Peierls instabilities in covalent structures I. Electronic structure, cohesion and the Z = 8 – N rule

Abstract

The vast majority of the molecular, crystalline or liquid structures of groups V, VI and VII of the periodic table and their compounds obey the octet rule (Z = 8 - N). The structure and stability of those structures are discussed in a simple tight-binding approximation. In this framework we show that the Peierls electronic instability of a simple cubic structure leads to the octet rule. This instability does not rely upon the periodicity and consequently may occur in crystalline, amorphous or liquid matter. In a general discussion on the stability of covalent structures, we show that the existence of a Peierls distortion is governed by the balance between the attractive (band) term and the empirical repulsive term. As the hardness of the latter increases when going down the periodic table, this explains why the Peierls distortion is stronger for the light elements.