Basin population

Table 2 Basin populations of the complexes. V (Clj ) with i = 1, 2 means the total valence population of Cl atoms.

Table 8 Excess loads of major elements normalized to basin population in industrialized regions (kg cap yr ).

FIGURE 20. Aspects of the electronic distribution in the vertical triplet aniline (triplet state at the singlet ground-state geometry) (a) Differential density Pink represents the Ap(r) = 0.005 an, and blue represents the Ap(r) = —0.005 an isosurface of the differential density, (b) ELF = 0.87 isosurfaces of the electron localization function. Values correspond to basin populations and integrated spin densities (s values)... 

Figure 25 displays various results probing the charge distribution of the anilino radical. Although this molecule has only one N—H bond, the properties of the atoms and bonds in both sides are almost identical (for example, the basin population for J(CA,ps,C2,nh ) is 2.51 e, while it is 2.50 e for V(Cl so,C6orAo)). The order of the Cl— C2 and C3—C4 bond is reduced due to the resonance structures similar to those of Scheme 1, indicated by the 2.50 and 2.64 e populations of V(C2,C2) and V(C3,C4), respectively, compared... 

Table 3 Computed AIM basin populations (e ) for the transition state and the ion-molecule complex...

Figure 6 Comparison between the variations of selected basin populations (C and H) and the sum of C-H distances (solid line) along a dynamic pathway from the transition state to the ion-molecule complex. Curves with markers carbon basin (lozenges) and sum of hydrogen basins (triangles) populations...

In equation 17, N i2i)N i2j) is the number of the electron pairs classically expected from the basin population whereas N(Qi, f2 ) is the actual number of pairs obtained by integration of the pair-electron function over the basins and i2j. The variance is then a measure of the quantum mechanical uncertainty of the basin population which can be interpreted as a consequence of the electron delocalization, whereas the pair covariance indicates how much the population flucmations of two given basins are correlated. Within the AIM framework, the atomic locahzation and delocalization indices X A) and 5(A, B) have been introduced and defined by equations 18 and 19 ... 

The V(Ci, Cj) basin populations, their variance and the electrophilic substitution positional indices of the studied CeHsX molecules are fisted in Table 21. The V(C, X) populations and their variance are close to their values in the CH3X series. As expected the V(C, C) basin populations are intermediate between those inherent to a single and a double C—C bond and subject to a large fluctuation of the charge density. The classical meaning of the variance is the square of the standard deviation though the standard deviation cannot be defined for a quantum system, the classical limit provides at least qualitative information about the delocalization. In the present case a 1.16, which is consistent with the resonance picture involving the Kekule structures. 

TABLE 21. Basin populations N(V), variance of the basin populations a (V) and electrophilic substitution positional indices RIc of the C6H5X molecules... 

Let us consider first the trans conformers in which the halogen substituent is not perturbed by an extra intramolecular interaction. In all molecules the V(Ci, O) basin population is slightly increased with respect to phenol the largest effect occurs for X = Cl, whereas for X = Br and I this effect is weaker than for the fluorinated species. The... 

Figure 22. Change of the bond ELF basin population of A-H donor bond. Dotted lines are values in the monomers (f formamide, fa formic acid, m methanol, w water).

Generations change and current generations only hear about the good old days in stories but may not have had first-hand experience with those days that were free of water and air pollution or days that were once relatively free of water scarcity problems in, for example, the lower reaches of the Amudarya and the Syrdarya. To a majority of the current Aral Basin population, there was always a Karakum Canal (begun in 1954) taking water out of the Amudarya. Most likely, they do not know what life was like before the canal was constmcted, except by way of history, documentaries, visits to the local museums and the reminiscence of their elders. 

The basin population of ofrcristobalite, stishovite and fluorite structures are listed in table 3. 

TABLE 3. Basin population of oxygen core, disynaptic and monosynaptic attractors. 

The topological analysis of the density and of the ELF funetion provides new information to understand the nature of the Si-0 bond. On the one hand, the atomic population and the bond ellipticities tell us that the SiO bond is partly ionic and also that there is no evidence for a partial double bond character. This latter point is confirmed by the analysis of the ELF function since there is only one attractor between the oxygen and silicon cores and that its basin population is always less than or equal to 2 electrons. Moreover, it appears more important to consider the oxygen than the silicon to discuss the bonding in silica. The Si-0 bond is found to belong to the electron shared interaction by the ELF analysis. 

ELF. - In order to understand depleted homopolar bonds better Llusar et performed an ELF study of the N-N, 0-0 and F-F bonds. Deformation density maps are known to show a depletion of p between formally covalent bonds. However a topological analysis of the ELF function demonstrates that bond strength appears to be correlated with the disynaptic basin populations. From a qualitative point of view, the splitting of a disynaptic basin into two monosynaptic ones upon bond stretching is the signature of the covalent bond. 

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