Crystal point-charge approximation

Electrostatic embedding In the case of ionic compounds, the largest contribution to the potential exerted by the rest of the crystal on the (central region of the) cluster is due to long-range electrostatic interactions. These are accurately represented by the point charge approximation, that is, the Madelung potential ... 

Crystal-field parameters are determined from a simple point-charge approximation using... 

In crystal field theory each ligand is approximated as a point charge or a point dipole and each metal-ligand interaction is taken to be purely electrostatic. So our problem is reduced to one of investigating the effect of point charges (or point dipoles) arranged tetrahedrally or octahedrally about an electron in a dai y or a dXI orbital. 

Ligand field theory may be taken to be the subject which attempts to rationalize and account for the physical properties of transition metal complexes in fairly simple-minded ways. It ranges from the simplest approach, crystal field theory, where ligands are represented by point charges, through to elementary forms of molecular orbital theory, where at least some attempt at a quantum mechanical treatment is involved. The aims of ligand field theory can be treated as essentially empirical in nature ab initio and even approximate proper quantum mechanical treatments are not considered to be part of the subject, although the simpler empirical methods may be. 

The crystal field interaction can be treated approximately as a point charge perturbation on the free-ion energy states, which have eigenfunctions constructed with the spherical harmonic functions, therefore, the effective operators of crystal field interaction may be defined with the tensor operators of the spherical harmonics Ck). Following Wyboume s formalism (Wyboume, 1965), the crystal field potential may be defined by ... 

The field evolved out of the simulation of liquids and solutions and has adopted many of the models from there. Water, ions, and atoms are described by point charge models, augmented by empirical or ab initio short-range and dispersion potentials, the use of which has been validated for the bulk phase. Many models of the interface have been employed, ranging from representations of simple, atomically smooth walls to parametrized interaction potentials from ab initio quantum chemical calculations that describe the interactions with atomic crystals. The metallic character of the solid phase has in most cases been approximated by the image charge model. 

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