Plot of the electron density

Figure B3.2.10. Contour plot of the electron density obtained by an orbital-free Hohenberg-Kolnr teclmique [98], The figure shows a vacancy in bulk aluminium in a 256-site cell containing 255 A1 atoms and one empty site, the vacancy. Dark areas represent low electron density and light areas represent high electron density. A Kolm-Sham calculation for a cell of this size would be prohibitively expensive. Calculations on smaller cell sizes using both techniques yielded densities that were practically identical.

An isosurface plot of the electron density is shown in Figure 7.8. 

Some of the major packages are better at visualization than others. In any case, there are a host of third-party providers with software on offer. Here then is what you might like to do with the results of the calculations above (and I used HyperChem to produce the following screen grabs). First of all an isosurface plot of the electron density (Figure 10.16). Next are isosurface densities for the highest... 

Figure 2.2 A contour plot of the electron density in a plane through the sodium chloride crystal. The contours are in units of 10 6 e pm-3. Pauling shows the radius of the Na+ ion from Table 2.3. Shannon shows the radius of the Na+ ion from Table 2.5. The radius of the Na+ ion given by the position of minimum density is 117 pm. The internuclear distance is 281 pm. (Modified with permission from G. Schoknecht, Z Naiurforsch 12A, 983, 1957 and J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed., 1993, HarperCollins, New York.)...

Figure 6.4 Contour plot of the electron density in the molecular plane of SCI2. The outer contour line corresponds to 0.001 au and the next contour lines correspond to values increasing according to the pattern 2 X 10", 4 X 10", 8X10" where n varies from —3 to 2.

Figure 6.5 Contour plot of the electron density in a plane containing the nuclei of (a) CO and (b) CI2. both drawn at the same scale. Along the internuclear axis, the electron density reaches its minimum value at a point marked by a square. For CI2 this is the midpoint.

Figure 1 3. Contour plot of the electron density of CO, showing the magnitudes and directions of atomic and charge transfer dipoles (arrow length is proportional to magnitude). Arrow heads point to the negative end. The molecular dipole moment is given by the vector sum of charge transfer terms (p.c.t.) and the atomic polarizations ( ra p). Values were obtained at the DFT level using the B3LYP functional and the 6-31 1+G(3df) basis set. The SCF molecular dipole = 0.096 D the computed molecular dipole ( Jtc.t.[0] + Aa.p.[0] + Hc.JC] + Aa.p.[C]) = 0.038 au = 0.096 D, close to the experimental value of 0.1 10 D (15).

Figure 14. Contour plot of the electron density of B2H6 in the plane of the bridging hydrogen. Each hydrogen is connected to the two boron atoms by a bond path to each. In contrast, the boron atoms do not share a bond path linking them to one another. (See legend to Fig. 2 for contour values.)...

Figure 9.7 Contour plot of the electron density for bifurcated S-H- -(H-B)2 dihydrogen bonds. The bond critical points are indicated as squares. (Reproduced with permission from ref. 8.)...

Figure 14. Contour plot of the electron density at one time step during the zero-voltage molecular dynamics run. The circles indicate the simultaneous positions of those water molecules with the oxygen atom within 3 a.u. of the plane of the contour plot. From Ref. 52, by permission.

FIGURE 6.9 Phenyl radical, atom numbering scheme and plot of the electron density difference between the and X Ai electronic states. The regions that have lost electron density as a result of the transition are shown in bright yellow, and the darker blue regions gained electron density. 

FIG. 17. A schematic overview of Cso represented by a stick model, 3D and 2D contour plots of the electron density. In the 3D plot in the middle the single contour has been chosen to show how the electrons are distributed in the bonds. The 2D contour plot shows the electron density in a plane that includes the center of the molecule. We clearly see that there is a void, which means that Ceo constitutes a spherical shell. 

All theoretical studies agree with this second picture [13-17,39,99]. This is shown by the plots of the electron density maps and in particular by density difference maps which show very clearly the electron localization at the center of the vacancy [39,55]. This is true not only for the bulk but also for the surface of MgO, Fig. 5. The localization of the electrons in the center of the vacancy is an indirect proof of the highly ionic nature of MgO. In fact, the electrons are trapped in the cavity by the crystalline Madelung potential. Calculations performed on cluster models have shown that in absence of the external field the electrons tend to distribute more over the 3s levels of the Mg ions around the vacancy [38]. The localization of the electron in the center of the vacancy is... 

Fig. 9.7 Relief map and contour plots of the electron density of C2H4 in the nuclear plane (adapted with permission from ref. 92 copyright 1981, Institute of Physics Publishing).

Figure 5-20 Plots of the electron density distributions associated with s orbitals. For any s orbital, this plot is the same in any direction (spherically symmetrical). The sketch below each plot shows a cross-section, in the plane of the atomic nucleus, of the electron cloud associated with that orbital. Electron density is proportional to r ip. ...

Figure la is a plot of the electron density and its associated gradient vector field of a planar molecule BF3 in the molecular plane. The figure illustrates how the zero-flux surfaces partition the molecular space into disjoint mononuclear regions, namely atomic basins, and how such surfaces differ from an arbitrary surface for which Vp(r) n(r) f 0. The left half of Fig. la is a contour plot of the electron density p(r), the contours increase in value as they approach the nuclei. Each contour line is a line with a constant value of the electron density. 

Figure 2 Contour plot of the electron density in the molecular plane of benzene.

Figure 4 Contour plot of the electron density of CO. Carbon is located to the left. The bond critical point is indicated by the X. The heavy dotted line indicates a partitioning surface perpendicular to the bond path through the bond critical point. The solid line follows the valley from the critical point. This is the intersection of the zero-flux surface and the particular plane shown here.

The computational advantage of the projected populations over the topological populations can be substantial. However, the volume assigned to each atom in the projected method has no quantum mechanical significance. Furthermore, the choice of projection plane can affect the projected populations. The major advantage of the projected method is the ability to present contour plots of the electron density that reflect the total elearon density. Visualization of four-dimensional plots is very difficult, and the projection method reduces the dimensionality. 

Fig. 5.10. Noise-induced front motion Space-time plots of the electron density for (a) D=0 (no noise), (b) D = 0.5 s /m, (c) D = jm . Light and dark shading...

Figure 1. Contour plot of the electron density distribution in the BF3 molecule. The lines connecting the nuclei are the bond paths along which the electron density is greater than along any other line connecting the two nuclei. The curved lines between the atoms are the lines along which the interatomic (zero-flux) surfaces cut the molecular plane.

Figure 18 Contour plot of the electron density of cisplatin using the MP2/6-311 + +G(2d,2pd) basis set with an ECP on Pi. The numbers indicate the positions of the BCPs in cisplatin 1 is the Pt-Cl BCP, 2 is the Pt-N BCP, and 3 is the N-H BCP...

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