Electron density plots

An electron density plot is useful because it represents the electron distribution in an orbital as a two-dimensional plot. These graphs show electron density along the y-axis and distance from the nucleus, r, along the x-axis. Figure 7-19a shows an electron density plot for the 2s orbital. 

Electron density plots are useful because those for several orbitals can be superimposed to indicate the relative sizes of various orbitals. The simplicity of such a graph is also a drawback, however, because it does not show the three-dimensionality of an orbital. 

Orbital pictures have an advantage over electron density plots in that they can indicate the three-dimensional nature of orbitals. One type of orbital picture is a two-dimensional color pattern in which the density of color represents electron density. Figure 7-19Z> shows such an orbital density picture of the 2s orbital. This two-dimensional pattern of color density shows a cross-sectional slice through the middle of the orbital. 

For any particular atom, the = 2 orbitals are larger than the Is orbital, the = 3 orbitals are larger than the = 2 orbitals, and so on. The electron density plots in Figure 7-20 show this trend for the first three s orbitals of the hydrogen atom. This plot also shows that the number of nodes increases as n increases. 

Electron density plots for the 1, 2, and 3 S atomic orbitals of the hydrogen atom. The vertical... 

C07-0082. Shown beiow are electron density pictures and electron density plots for the Is, 2s, 2p, and 3p orbitals. Assign the various depictions to their respective orbitals. 

Make an electron density plot showing the 1. S, 2 p, and 3 d orbitals to scale. Label the plot In a way that summarizes the screening properties of these orbitals. 

Figures, and show electron density plots of the = 1, a = 2, and a = 3 orbitals. We extract the shapes of the 12 p, and 3 d orbitals from these graphs. Then we add labels that summarize the screening properties of these orbitals. Screening is provided by small orbitals whose electron density is concentrated inside larger orbitals. In this case, 1 s screens both 2 p and 3 d 2 p screens 3 d, but not 1 s and 3 d screens neither 1 s nor 2 p. The screening patterns can be labeled as shown.

C08-0002. Figures 8-6, 7-20, and 7-21 show electron density plots of a = 1, M = 2, and = 3 orbitals. Draw a plot that shows the — 1 and = 3 orbitals to scale. Use different colors to keep the figure as clear as possible. Shade the regions of the 3, 7 and 3 p plots where screening by 1 electrons is relatively Ineffective. 

C08-0120. Make an electron density plot that shows how the 3. S and 3 p orbitals are screened effectively by the 2 p orbitals. Provide a brief explanation of your plot. 

Fig. 7.15 Calculated (with FP-LMTO method) electron densities plotted versus measured isomer shifts (not corrected for SOD) (from [32])...

Figure 1,8 Electron density plots along (110) plane of BeO (A) effective total electron density (pseudoatom approximation) (B) total electron density of lAM (C) deformation density (pseudoatom-IAM). From Downs (1992). Reprinted with permission of Springer-Verlag, New York.

Electron distributions are ascertained by means of a Mulliken population analysis of the ir-electron atomic populations (in the case of complete n-delocalization, each atom in the 67r-electron five-membered ring would have 1.20 7r-electrons associated with it) by determining the spatial extent of the localized orbitals of both the out-of-plane lone pair of the heteroatom and the C=C double bonds as well as through comparing the total electron density plots in planes parallel to the molecular plane. 

View the electron density plots for the noble gases helium, neon, and argon in the Radial Electron Distribution movie (eChapter 5.8). 

Figure 2 (a) VMC (solid lines) and LDA (dashed lines) snxc(r,s) plotted for an electron moving along . Arrows on the electron density (plotted on top), mark the position of the electron, (b) Exact sh frjs) plotted in the same direction and at the same points as in (a) (solid lines) and the corresponding LDA approximation (dashed lines). 

The compound KrF2 is of great importance in the chemistry of krypton, and the nature of the binding is a challenge to the theoretical chemist. Early calculations at the minimal-basis-set level were reported by Collins et al,389>39<> using STO-3G expansions. Extra valence orbitals were added to the basis set. Electron-density plots showed the three-centre nature of the bond. 

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... 

Figure 2 The electron density plot of one of the two n donating orbitals in Cr(NH3)5PH3, omitting the phosphorus d orbitals from the calculations. (Reprinted with permission from Ref. 70. 1984 American Chemical Society)...

The FPLAPW method has also been used to study bimetallic bonding in PdAV(llO), Pd/Re(0001) and Pd/Ru(0001) [34], In general, electron density plots show an important shift of electrons from the Pd layer toward the metal-metal... 

Fig. 2. Difference electron density plots from X-ray data showing density according to Si-Si and Ge-Ge bond bending in the cyclotrisilane 2 and cyclotrigermane 6, respectively.

Figures 10.10a and b show, respectively, space-filling models and electron density isosurfaces plotted at 0.002 e/(tZo) for water, ammonia, and methane. The electron densities plotted here include all of the electrons in the molecule. They are calculated using state-of-the-art ab initio quantum chemical methods (see discussion in Chapter 6).

The results, in fact, are often quite informative. His group has attempted to get some idea of the charge distribution by using a Mulliken population analysis to determine the charges associated with the atoms. However, because of certain arbitrary features in the Mulliken scheme, a charge density plot is probably a more satisfactory way of looking at molecular charge distribution. A recent compilation of such electron density plots has been published by Streitwieser and Owens. ... 

Density functional theory (DFT) calculations [33] on the model complex Cp2Ti 72-HB(OH)2 2 accurately reproduced the short B- -B distance. A Laplacian electron density analysis (Fig. 2) based on the DFT calculations showed that significant electron density concentrations were found along the B- -B bonding path, indicating bonding interactions between the two borons. The four concentrations around the Ti center shown in the Laplacian electron density plot have been associated with the electron density contributed from... 

Fig. 1.4. Contour maps of electron density for 1,3,5-hexatriene and benzene in the planes of the molecules. Electron density was calculated at the HF/6-31IG level. Electron density plots were created by applying the A1M2000 program E.Biegler-Koenig, J.Shoenbohm and D.Dayles, J. Compt. Chem., 22, 545-559 (2001).

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