Pair and Shell Model Potentials

The fundamental assumption in Born s description of the solid is that the crystal is composed of spherically symmetric positive and negative ions. These ions interact with one another according to their separation (except at short distances, where atoms begin to collide). The value of their energetic interaction is given by Coulomb s law  

Because a crystalline solid is composed of a three-dimensional array or lattice of ions, the total electrostatic energy of interaction E i must account for all the resulting pairwise interactions  

The Vi appears before the summation because the complete summation counts each electrostatic interaction twice. (Alternatively, one could sum over i / and remove the factor Vi.) 

However, as Madelung and Born originally pointed out, the summation of the totality of ion-ion interactions can be reduced to a simple electrostatic term and a structure-dependent constant, the value of which is uniquely determined by the lattice in question. The resulting Madelung constants capture the limiting values of the conditionally convei ent sums of electrostatic interactions. 

Here Madelung the electrostatic energy of the crystal, e the electronic charge multiplied by the valence of the ions of the structure, r a measure of the lattice constants of the crystal, and A the Madelung constant, which depends only on the crystal structure. 

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Characteristics Ion Pair and Shell Model Potentials Molecular Mechanics Potentials... 

Ion pair and shell model potentials are in general computationally simpler than molecular mechanics force fields because the former have simple functional forms and use relatively few parameters. The accuracy of these potentials may, however, be limited, especially for the detailed simulation of vibrational spectra. The use of ab initio data for the construction and parameterization of a... 

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