Chemical Bonds in Minerals: Topological Analysis of the Electron Localization Function

Abstract

The characterization of the chemical bonds in minerals and particularly in silicates is a puzzling problem which is related to the criteria used to classify them. As discussed by Tossell and Vaughan (1992), the availability of an absolute description of covalency versus ionicity in terms of observable properties is questionable. From the experimental point of view, the relevant information is provided by the analysis of the electron density. However, different schemes can be applied to partition the crystal into atomic domains which yield slightly different atomic charges. Moreover, the nature of chemical bond is not only a matter of electron distribution, but above all, of distribution of electron pairs. Theoretically most analyses of the bonding rely either on the valence bond (VB) or molecular orbital (MO) schemes, in which the VB and MO functions are themselves expressed in terms of atomic basis functions. Therefore, the guidelines used to characterize the bonding depend upon the level of approximation, they cannot be applied with exact wavefunctions. The characterization of chemical bond is qualitative, not quantitative. The topological analysis of the gradient field of local functions is the mathematically founded approach to go from quantitative to qualitative. This method has been pioneered by Bader (1990) who emphasized the role ofthe electron density. It allows to define bond paths and atomic basins and therefore rationalizes the concept of bonded atoms, provides an objective partitioning scheme and gives a theoretical foundation to structural chemistry. However, as already mentionned, with the electron density alone it is not easy to reveal the formation of electron pairs which are the consequences of the Pauli exclusion principle. In this communication, we apply such a topological analysis to the gradient field of local functions, named hereafter localization functions, which measure the Pauli repulsion. This enables us to propose a new set of criteria to classify chemical bonds which are applied to silica and related materials. A sketch of the topological theory of chemical bonds.