Introduction

The defining characteristic of a covalent bond is the existence of a local maximum in the valence electron density in the regions between the atomic cores. For example, the experimentally measured charge density in Si, illustrated in Fig. 9.1, shows peaks between the atomic positions. From this phenomenon comes the simple idea that two atoms forming a covalent bond share their valence electrons. Concentrating the valence electrons in the spaces between the atomic cores is clearly distinct from the ionic bonding model, where the valence electrons are centered on the anion positions, and the metallic bonding model, where the valence electrons are uniformly distributed in the free electron sea. Therefore, we will have to adopt an alternative model for the description of the valence electrons in a covalently bonded crystal. In the ionic bonding model, it was assumed that valence electrons were transferred from atomic states on the cation to atomic states on the anion. In the metallic bonding model, it was assumed that valence electrons were transferred from atomic energy levels to free electron states. The objective of this chapter is to describe a model for the transfer of valence electrons from atomic energy levels to a new set of crystal energy levels which can be simply thought of as having properties that are intermediate between the atomic energy levels used in the ionic bonding model and the free electron energy levels used in the metallic bonding model.