We show that a simple tight binding model with a repulsive potential describes the Peierls distortions in covalent systems and the well-known octet rule. The existence and the intensity of the Peierls distortion is mainly related to the hardness of the repulsive potential as demonstrated both by theoretical calculations and by the experimental systematic analysis of liquid structures. In particular, As is threefold coordinated and Sb is sixfold coordinated in the liquid, the qualitative difference is explained by the ratio of the distortion energy ΔE to the thermal energy kBT. The Asx Sb1-x alloys show continuously varying average coordination numbers showing: the semiconductor-metal transition is continuous with concentration.
In addition, we illustrate in the case of liquid Se that, tight binding Monte Carlo simulations are able to describe quantitatively the structure of liquid elements provided the Van der Waals potential is added.