Electron-density plot, scaled

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. 

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. 

Figure 6, Electron-density plots for the valence-shell atomic orbitals of sulfur, oxygen, and hydrogen as the free atoms. These plots are to the same scale as those given in Figures 2 through 5 and 7 through 10.

This Is a qualitative problem that asks us to combine information about three different orbitals on a single plot. We need to find electron density information and draw a single graph to scale. 

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.

The small correlation effects on the s and (pi s also lead to slight changes in the electron density p(r) (Eq. (1.15)), which would be perceptible only on a highly expanded plotting scale. 

In this plot, we can see that if we increase the pressure, the energy also will be increased but the rate of this increment will be different for each state. The results discussed for the PIAB model are particular situations of generalizations reported for systems confined with Dirichlet boundary conditions [2]. We must remember these results for further discussion through this chapter. Let us conclude this section with the remark that the state dependence of the effective pressure at the given value of Rc can be analogously understood in terms of the different electron densities and their derivatives at the boundaries. In most general case of atoms and molecules, scaled densities may have to be employed in order to include the excited states. In the next section, we present some basic results on such connections between wave function and electron density. 

Figure 14 Radial charge density plot from the orhital/Feynman-Dyson (FD) amplitude for the Ss orbital in Be from zeroth order (SCF ), the second order (E2 A) and diagonal 2ph-TDA decouplings /EJph-TDA ). On the scale employed in the main plot, distinguishing the orbital/FD amplitudes from different decouplings is not possible but in the inset the difference between radial charge densities from the second and zeroth order (bi-variaiional SCF) decouplings clearly reveals the role of correlation and relaxation effects in changing the ionization potential from 8.44 cV at the SCF level to 8.79 eV at second order. The maximum in the electron density is at imu = 2.1 a.u.

When comparing two maps, the comparison is useful only if they are plotted using the same scale of color gradation. For this reason, whenever we compare two plots in this text, they will be drawn side by side using the same scale. It will be difficult to compare two plots in different parts of the book, because the scale may be different. Despite this limitation, an electrostatic potential plot is a useful tool for visually evaluating the distribution of electron density in a molecule, and with care, comparing the electron density in two different molecules. 

FIGURE 9.3. Numerical values for the calculated electron density (a) at grid points, and (b) a two-dimensional plot, showing how contours are drawn in two dimensions. The level of contours (in electrons per cubic A) can be calculated if the volume of each three-dimensional grid block is known in A , and the absolute scale is know for the electron density (from the Wilson plot initially, and then from the subsequent lecist-squares refinement). 

FIGURE 4.30 The plots as local representation (upper draws) and linear regressions like global representation (lower draws) for the atomic radii scales abstracted from Slater electronic density picture, both in related and non-related electronegativity methods, as indicated in the brackets < > referred to the Table 4.16 after Putz et al. (2003,2012b,c). 

Fig. 15. ORTEP plot of Lii(PcXOAcXH20)2. Ellipsoids are scaled to enclose 50% of the electron density. Hydrogen atoms are omitted. (From De Cian et al. 1985 with permission.)...

Figures 1.21 and 1.22 are another type of representation of the ethylene molecule derived from MO calculations. Figure 1.21 is a log scale plot of the cr-electron density. It shows the highest density around the nuclear positions as indicated by the pronounced peaks corresponding to the atomic positions and also indicates the continuous nature of the cr-electron distribution. A representation of the 7r-electron density is given in Fig. 1.22. This depicts the density in a plane bisecting the molecule and perpendicular to the plane of the molecule. The diagram shows that the TT-electron density drops to zero in the nodal plane of the tt system.

Fig. 1.21. Log scale plot of o--electron density in a plane bisecting the carbon atoms and perpendicular to the plane of the molecule. (From A Streitwieser, Jr., and P. H. Owens, Orbital and Electron Density Diagrams, Macmillan, New York, 1973. Reproduced with permission.)...

Log scale plot of (T-electron density in a plane bisecting the carbon atoms and perpendicular to the plane of the molecule... 

When you have finished the calculations, display all three maps on the screen at the same time. To compare them, you must adjust them all to the same set of color values. This can be done by observing the maximum and minimum values for each map in the surface display menus. Once you have all six values (save them), determine which two numbers give you the maximum and minimum values. Return to the surface plot menu for each of the molecules and readjust the limits of the color values to the same maximum and minimum values. Now the plots will all be adjusted to identical color scales. What do you observe for the carboxyl protons of acetic acid, chloroacetic acid, and trichloroacetic acid The three minimum values that you saved can be compared to determine the relative electron density at each proton. 

We have studied luminance versus current density plots in devices based on SA films deposited at different polyanion pHs. Luminance has been detected only under forward bias directions. Luminance versus current density plots for devices based on different SA films are presented in Fig. 5. Similar plot for devices with spin-cast film of alizarin violet has also been shown in the figure for comparison. Each of the plots shows a sharp tum-on followed by a linear behaviour in the log-log scale. The turn-on current is generally determined by the amount of electron injection required for light emission in these devices. The turn-on current and the luminance from the LEDs at any current density depended on the polyanion pH used in SA film deposition. The figure shows that the LEDs based on SA films (deposited at a suitable polyanion pH) can yield higher luminance than the devices based on spin cast films. The tum-on currents in such devices are also lower as compared to the spin-cast counterpart. 

Above the tum-on current, the linear behaviour of luminance-current density plots in the log-log scale can be explained in terms of FN tuimelling model. Considering the FN mechanism to be valid for both electron and hole injections, a relationship between luminance (L) and current density J) can be established as [14] ... 

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