Electronic structure, metals quantum free-electron theory

This rule conforms with the principle of equipartition of energy, first enunciated by Maxwell, that the heat capacity of an elementary solid, which reflected the vibrational energy of a three-dimensional solid, should be equal to 3RJK-1 mol-1. The anomaly that the free electron theory of metals described a metal as having a three-dimensional structure of ion-cores with a three-dimensional gas of free electrons required that the electron gas should add another (3/2)R to the heat capacity if the electrons behaved like a normal gas as described in Maxwell s kinetic theory, whereas the quantum theory of free electrons shows that these quantum particles do not contribute to the heat capacity to the classical extent, and only add a very small component to the heat capacity. 

The first solution to this problem was produced phenomenologically by Mooser and Pearson. The solution for A B compounds is reproduced in Figure 9. Similar solutions apply not only to A"B semiconductors and insulators, but also to many intermetallic compounds including transition metals. This work provides the first step toward explaining structural and phase transitions in chemically homologous families of binary crystals. It has made the question of the proper treatment of chemical bonding in crystals susceptible to theoretical analysis, whereas formerly work based on mechanical models (ionic compounds) or quantum mechanical perturbation theory (nearly-free-electron metals) made the same problem appear insoluble. 

Models for the electronic structure of polynuclear systems were also developed. Except for metals, where a free electron model of the valence electrons was used, all methods were based on a description of the electronic structure in terms of atomic orbitals. Direct numerical solutions of the Hartree-Fock equations were not feasible and the Thomas-Fermi density model gave ridiculous results. Instead, two different models were introduced. The valence bond formulation (5) followed closely the concepts of chemical bonds between atoms which predated quantum theory (and even the discovery of the electron). In this formulation certain reasonable "configurations" were constructed by drawing bonds between unpaired electrons on different atoms. A mathematical function formed from a sum of products of atomic orbitals was used to represent each configuration. The energy and electronic structure was then... 

How close do solvent molecules come to the metal Where is the boundary of the metal To answer these questions, we must go back to the structure of the metal surface. The existence of a tail of quasi-free electrons spilled out of the ionic skeleton of the metal was predicted in the early days of quantum mechanics [108]. In the 1970s, this picture was approved and detailed by the electron-density functional theory of the inhomogeneous electron gas (later leading to Nobel fame for Walter Kohn in 1998) applied to metal... 

Halley and Mazzolo l develop>ed a flrst-principles-based direct dynamics method to examine the water/copper metal interface. Previous models on the electrochemical metal/ water interface published in the literature could not straightforwardly describe the asymmetry of the capacitance measured experimentally in the double layer. In approach taken by Halley and MazoUo, the electrons in the metal are modeled quantum mechanically using a jellium-type free electron model where only the s-electrons in copper are treated. Pseudopotentials are used to describe the electron interactions with water. The water solution phase is decoupled from the electronic structure and treated by molecular dynamics simulations with explicit water molecules using classical force fields. Gouy-Chapman theory is used to treat ionic screening. The electronic structure at the interface between the metal and the water is carefully matched by p>erforming electronic structure calculations on the metal substrate after each time step in the water MD simulation. The approach was used to examine the influence of applied potential on the structm-e of the metal-water... 

Recall the other serious difficulty discussed in Chapter 17 that arises from the fact that the classically predicted heat capacity of the electrons is not observed even though they are the major contributor to both the thermal and electrical conductivity of metals. We will find yet another problem with the classical theory when we take up the topic of paramagnetism and find that the electronic contribution expected from classical theory is not observed. Despite the success of the classical Drude theory of the free electron gas in being able to describe many of the observed properties of metals, it was these discrepancies between the classical theory and observation that prompted theorists to reexamine the classical theory of the electron and to apply the quantum mechanical treatment that had been developed to explain the electronic structure of atoms and molecules to describe the behavior of electrons in metals. 

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