). 

In terms of hybrid-bond theory it appears reasonable that the deformation density could be negative in some bonds. When a p-block atom with n valence electrons forms a bond, the valence shell is polarized into a tetrahedral distribution with n/4 electrons concentrated around each potential... 

The electron density distribution in the Se02Cl anion of [ (CH3)4N ][Se02Cl ] has been studied by an X-X deformation density analysis using high-angle diffraction data at 120 K (405, 406). The deformation density maps clearly reveal the presence of lone-pair (E) density (maximum of 0.40 0.04 e x at a distance of ca. 0.75 A from Se) consistent with model predictions for an approximately i )-tetrahedral Se02ClE arrangement with additional tt density in the Se-0 bonds and with a rather polar Se-Cl bond. 

A CNDO/2 method has been applied to calculate structural parameters of 5-azauracil <82ACH35l>. Ab initio and x-ray deformation densities have been compared in cyanuryl chloride the basis sets examined range over STO-3G, 3-21G, 4-31G, 6-31G, and 6-31G. Good agreements were found when a polarization basis set was employed in the calculation of the electronic structure <89JST(202)111>. 

Fig. 12.6. Polarization of the hydrogen atom in an electric field. The wave functions for (al the unperturbed atom (bl the atom in the electric field (a.u.) = (0.1, 0,0) are shown. As we can see, there are differences in the corresponding electronic density distributions in the second case, the wave function is deformed toward the anode (i.e., leftward). Note that the wave function is less deformed in the region close to the nucleus than in its left or right neighborhood. This is a consequence of the fact that the deformation is made by the —0.1986(2p., ) function. Its main role is to subtract on the right and add on the left, and the smallest changes are at the nucleus because 2px has its node there.

In the second order, the Pauli deformation (cf. Appendix Y available at booksite. elsevier.com/978-0-444-59436-5 on p. el83) of the electronic density in the AB complex results in exchange-based modifications ( ind exch - disp-exch) the induction and dispersion interactions ( ind and Ejisp) that are known from the polarization perturbation theory. 

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