Physics and chemistry of minerals vol:20 issue:8 pages:601-616
In this paper the validity of the classical ionic model, using a Madelung term and a Born-Mayer repulsive term, is investigated quantatively for systems with a considerable overlap of the electron clouds of neighbouring ions, such as silicates with a high degree of polymerisation. A modified ionic model is presented which takes into account the spatial extent of the ions within the approximation of spherical atoms. Both models are tested against quantum mechanical electron densities and energies for SiO44--clusters. The data demonstrate the validity of the Spherical atom approximation, producing a fit of 99.995%, and the importance of many-body effects maintaining the spherical symmetry of the electron clouds as contraction/expansion of the ions and charge transfer between ions. Although the new interaction potential is physically more plausible than the classical Born-Mayer model, both models reproduce the quantum mechanical potential surface with numerical accuracies of the same order of magnitude. The new model provides an improved tool for judging between ionic and non-ionic effects and for analysis of the quantum mechanical electron densities and interaction energies.