PEIERLS INSTABILITIES IN COVALENT STRUCTURES - I - ELECTRONIC-STRUCTURE, COHESION AND THE Z = 8-N RULE

The Vast majority of the molecular, crystalline or liquid structures o f 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 struc tures are discussed in a simple tight-binding approximation. In this f ramework we show that the Peierls electronic instability of a simple c ubic structure leads to the octet rule. This instability does not rely upon the periodicity and consequently may occur in crystalline, amorp hous or liquid matter. In a general discussion on the stability of cov alent structures, we show that the existence of a Peierls distortion i s governed by the balance between the attractive (band) term and the e mpirical repulsive term. As the hardness of the latter increases when going down the periodic table, this explains why the Peierls distortio n is stronger for the light elements.