Charge distribution, modelling

Fnuc is the nuclear attraction potential. In the uniform charge distribution model used here, the charge of a nucleus of atomic mass A is distributed uniformly over a sphere with radius R = 2.2677 x 10 . The nuclear potential for a nucleus with charge Z is then... 

Equipped with this refined charge distribution model, it is now possible to compare... 

In the recent CD [94] (charge distribution) model the charge of the specifically adsorbed ions is distributed between the surface plane and another electrostatic plane (whose distance from the surface corresponds roughly to the /3-plane distance), thus, the center of charge of specifically adsorbed ions is located between these two planes. The CD concept was originally introduced to model adsorption of... 

Fig. 22. The magnetic loop splitting energy Eml of the ground state, normalized to a(Za)AE ° , which is the leading term in a non-relativistic expansion. The dashed line refers to a relativistic point nucleus calculation whereas the solid line indicates the corresponding value for extended nuclei. The difference between both charge distribution models is notable. Note the logarithmic scale of the ordinate where 10° indicates 1.

FIGURE 12.15 The adsorption of PO4" by monodomainic goethite used by Hiemstra and Van Riemsdijk (1996) and that of Bowden et aL (1980). The lines are calculated with the charge distribution model and are consistent with the surface species observed by cylindrical internal reflection-Fourier transform infrared spectroscopy. (Reprinted from Journal of Colloid and Interface Science, 179, Hiemstra, T. and Van Riemsdijk, W. H. 488-508. Copyright 1996, with permission from Elsevier.)... 

Table 5 Number of water molecules in the micro-, first and second solvation shells and the hydrogen-bonded (HB) to the mesityl oxide, and the statistical analysis (average and standard deviation values) of HB properties for two different charge distribution models used in the MC simulations non-polarized (gas phase) and polarized in water (see Table 1) ...

Surface species and surface complex stability constants These aspects are, to some extent, interrelated. The term surface species might comprise such aspects as the polydentate character of the surface complex, inner- versus outer-sphere siuface complexation, or charge distribution. Whether surface species are plausible can be checked either by surface spectroscopy or by appUcation of the bond-valence principle, which can be coupled with specfroscopic information [110]. The latter can also help to estimate reasonable values for the charge distribution factors in charge distribution models. All of this certainly allows a restriction in the many options which... 

Function e provides a critical test for the approximate charge distribution model related to real applications. As the first example, we used imidazole, which frequently models histidine residue. In the Table 3 we compare results obtained for four different molecular charge density models Mulliken [27], CHELP [28] and ESP [29] charges and CAMM (up to quadruples). In general, electrostatic potentials on solvent accessible surfaces described by CAMM series truncated at quadrupole term tend to perform slightly better s = 2-10% than those calculated using potential-derived atomic charges. 

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