Homogeneous Electron Gas and Simple Metals

In this chapter we consider a gas that consists of free electrons. The homogeneous gas of interacting electrons, in which the positive charges are assumed to be uniformly distributed in space, is the simplest model representing condensed matter. This model is completely specified by the density n of the electron gas or by the average distance Vs between electrons. 

The second assumption is that the electrons move independently of each other, so that each electron feels the average repulsive electrostatic field from all other electrons. This field would be completely canceled by the attractive electrostatic potential from smeared-out ionic background. Thus, one treats the s- and sp-valent metals as a metallic jeUium within the independent particle approximation. 

As a matter of fact, the state of electrons is correlated. The energy of electrons depends also on their spin. We shall recur to the interaction of electrons later. 

Interatomic BoniUngin Solids Fundamentals,Simulation,andApplications, First Edition. Valim Levitin. 

The Schrbdinger equation for a free-electron gas takes the form 

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Another important issue in density functional theory is the form of the exchange and correlation potential. In most investigations of metal surfaces, the simple local density approximation is used, again, with surprisingly successful results. In the case of a homogeneous electron gas, the effective exchange-correlation potential is given exactly by and is accurately known from quantum Monte Carlo calculations. Outside the metal, decays... 

In the effective medium theory, the electronic interaction between an atom and the solid is replaced by that of the atom and a homogeneous electron gas. The approach is based upon density functional theory, but since the solid is not really behaving as a homogeneous electron gas, gradient corrections to the theory have been devised [210]. Simple model hamiltonians have also been used to study chemisorption of atoms and molecules at metals. Here we mention the Anderson-Grimley-Newns model hamiltonian of the type... 

We consider a homogenous gas that consists of free electrons in Chapter 5. Notions of exchange energy and correlation energy of electrons are introduced. The theory enables one to calculate some macroscopic properties of simple metals, which have the ns external electronic shell. The calculated cohesive energy of simple metals turns out to fit the experimental values satisfactorily. 

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