Radial electron localization function

FIGURE 5.9 Comparison of the Li-radial density given with the electron localization function for the simplified self-consistent approximation for Li atomic structure after Putz et al. (2006). 

FIGURE 5.10 Comparative analysis of the charge density contours, electronic localization functions (ELFs), and radial densities for the H (dashed lines), F, Cl, Br, and I (full lines) atoms in molecular combinations HF, HCl, HBr, and HI, respectively after Putz Chiriac (2008). 

Analysis of the radial pair distribution function for the electron centroid and solvent center-of-mass computed at different densities reveals some very interesting features. At high densities, the essentially localized electron is surrounded by the solvent resembling the solvation of a classical anion such as Cr or Br. At low densities, however, the electron is sufficiently extended (delocalized) such that its wavefunction tunnels through several neighboring water or ammonia molecules (Figure 16-9). 

The presence of local cation ordering in Mg2Ga and MgsGa - CO3 LDHs noted in Sect. 3.3.1 has been confirmed by means of both EXAFS and by calculation of the electron radial distribution function from the Fourier transform of the diffracted X-ray intensity. In each case the gallium was found to have six magnesium ions and no galhum ions as next-nearest neighbors [39]. 

The average local electrostatic potential V(r)/p(r), introduced by Pohtzer [57], led Sen and coworkers [58] to conjecture that the global maximum in V(r)/p(r) defines the location of the core-valence separation in ground-state atoms. Using this criterion, one finds N values [Eq. (3.1)] of 2.065 and 2.112 e for carbon and neon, respectively, and 10.073 e for argon, which are reasonable estimates in light of what we know about the electronic shell structure. Politzer [57] also made the significant observation that V(r)/p(r) has a maximum any time the radial distribution function D(r) = Avr pir) is found to have a minimum. 

The EXAFS spectroscopy results strongly confirm the existence of local order in the mineral part of lead isooctane reverse micelles in dodecane and reveal quantitative information concerning the first and second coordination shells. The radial distribution functions (RDFs) exhibit peaks at around 0.19 nm, corresponding to the first shell of oxygen atoms and at around 0.35 nm corresponding to the shell of lead. Analytical transmission electron microscopy (ATEM) indicates the size of the mineral core of the micelles (1-1.5 nm) and the discoid shape of the particles when the micelles aggregate (Mansot et al. 1994). 

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