Electron density relief map

For a homonuclear diatomic molecule such as Cl2 the interatomic surface is clearly a plane passing through the midpoint between the two nuclei—in other words, the point of minimum density. The plane cuts the surface of the electron density relief map in a line that follows the two valleys leading up to the saddle at the midpoint of the ridge between the two peaks of density at the nuclei. This is a line of steepest ascent in the density on the two-dimensional contour map for the Cl2 molecule (Fig. 9). 

Figure 9.11 depicts this fact in three ways a cross-section of a space-filling model an electron density contour map, with lines representing regular increments in electron density and an electron density relief map, which portrays the contour map three-dimensionally as peaks of electron density. 

NaCl. Sodium chloride is a white (colorless) crystalline solid with a AEN of 2.1, a high melting point, and high electrical conductivity when molten—ionic by any criterion. Nevertheless, just as for LiF (Figure 9.22B), a small but significant amount of electron sharing appears in the NaCl electron density relief map. 

Mode of Overlap, Bond Strength, and Bond Order Because orbitals overlap less side to side than end to end, a tt bond is weaker than a ct bond thus, for carbon-carbon bonds, a donble bond is less than twice as strong as a single bond (Table 9.2). Figure 11.12 shows electron density relief maps of the three types of carbon-carbon bonds note the increasing electron density between the nnclei from single to double to triple bond. 

Figure 16.16 Depicting the reaction between BrCH3 and OH . A plot heat of reaction. The electron density relief maps, structural formulas,...

Figure 2-1. Representations of the electron density of the water molecule (a) relief map showing values of p(r) projected onto the plane, which contains the nuclei (large values near the oxygen atom are cut out) (b) three dimensional molecular shape represented by an envelope of constant electron density (0.001 a.u.). 

Figure 6.2 Relief map of the electron density in the molecular plane of SCI2. The vertical direction (z axis) is used to show the value of p, which depends on the two coordinates (x,y) describing the molecular plane. The value of p at the nuclear positions is of the order of 3 X 103 au but the peaks have been truncated at 15 au. Note the dramatic behavior of the electron density in the vicinity of the nuclei there are huge peaks appearing on a nearly flat landscape.

Figure 6.4 shows a third and commonly used way of representing electron density profiles the two-dimensional contour map. This map for the SCI2 molecule corresponds to the relief map in Figure 6.2. Although this map is able to show very detailed information, we are restricted to a particular choice of plane, or to a selection of planes. To obtain an approximately equally dense distribution of contour lines, contour values used in this book increase in the nearly geometrical sequence, I0 3, 2 X 10 3, 4 X 10 3, 8 X 10-3. 2 X 10-3.

Figure 6.6 Relief map of the electron density for CO in a plane containing the molecular axis. The electron density falls off more rapidly for displacements perpendicular to the internuclear axis than along the internuclear axis.

Figure 6.13 Relief map of the electron density for methanal (formaldehyde) in the molecular plane. There is a bond critical point between the carbon and the oxygen nuclei, as well as between the carbon nucleus and each hydrogen nucleus. No gradient path or bond critical point can be seen between the two hydrogen nuclei because there is no point at which the gradient of the electron density vanishes. There is no bond between the hydrogen atoms consistent with the conventional picture of the bonding in this molecule.

As for the one-dimensional case, the function L makes features emerge from the electron density that p itself does not clearly show. What then does the function L reveal for the spherical electron density of a free atom Because of the spherical symmetry, it suffices to focus on the radial dimension alone. Figure 7.2a shows the relief map of p(r) in a plane through the nucleus of the argon atom. Figure 7.2b shows the relief map of L(r) for the same plane, and Figure 7.2c the corresponding contour map. Since the electron density distribution is... 

Figure 1. Relief maps of the electron density of (a) SCI2 and (b) H2O in the plane of the nuclei (density and distances from the origin of the coordinate system in au). Isodensity contour lines are shown in the order 0.001,0.002,0.004,0.008 (four outermost contours) 0.02,0.04,0.08 (next three) 0.2,0.4,0.8 (next three). The density is truncated at 2.00 au (innermost contour). These contours are shown in blue, violet, magenta, and green, respectively, on the figure in the table of contents (p 1028).

Another common method of representing the electron density distribution is as a contour map, just as we can use a topographic contour map to represent the relief of a part of the earth s surface. Figure 7a shows a contour map of the electron density of the SCI2 molecule in the Oh (xy) plane. The lines in which the interatomic surfaces, that are discussed later, cut this plane are also shown. Figure 7b shows a corresponding map for the H20 molecule. 

Fig. 7.1 The electron density p(t) is displayed in the and

Figure 2.6 Relief map of the electronic density corresponding to the complex FH- . CNH obtained in the framework of the AIM methodology. (Reproduced with permission from ref. 3.)...

Figure 11.1 Relief map of the electron density calculated for the charge-assisted dihydrogen complex H20H+- HBeBeH shown in the plane of the HBeBeH molecule. The electron density of the HBeBeH molecule is located on the left side of the figure, and the electron density of the H-0 bond, which is the proton-donating site, is shown on the right side. (Reproduced with permission from ref. 2.)...

Relief maps of the charge density and L(r) in the plane of the water molecule are shown in Fig. 6.9. The L(r) at the bond critical point shows an accumulation in the internuclear surface. This is due to the shared electrostatic attraction of the electrons by both nuclei. Such a shared interaction is typical for covalent bonds. 

Fig. 8. Relief map of the total electron density in p-NTO truncated close to the nuclear positions for clarity.

C) Relief map of the negative Laplacian of the charge density, -V2p, of the chlorine molecule. One can notice three depletions of the electron charge density in the region perpendicular to the bond, and along the interatomic axis, for the colinear approach at the both ends. 

Fig, 2.4. Relief map of ihe electronic charge density in the tetrahedrane molecule, C4H4. The plane shown is a 0-4 symmetry plane and contains two carbon nuclei and their associated protons. The charge density at the central critical point is a local minimum with a value of 0.165 au. The two-dimensional maximum in the foreground is the (2, — 2) maximuln in p in the interatomic surface of the out-of-plane carbon nuclei. The value of p at this point is 0.246 au. A contour map of the charge density in the same plane is shown in Fig. 2.10. 

Fig. 3.8. Relief maps of the electronic charge density in the symmetry plane bisecting the bridgehead bond in the propellanes, shown on the right, and in the corresponding symmetry plane in each of ihe related bicyclic structures, shown on the left, (a) [2.2.2]propeliane and bicyclooctane (b) [2.2.1]propellane and norborane (c) [2.1.1]propellane and bicyclohexane (d) [l.l.ljpropellane and bicyclopentane. Contrast the presence of a central maximum in p in [2.2.2]propellanc with its absence in the bicyclic compound. There is a bridgehead bond in the former, but not in the latter.

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