Quantum mechanical concepts

Abstract

Abstract The experimental trends in bonding and structure which we have discussed in the previous chapter cannot be understood within a classical framework. None of the elements and only very few of the thousand or more binary AB compounds are ionic in the sense that the electrostatic Madelung energy controls their bonding. And even for ionic systems, it is a quantum mechanical concept that stops the lattice from collapsing under the resultant attractive electrostatic forces: the strong repulsion that arises as the ion cores start to overlap is direct evidence that Pauli’s exclusion principle is alive and well and hard at work! In this chapter we will briefly outline the key experiments which led to the breakdown of the classical world view and the birth of quantum mechanics. The concept of a wave packet will be used to resolve the problem of wave-particle duality and to underpin Heisenberg’s uncertainty principle. A plausibility argument will then be given for the derivation of the Schrodinger equation. It will be solved both for the free-electron gas and free atoms as the former is the starting point for our treatment of the bonding and structure of sp-valent metals, the latter for our treatment of covalent systems. Although this chapter is primarily concerned with introducing the concepts behind quantum mechanics, we will end with a short section on the recent predictive power of first principles calculations. It is these computationally intensive calculations that have given credence to the simple models which are developed and presented in subsequent chapters.