Electronic charge density local maxima

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. 

As mentioned in Chapter 8 (page 172), the double bond is associated with an elliptical distribution of electronic charge in the plane perpendicular to the CC nuclear axis and containing its mid-point where the electronic density has a local maximum (critical point in the theory of Bader). The relief diagram and the contour plots of Fig. 9.7 taken from the work of Bader et al. (ref. 92) show the distribution of the electronic charge density in the nuclear plane of the molecule. 

The theory of atoms in molecules defines chemical properties such as bonds between atoms and atomic charges on the basis of the topology of the electron density p, characterized in terms of p itself, its gradient Vp, and the Laplacian of the electron density V p. The theory defines an atom as the region of space enclosed by a zero-/lMx surface the surface such that Vp n=0, indicating that there is no component of the gradient of the electron density perpendicular to the surface (n is a normal vector). The nucleus within the atom is a local maximum of the electron density. 

SoKtons produced in polyacetylene are delocalized over approximately 12 CH units, with the maximum charge density to the dopant counterion. Soliton formation results in the creation of a new localized electronic state which is in the middle of the energy gap. At a high level of doping the charged sohtons produce soliton bands that can merge to behave hke a metalhc conductor. 

It is reasonable to speculate that the differences in elemental densities at the MNM transition are related to characteristic atomic properties. One such property, for example, is the radius of the principal maximum in the charge density of the ns valence orbital, a which enters into the Mott criterion (Section 2.3.4). A related property is the static polarizability a of the isolated atom. The polarizability formed the basis of very early discussions of the MNM transition by Goldhammer (1913) and Herzfeld (1927). They pointed out that electrons localized around atomic nuclei constitute polarizable objects and their internal dynamics in dense assemblies leads to local corrections to the polarizing tendency of any external field impressed on the system. For an isotropic material, the correction factor has the form [1 — (4Tr/3)lVa] where N is the number of atoms per unit volume. If a is taken to remain roughly... 

---