Radial effective charge model

Baldovi, J.J., Clemente-Juan, J.M., Coronado, E. and Gaita-Arino, A. (2013) Two pyrazolylborate dysprosium(III) and neodymium(III) single ion magnets modeled by a radial effective charge approach. Polyhedron, 66, 39—42. 

The effective CF models, intended to include covalence effects via effective charges and shielding parameters [46] (superposition model [47], effective charge model [48], simple overlap model [49, 50]), keep the radial (M-L distance) dependence of the CF parameters as in the simple (point charge) electrostatic model. Dedicated studies have shown, however, that the radial dependence of these parameters deviates strongly from the latter for the whole series of lanthanide ions [51, 52]. 

As an application to atomic systems, the efifective Slater atomic model will be considered (Slater, 1930 dementi Raimondi, 1963 dementini et al., 1967) that is employing the Slater effective charge and the valence electrons through the potential (4.312) and the radial electronic density for a given quantum (shell) number n and the orbital exponent related with Eqs. (4.317) and (4.131), here as... 

In the REC model, the ligand is modelled through an effective point charge situated in the axis described by the lanthanide-coordinated atom axis, at a distance R, which is smaller than the real metal-ligand distance (Figure 2.6). To account for the effect of covalent electron sharing, a radial displacement vector (Dr) is defined, in which the polar coordinate R is varied. At the same time, the charge value (q) is scanned in order to achieve the minimum deviation between calculated and experimental data, whereas 9 and cp remain constant. 

Rate equation analyses for classical size exclusion chromatography have been based on treating the porous matrix as a homogeneous, spherical medium within which radial diffusion of the macromolecular solute takes place (e.g. (28,30,31)) or If mobile phase lateral dispersion Is considered Important, a two dimensional channel has been used as a model for the bed (32). In either case, however, no treatment of the effects to be expected with charged Brownian solute particles has been presented. As a... 

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