The hierarchy of localization basins:: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1-4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the "elfological" framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VOx and VOx+ (x = 1-4) oxides in their ground state and in some excited states.