Radial charge density distribution function

A radial expectation value of the normalized charge density distribution function for an arbitrary function of the radius, f r), is obtainable from the general formula... 

Figure 1.7 Plots of (a) the radial wave function (b) the radial probability distribution function and (c) the radial charge density function 4nr Rl( against p...

Additionally, from Fig. 29 one sees that, if, as proposed by Frost 42), a spherical gaussian function is a fair representation of the distribution of charge within an electride ion, there should he, as found by Slater 97>, a very good correlation, and in many cases practically an equality, between the atomic radii. . . and the calculated radius of maximum radial charge density in the outermost shell of the atom". 

It is worthwhile to demonstrate the competition between interactions by means of a qualitative evaluation of the strengths of the various interactions. This ev iluation is based on the properties of the radieil wavefunctions Rni(r) of the 4f, 5d, 6s and 6p electrons. In fig. 1.20 the radial charge densities Rh(r) are plotted as functions of r for the 4f, 5s, 5p, 5d, 6s and 6p electrons of Ce I 4f5d6s6p. These charge distributions, which are characteristic of all lanthanides were obtained by Z.B. Goldschmidt (1972) by performing Hartree-Fock calculations. 

Fig. 10 shows the radial particle densities, electrolyte solutions in nonpolar pores. Fig. 11 the corresponding data for electrolyte solutions in functionalized pores with immobile point charges on the cylinder surface. All ion density profiles in the nonpolar pores show a clear preference for the interior of the pore. The ions avoid the pore surface, a consequence of the tendency to form complete hydration shells. The ionic distribution is analogous to the one of electrolytes near planar nonpolar surfaces or near the liquid/gas interface (vide supra). 

Figure 3. Charge density about a chloride anion in molten NaCl (simulation as per Fig. 2), taken from Ref. [239]. Solid Results of simulation data. Dashed Best-fit based on Eq. 3. Cation-cation and cation-anion radial distribution functions for molten NaCl, obtained from simulation (force field given in Ref. [285]).

Figure 17-12. Radial distribution functions (RDFs) of the oxygen of water solvent around the nitrogen in the neutral glycine (NF). The solid line is for the solute with average electron density and the broken line is for the solute with a set of point charges...

FIG. 16 Ion distribution function P(r) (left) and mean electrostatic potential if/j) (right) for DNA-like systems (see Table 1) with 0.5 mol/L added 2 2 salt. The six curves differ in the line charge density of the rod, producing Manning parameters between 1.05 and 10.5 as indicated in the key. The value 4.2 corresponds to DNA. Notice that the radial distance is only plotted up to one third of the cell radius. 

There is a continuing interest in exploring possible relationships between the shell structures of atoms and their electronic density distributions [31-39]. In this respect, considerable attention has focused upon the radial density function, D(r) = 4nr p(r), which goes through a series of maxima and minima with increasing radial distance from the nucleus [6,31-36,40], [p(r) is the electronic density function since atomic charge distributions are spherically symmetric... 

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