Overlapping ion model

Overlapping Ion Model. The ground-state wave function for an individual electron in an ionic crystal has been discussed by Lowdin (24). To explain the macroscopic properties of the alkali halides, Lowdin has introduced the symmetrical orthogonaliz tion technique. He has shown that an atomic orbital, x//, in an alkali halide can be given by... 

Figure 4, Experimental (13) and calculated (11) isomer shifts for alkali iodides. Overlapping ion model predicts that shifts will be proportional to the sum of the overlaps. Equation 13...

The Electrostatic Energy for the Point-Charge and Overlapping-Ion Models... 

Retention of proteins in ion exchange chromatography is mainly caused by electrostatic effects. Because both the protein and the surface have an electrical double layer associated to it, there is an increase in entropy when the two surfaces approach each other. This is due to a release of counter ions from the two double layers when they overlap. The model that is discussed here is based on a solution of the linearized Poisson-Boltzmann for two oppositely charged planar surfaces. We also show the result from a model where the protein is considered as a sphere and the... 

Seen from the point of view of quantum chemistry, this model divides the interelectronic repulsion effects into two categories the intra-atomic effects which are approximated by an analytic function corresponding to a smoothly varying valence state energy as function of ionicity, and interatomic effects which are represented by the Madelung potential valid for spherically symmetric, non-overlapping ions. 

Such anion-anion overlap causes a broadening of the Compton profile, and it has been shown that quite good agreement between experiment and a free ion model may be obtained for other rock-salt compounds if the effect is included, although it is always smaller than in LiH. Thus for LiF and LiCl< > the anion-anion overlap is calculated to have a 10% effect on the Compton profile at low momentum values but only a 1 % effect on x-ray scattering factors. As expected, MgO shows larger overlap effects than the halides. In other, more covalent compounds, for example BeO< > and A1N< >, the expected large departures from ionic model behavior have been observed but have yet to lead to improved wavefunctions for the solids. 

Such studies, which give direct information on the distribution of electrons in specific valence orbitals, have rarely been performed in the required detail to give quantitative information on bonding. The form factor of single crystal antiferromagnetic NiO< > showed an expansion which fitted closely with the free ion model including overlap and orbital effects. Indeed, the measurement of the covalently reduced moment and form factor expansion for this compound preceded the understanding of these effects. Early measurements on several polycrystalline Mn + compounds indicated a form factor contraction< > which was taken to be a reflection of the nephelauxetic effect—the expansion of the... 

The interaction potential used in these simulations derives from the polarizable ion model [15]. It can be described as the sum of four different contributions charge-charge, dispersion, overlapped repulsion, and polarization, as previously described by Salanne et al. [16].This code is dedicated to calculations in ionic liquids. Via classical MD calculations, it allows generating the trajectories of ions inside a periodically replicated simulation cell, and then extracting the relevant physico-chemical properties of the melt. 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

With correct experimental procedure TDS is straightforward to use and has been applied extensively in basic experiments concerned with the nature of reactions between pure gases and clean solid surfaces. Most of these applications have been catalysis-related (i. e. performed on surfaces acting as models for catalysts) and TDS has always been used with other techniques, e.g. UPS, ELS, AES, and LEED. To a certain extent it is quantifiable, in that the area under a desorption peak is proportional to the number of ions of that species desorbed in that temperature range, but measurement of the area is not always easy if several processes overlap. 

Sharma, R.R., Das, T.P., and Orbach, R. 1967. Zero-field splitting of S-state ions. II. Overlap and covalency model. Physical Review 155 338-352. 

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