Accumulation of electron density

The effective cyclic configuration interaction is required for an enhancement of the delocalization-polarization processes via different radical centers. The requirement is satisfied when any pair of the configuration interactions simultaneously contributes to stabilization or to accumulation of electron density in the overlap region. The condition is given by the overlap integrals, S, between the configurations QG, and involved in the proposed delocalization-polarization processes (Fig. 5). Therefore, an effective cyclic configuration interaction needs... 

Interaction 2 Back donation from a relatively high-lying b2 MO into the 7t MO of A=A leads to an accumulation of electron density in the periphery of the ring, which determines the bending of bond paths. 

Figure 15. Radial charge density plot for the resonant p-type virtual orbital for dilation angles 9 = 0.0 and 6 = 90pt (0.42 radians) in e-Be scattering. The role of optimal theta in the accumulation of electron density near the nucleus is clearly seen. In the inset, the maximum is seen to occur at rmaz — 2.5 a.u., very close to that for the rmax of the outer valence 2s orbital, seen in fig. 14- Though a cursory look at the nodal pattern identifies this as a 4P orbital, the dominant contribution to the charge density distribution is mainly of 2p-iype.

Figure 17. Radial charge density plot for the resonant FD amplitude in e-Mg scattering. Fora = 0.75 considered here, only the root labelled I is resonant. The role of optimal theta (6=0.12 radians) in accumulation of electron density near the nucleus is evident.

Closer inspection of the Sb Mossbauer parameters (79, 19a) showed that the decreasing antimony(V) chemical isomer shifts with decreasing antimony content in materials calcined for long periods or at high temperatures were consistent with increasing electron density at the antimony nuclei. Such data are compatible with the accumulation of electron density over the cationic species as the antimony content approaches 10%. It has... 

The prototypical hydrocarbon examples of sjp- and sp hybridization are ethene and ethyne, respectively. The total electron density between the carbon atoms in these molecules is the sum from the tt and a bonds. For ethene, the electron density is somewhat elliptical, because the tt component is not cylindrically symmetrical. For ethyne, the combination of the two tt bonds restores cylindrical symmetry. The electron density contours for ethene are depicted in Figure 1.2, which shows the highest density near the nuclei, but with net accumulation of electron density between the carbon and hydrogen atoms. 

To complicate matters even further, molecular orbital calculations of electron densities of nucleosides within the DNA strand showed that the accumulation of electron density among the various O and N nucleophilic centers and accessibilities to external electrophiles varies greatly with the particular position that the bases hold in the polymer [261]. The disagreement between these predictions and the observed reactions may be reconciled by the gross difference between in vitro reactions and those occurring within the cell. 

Rather large C-Cd(Hg) and H-Cd(Hg) couplings which are transmitted directly between the metal and the arene (a through-space mechanism) have been observed by Stgpien et in the spectra of Cd(II) and Hg(II) complexes of benziporphyrins. DFT calculations performed for two Cd(II) species and the subsequent AIM analysis have shown that the accumulation of electron density between the metal and arene necessary to induce these couplings is fairly small and the interaction is steric in nature. 

The above mentioned formulae are based on the assumption that a vdW interaction of the atoms at any distance do not affect their polarizabilities. In fact, the observed polarizabilities of rare gases and molecular substances vary, depending on the aggregate state. The relative variations range from 0.3 % for Ar to 16.8 % for I2 [19]. On condensation of molecules, the polarizability can decrease (e.g., by 3.2 % for CF4 or SnBr4) or increase (by 3.0 % for CI2, 6.6 % for Br2, 16.8 % for I2) [20]. Given that the effective molecular volume always decreases on condensation, this increase of polarizability can be caused only by accumulation of electron density between molecules. Some clue can be provided by the so-called Muller s factor, the ratio between the (relative) changes of refraction, E, and of volume, V [21],... 

The most usual way is effectively the same as is used for completion of crystal structures during structure solution (Section 10.7.6 andEq. 10.12). When a reasonable part of the structure has been described and some atoms positions have been defined, along with correct scattering factors and thermal parameters, a difference map can be calculated between this (incomplete) model and the Fourier transform of the experimental structure amplitudes. This map is a representation of the difference between the electron density of the model and that determined by the experiment. The biggest accumulations of electron density are assigned as new atoms until the structural model is complete. But even then there is residual electron density, which describes the difference between the true electron density and the model of a sum of independent spherical atom contributions, taking some simplified model of displacement into account There is also some random noise. 

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