Outer electron density

Element Atomic number Outer electrons Density (gem ) m.p. (K) h.p. IK) Hardness 1 Brineii)... 

A small, positively charged ion (a cation) in an ionic compound can attract the electrons of a neighbouring negatively charged ion (an anion) towards it and distort the anion. When this happens, the anion is said to be poiarized. This distortion can be better represented by using the electron density model of an ionic compound, rather than using Lewis symbols. The outer electron density contours of a purely ionic bond, and an ionic bond which is polarized, are shown in Fig. 4.7. 

Several attempts have been made to alleviate the problems of the atom cores dominating the MQSM by emphasizing the role of the chemically more interesting outer electron density. Because no physical ground exists to... 

The outer diameter of the shell is approximately 180 A and the inner diameter about 125 A except around the threefold axes, where the N-ter-minal a helices project about 20 A into the core. The RNA molecule that is present in the core is not visible in the electron density map. 

We can also mark the rest of the molecule s boundary by finding all of the other points where the molecule s electron density has the same critical value. When all of these boundary points are joined together they form a surface that looks like the molecule s outer skin , and we can use the volume inside this surface to define molecular size. This approach is used throughout this book, but to simplify things we will abbreviate outer skin electron density surface to just electron density surface . 

A reliable calculation of polarizabilities requires an adequate description of the outer part of the electron density. For this reason Kassimi and Lin [98JPC(A)9906] used augmented basis sets of triple- quality to study polarizabilities and dipole moments of thiazoles and thiadiazoles. They expect their results to be reliable within 5%. In addition, the authors provide MP2/6-31G geometries for most of their structures. Hyperpolarizabilities for substituted thiazoles obtained from calculations at lower levels are also provided [99MI2]. 

This example shows that a homonuclear polyatomic molecule (Os) can be polar shape is more important than differences in atoms and O, is polar despite all three atoms being oxygen. In this case, the central O atom has a different electron density associated with it than the outer two O atoms it is bonded to two O atoms whereas the outer atoms are bonded only to one O atom. 

FIG. 11 TEM images of (a) a [(Si02/PDADMAC)2]-coated PS particle and hollow silica capsules produced from PS latices coated with (b) one, (c) two, or (d) three Si02 layers. The hollow silica capsules maintain the shape of the original PS particle template. Removal of the core by calcination is confirmed by the reduced electron density in the interior of the capsules (compare b-d with a). The images of the hollow silica capsules show the nanoscale control that can be exerted over the wall thickness and their outer diameter. (From Ref. 106.)... 

Figure 6.3 Constant electron density envelope maps for SCI2 for three different contour values (a) p = 0.001 au, (b) p = 0.200 au and (c) p = 0.133 au. (a) This constant density envelope shows the practical outer boundary of the molecule broadly corresponding to the van der Waals envelope, (b) This constant density envelope demonstrates that for higher p values the envelope becomes disconnected into three surfaces each encompassing a nucleus, (c) This constant density envlope is plotted at the highest p value for which the molecular envelope is still connected or encompasses the whole molecule.

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.

Here we see clearly the large concentration of density around the oxygen nucleus, and the very small concentration around each hydrogen nucleus. The outer contour is an arbitrary choice because the density of a hypothetical isolated molecule extends to infinity. However, it has been found that the O.OOlau contour corresponds rather well to the size of the molecule in the gas phase, as measured by its van der Waal s radius, and the corresponding isodensity surface in three dimensions usually encloses more than 98% of the total electron population of the molecule (Bader, 1990). Thus this outer contour shows the shape of the molecule in the chosen plane. In a condensed phase the effective size of a molecule is a little smaller. Contour maps of some period 2 and 3 chlorides are shown in Figure 8. We see that the electron densities of the atoms in the LiCl molecule are only very little distorted from the spherical shape of free ions consistent with the large ionic character of this molecule. In... 

The three quantum numbers may be said to control the size (n), shape (/), and orientation (m) of the orbital tfw Most important for orbital visualization are the angular shapes labeled by the azimuthal quantum number / s-type (spherical, / = 0), p-type ( dumbbell, / = 1), d-type ( cloverleaf, / = 2), and so forth. The shapes and orientations of basic s-type, p-type, and d-type hydrogenic orbitals are conventionally visualized as shown in Figs. 1.1 and 1.2. Figure 1.1 depicts a surface of each orbital, corresponding to a chosen electron density near the outer fringes of the orbital. However, a wave-like object intrinsically lacks any definite boundary, and surface plots obviously cannot depict the interesting variations of orbital amplitude under the surface. Such variations are better represented by radial or contour... 

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