Electron-density contour map

Figure 5.2 (a) Electron density contour map of the CI2 molecule (see Chapter 6) showing that the chlorine atoms in a CI2 molecule are not portions of spheres rather, the atoms are slightly flattened at the ends of the molecule. So the molecule has two van der Waals radii a smaller van der Waals radius, r2 = 190 pm, in the direction of the bond axis and a larger radius, r =215 pm, in the perpendicular direction, (b) Portion of the crystal structure of solid chlorine showing the packing of CI2 molecules in the (100) plane. In the solid the two contact distances ry + ry and ry + r2 have the values 342 pm and 328 pm, so the two radii are r 1 = 171 pm and r2 = 157, pm which are appreciably smaller than the radii for the free CI2 molecule showing that the molecule is compressed by the intermolecular forces in the solid state. 

Fig. 22. Electron density contour maps of the three frontier orbitals of electron-deficient M(it-C5Hs)2 fragments. The plots represent a section through the yz plane. [Reproduced from Lauher and Hoffmann (134), by permission of the American Chemical Society.]...

Consider Fig. 6.32 which is an electron density contour map of the sodium cyanide crystal Interpret this diagram in terms of everything that you know about the structure of solid sodium cyanide. 

In a later paper, the authors218 analysed the charge re-distribution in more detail, using electron density contour maps. An energy-level correlation diagram shows no correlations between bonding levels and antibonding levels in the product. 

One interesting species, unknown until recently, is HOF, which was studied by Peslak et al.,611 and electron-density contour maps were described. More recently, it was studied by Kim and Sabin.512 The computed bond lengths with a near-minimal GTO basis were i (H—O) = 1.080 A, J (0—F) = 1.450 A, and 0 = 100.8°, in fair agreement with the results of a microwave investigation. Force constants were computed and the population analysis was reported. A more extensive basis set was used in a similar calculation by Ha, who computed a dipole moment of 2.72 D.513... 

Fig. S. (A) Emergent hybrid d orbitals at a metal surface (schematic). [After Bond 24).] (B) (Left) Electron-density contour map for the occupied a2, antibonding surface orbital of a cubooctahedral Ni,3 cluster, corresponding to the energy level —0.413 Ry, plotted in the plane of the square face containing atoms 1-4 of the cubooctahedron structure. (Right) Equivalent map but corresponding to the energy level -0.413 Ry plotted in the equatorial plane containing atoms 5-8 and 13 of the cubooctahedron structure.

Such an expression has previously been used for comparative purposes, for the study of interaction between two molecular species, by computing the electrostatic potential of the first partner and by assuming some point charge model as representative of the charge distribution of the second partner. We also plan to extend this concept in a more subtle way by using an electron density contour map to describe the charge distribution of the second partner as a function of the space surrounding this second partner. 

The X-ray diffraction technique offers the most accurate method for determining bond lengths and bond angles in molecules in the solid state. Because X rays are scattered by electrons, chemists can construct an electron-density contour map from the diffraction patterns by using a complex mathematical procedure. Basically, an electron-density contour map tells us the relative electron densities at various locations in a molecule. The densities reach a maximum near the center of each atom. In this manner, we can determine the positions of the nuclei and hence the geometric parameters of the molecule. 

Fig. 2.1. Electron density contour maps for the model MggOg of the MgO(OOl) surface in the plane containing the fourfold symmetry axis and the moiety O-Mg-O a) Mgpp +PC embedding b) PC only embedding c) electron density difference Ap = p(Mg909, Mg +PC) - p(Mg909,PC) with negative values indicated by dashed lines.

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 densit > relief map, which portrays the contour map three-dimensionally as peaks of electron density. 

Definition of the ionic radius as viewed from a hard-spheres ionic crystalline lattice (a) and an electron density contour map (b). [Reproduced from Kittel, C. Introduction to Solid State Physics, 6th ed., John Wiley Sons, Inc New York, 1986. This material is reproduced with permission of John Wiley Sons, Inc.]... 

These corrected ionic radii are a much better approximation to the experimental values derived from X-ray diffraction data and electron density contour maps, such as the one shown in Figure 12.6 for TiC. The experimentally determined values, defined by where the electron density of one ion ends in the contour map. 

Electron density contour map for TiC, which assumes the halite lattice structure. [Reproduced by permission. Blaha, R ... 

Figure 5 Projection of the electron density contour map for benzene on the plane of the molecule. The positive and zero isocontours are represented by solid and dashed lines, respectively.

Rgure 21.29 Electron density contour map of urea and its structural formula... 

Figure 20.26 Electron density contour map for band 90 and the top of valence band. Zn (light gray), Ge (dotted area), and O (black)...

Figure 20.27 Electron density contour map for the bottom of conduction band at contour of (a) 0.1 and (b) 0.05...

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