Contour 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.

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.

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. 

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 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. 

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...

Electron density plots of trans-Ammne, HN=NH, as relief plots (a) in the plane of symmetry and (b) perpendicular to it, and the same represented as contour line plots (c) and (d). (e) Gradient vector field of the electron density of trans-diimine, HN=NH. (f) Contour plot of the electron density with interatomic surface lines partitioning the molecular space into atomic basins (interatomic surfaces (IAS) and atomic interaction lines overlaid. All plots are based on calculations at the MP2/6-311G level of theory. 

The 3D contour plots of the electron density changes accompanying the beryllium bond formation in H2Be-OH2 and p2Be-OH2 are reported in Pig. 17.2, as a suitable example. Beryllium bonds for both the complexes are characterized by significant electron density rearrangements all over the whole molecular region of... 

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