Point-ion model

Computations of minimum-energy configurations for some off-centre systems were first carried out on the basis of polarizable rigid-ion models, mainly devoted to KChLi" " [95,167-169]. Van Winsum et al. [170] computed potential wells using a polarizable point-ion model and a simple shell model. Catlow et al. used a shell model with newly derived interionic potentials [171-174]. Hess used a deformation-dipole model with single-ion parameters [175]. At the best of our knowledge, only very limited ab initio calculations (mainly Hartree-Fock or pair potential) have been performed on these systems [176,177]. 

Recently, wave functions for an F center in sodium azide have been calculated using the point-ion model, and the electronic structure of the center has been elucidated [19]. In the monochnic phase the point symmetry at the anion site is C2h- There are two allowed transitions of the F center in this symmetry (corresponding to to A and A" to B transition). The calculation predicts that the bands due to these transitions should occur in the area of 730 nm and that the two bands would be very close, perhaps experimentally unresolvable. The calculation also predicts an absorption in the near-infrared due to the A" to B" transition. The energy levels of the F center in C2h symmetry of NaNa are depicted in Figure 6. 

Excluded-volume models take into account the fact that the finite size of the ions leads to a lower counterion concentration near a charged surface, and to a weaker Debye screening of the electrostatic field (in comparison with the point-ion model), which results in a stronger repulsion between two charged surfaces at short separations [587,588]. 

The electrolyte solution is modelled as a two-component, electroneutral system of point ions with charges ez, = ezL = ez. The density of the fluid is (p+ = pL = p /2). The fluid-fluid and fluid-matrix Coulomb interactions are... 

The representation of an essentially infinite framework by a finite SCF treated cluster of atoms, (with or without point-ions), inevitably leads to the problem of how to truncate the model-molecule . Previous attempts at this have included using hydrogen atoms l and ghost atoms . Other possibilities include leaving the electron from the broken bond in an open shell, or closing this shell to form an ionic cluster. A series of calculations were performed to test which was the host physically realistic, and computationally viable, solution to this problem for this system. 

Sharma, R.R., Das, T.P., and Orbach, R. 1966. Zero-field splitting of S-state ions. I. Point-multipole model. Physical Review 149 257-269. 

We have shown in this chapter that the major electronic features that determine the spin dynamics of SIMs based on lanthanides can be directly correlated with the local coordination environment around the 4f metal ions. By using an effective point-charge model that accounts for covalent effects, we have shown that the splitting of the ground state,/, of the lanthanide into Mj sublevels, caused by the influence of the CF created by the surrounding ligands, is consistent with... 

The Gouy-Chapman theory treats the electrolyte as consisting of point ions in a dielectric continuum. This is reasonable when the concentration of the ions is low, and the space charge is so far from the metal surface that the discrete molecular nature of the solution is not important. This is not true at higher electrolyte concentrations, and better models must be used in this case. Improvements on the Gouy-Chapman theory should explain the origin of the Helmholtz capacity. In the last section we have seen that the metal makes a contribution to the Helmholtz capacity other contributions are expected to arise from the molecular structure of the solution. 

Since the unpaired electron in transition metal complexes is generally localized near the central ion and the ligand atoms in the first coordination sphere, summation in (5.5) over these nuclei is often sufficient. In this approximated form, the point-dipole model has frequently been applied in ENDOR studies of transition metal complexes to determine the proton positions from their hfs tensors (Sect. 6). In some cases the accuracy of this method has turned out to be significantly higher than that of an X-ray diffraction analysis62,130 131). 

Figure 8. Distributions of ESP of single (remotedfrom crystal) non-point ions Li+, Na+, F+, reconstructed on the parameters of the k- model...

Dubye-Hiickel Theory of Activity Coefficient Point-Charge Model. The Debye-Hiickel theory of ion-ion interactions (Chapter 2) gives the following theoretical... 

It is quite remarkable that electrostatic calculations based on a simple model of integral point charges at the nuclear positions of ionic crystals have produced good agreement with values of the cohesive energy as determined experimentally with use of the Born-Haber cycle. The point-charge model is a purely electrostatic model, which expresses the energy of a crystal relative to the assembly of isolated ions in terms of the Coulombic interactions between the ions. 

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

In point defect models, vacancies and interstitial ions may be responsible for point defects. These defects may be independent of both the composition and external conditions. 

The cohesive energy of ionic crystals is mainly due to electrostatic interaction and can be calculated on the basis of a point-charge model. Following Born, the cohesive energy (U) of a crystal containing oppositely charged ions with charges Zj and Zj is written as the sum of two terms, one due to attraction and the other due to repulsion ... 

All symbols have their usual meaning in the c.g.s. system of units, as given in Ref. 3. The common interpretation that the central ion sees its ionic cloud at a distance k 1 away is valid for the point-charge model only. For the DH second approximation the ionic cloud can be reduced to a charge located on a spherical surface at k 1 so as to maintain a constant potential at the surface of the central ion. Therefore, it cannot be replaced by a point charge. 

---