Laplacian of electron density

A much less basis set dependent method is to analyze the total electron density. This is called the atoms in molecules (AIM) method. It is designed to examine the small effects due to bonding in the primarily featureless electron density. This is done by examining the gradient and Laplacian of electron density. AIM analysis incorporates a number of graphic analysis techniques as well as population analysis. The population analysis will be discussed here and the graphic techniques in the next chapter. 

Figure 11. Laplacian of electron density for Ge - V2 p (r) for small fragment in Ge curvature of electron density along Ge-Ge bond shows only small shift of electrons to the...

Finally, it is important to add that the regions of reduced (or enhanced) repulsion may be directly related to the regions of depletion (or concentration) observed in the diffuse part of the Laplacian of electron density plots proposed by Bader [33]. You may see this in Fig.2, where... 

Towards the O atoms, beginning at 40°, the HL-exchange rapidly rises. Of particular interest is that no additional depletions or concentrations of electron density appear at the outskirts of the terminal O atoms, i.e., there is no evidence of the lone pairs at the O atoms. This is, again, in accord with the plots of Laplacian of electron density in Fig. 5. A. 

Keywords Hydrogen bond AIM electron density Laplacian of electron density water DNA ... 

Table 3. Number of hydrogen bonds (nHB), hydrogen bond critical points (nHBCP), ring critical points (nRCPs), cage critical points (nCCPs), stabilization energies (SEs, kcal/mol), range of electron density (p(rc)), and Laplacian of electron density (V p(rc)) for the most stable water clusters...

Table S. Electron density (p(rc)) and Laplacian of electron density (V p(r )) for various phenol-water clusters...

It is found that the total electron density (Sp(rc)) and total Laplacian of electron density (SV p(rc)) at all HBCPs bear a linear relationship with the SE for all the H-bonded clusters as illustrated in Fig. 6. A linear regression analysis... 

Fig. 2 Selected distances (A) in Cp2Ti( 2-HBcat)2, a plot of the Laplacian of electron density for Cp2Ti 2-HB(OH)2 2 on the B - Ti - B plane and a three-center-two-electron bonding molecular orbital describing the bonding interaction of the TiB2 triangle...

Fig. 5 a Calculated structure for Cp2Ti( 2-HB(OCH)2)(HC=CH). b A resonance hybrid describing the calculated structure, c Plot of the Laplacian of electron density on the plane containing the Ti-Cl-C2-B-H five-membered ring (Adapted from [34])... 

The values of electron density and Laplacian of electron density at the BCP for all of these hydrogen bonds meet Popelier s criteria. The range of variation of the properties of the BCP for well-defined hydrogen bonds (p>0.015a.u., V )>0.044 a.u.) may be used for further classification of other intramolecular interactions in DNTs. An analysis of the elhpticity of these hydrogen bonds ( <0.09) and the distance between BCP and RCP (Lp > 1.5 a.u.) does not indicate arty instability of these interactions, and these values also may be used as a reference for further consideration. 

This picture closely agrees with predictions of the structural correlation method (Sect. 1.3.5.3, Fig. 1.18) and conforms well to the predictions founded on a study of the regions of charge concentration and charge depletion, as defined by the Laplacian of electron density, to identify the sites of nucleophilic attack of formaldehyde and acetaldehyde [112]. It may easily be interpreted by considering the interactions between the frontier orbitals of reactants. The main... 

Fig. 15.1 The molecular graph of the C6EH5-H2O complex, solid and broken lines correspond to bond paths, big circles to attractors and small circles to critical points (green-bond critical points, red-ring critical points), the isolines of laplacian of electron density are also presented positive values are depicted in solid lines and negative values in broken lines (this is the rule for the other figures of this chapU ) the laplacian isodensity lines in the plane of the complex based on the MP2/aug-cc-pVTZ results of calculations...

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