Metals, quantum-mechanical theory

While there is no complete theory of surface reactivity, an understanding of how reactant, intermediate, and product adsorbates interact with a surface often gives insight into the catalytic properties of a metal. Quantum mechanical theories show that as long as the perturbation due to the interacting systems is small, the interaction of two isolated systems can be estimated using second order perturbation theory ... 

The other place to read an authoritative histoi7 of the development of the quantum-mechanical theory of metals and the associated evolution of the band theory of solids is in Chapters 2 and 3 of the book. Out of the Crystal Maze, which is a kind of official history of solid-state physics (Hoddeson et al. 1992). 

Electron work functions of metals in solution can be determined by measurements of the current of electron photoemission into the solution. In an electrochemical system involving a given electrode, the photoemission current ( depends not only on the light s frequency v (or quantum energy hv) but also on the potential E. According to the quantum-mechanical theory of photoemission, this dependence is given by... 

The free-electron model is a simplified representation of metallic bonding. While it is helpful for visualizing metals at the atomic level, this model cannot sufficiently explain the properties of all metals. Quantum mechanics offers a more comprehensive model for metallic bonding. Go to the web site above, and click on Web Links. This will launch you into the world of molecular orbitals and band theory. Use a graphic organizer or write a brief report that compares the free-electron and band-theory models of metallic bonding. 

In the past decade, many new techniques have been developed and applied to the study of interfaces. While earlier measurements involved only macroscopic characteristics of the interface (e.g., surface charge, surface tension, and overall potential drop), new spectroscopic techniques have opened a window to the microstructure of the interface, and insight at the atomic level in this important region is now possible. Parallel to these discoveries and supported by them, more realistic theoretical models of the interface have been developed that combine quantum mechanical theories of metal surfaces and the statistical mechanics of solutions. 

The quantum-mechanical theory of metals has been extensively developed hy Sommerfeld and many other investigators.3 Discussion of it is beyond the scope of this book, however, and instead we shall consider the problem of the structure of metals from a more chemical point >f view. The treatment given in the following sections is not to be interpreted as being a rival of the quantum-mechanical theory, but rather as offering an alternative avenue of approach toward the same goal as that of the theoretical physicists. 

Nov. 21, 1931, Tbilisi, Georgia, USSR - May 13, 1985) Dogonadze was one of the founders of the new science - electrochemical physics [i]. The main scientific interests of Dogonadze were focused on condensed-phase reactions. His pioneering works of 1958-59 have laid the foundations of the modern quantum-mechanical theory of elementary chemical processes in electrolyte solutions. He developed a comprehensive quantum-mechanical theory of the elementary act of electrochemical reactions of -> electron and -> proton transfer at metal and - semiconductor electrodes [ii—v]. He was the first to obtain, by a quantum-mechanical calculation, the expression for the electron transfer probability, which was published in 1959 in his work with -> Levich. He conducted a number of studies on the theory of low-velocity electrons in disordered systems, theory of solvated electrons, and theory of photochemical processes in solutions. He made an impressive contribution to the theory of elementary biochemical processes [vi]. His work in this area has led to the foundation of the theory of low-temperature -> charge-transfer processes cov-... 

Many solid-state physicists discuss the structure and properties of metals and alloys with use of the band theory, in its several modifications. This theory is also a quantum mechanical theory, which starts with a solution of the wave equation for a single electron, and introduces electron-electron correlation in one or another of several ways. The resonating-valence-bond theory introduces electron-electron correlation in several stages, one of which is by the formation of covalent bonds between adjacent atoms, and another the application of the electroneutrality principle to restrict the acceptable structures to those that involve only M+, M°, and M-. It should be possible to find a relationship between the band-theory calculations and the resonating-covalent-bond theory, but I have been largely unsuccessful in finding such a correlation. I have, for example, not been able to find any trace of the metallic orbital in the band-theory calculations, which thus stand in contrast to the resonating-valence-bond theory, in which the metallic orbital plays a predominant role."... 

Moffitt (9) introduced the first quantum mechanical theory of optical activity in chiral transition metal complexes. He... 

Brodskii and Gurevich developed a quantum mechanical theory of photoemission at the metal-electrolyte interfaces. They have given an expression for the photocurrent which involved the following assumptions ... 

One of the most fundamental problems in electrochemical surface science is distribution of the electric potential and the particles at the interface. The classical model which prevailed until about 1980 treated the electrode surface as a perfect and structureless conductor and did not take into account the surface electronic structure. The electrolyte was considered as an ensemble of hard, point ions immersed in a dielectric continuum. This approximation neglected the fine structure of the solvent molecules and the solute as well as their discrete interactions. In recent years, much progress has been made in providing a more realistic model of the solid-liquid electrochemical interface by applying quantum mechanical theories to model the metal... 

As you have seen, the periodic table is a result of empirical observation (i.e., the periodic law), but quantum-mechanical theory explains why the table is so arranged. Suppose that, in another universe, quantum theory was such that there were one s orbital but only two p orbitals (instead of three) and only three d orbitals (instead of five). Draw out the first four periods of the periodic table in this alternative universe. Which elements would be the equivalent of the nohle gases Halogens Alkali metals ... 

Unfortunately there are no simple theories to predict the cohesive energies of the metals like the coulomb attraction in ionic crystals. More sophisticated quantum mechanical theories using pseudopotential or other modeling techniques are generally required. There are some interesting correlations, however. 

Before leaving this section, mention should be made of attempts to devise quantum mechanical theories for a one-step model of photoemission, i.e., treating the excitation of the photoelectron, its transmission within the metal and through the interface, and its capture in the condensed phase as a single event. Grider has described this approach in some detail. The escape... 

The initial thrust in studying photoemission from metal electrodes into solutions was to confirm the form of the photoemission rate laws at amorphous electrodes. Mercury was the natural choice of substrate because of its wide range of polarizability and its surface integrity. Although the rate measurements agreed well with the quantum mechanical theory of Gurevich et al. (Sections... 

Soon after it was established that the discharge stage has a finite rate, efforts began to be made to develop a quantum-mechanical theory of an elementary act. The first important step in this direction was taken by Gurney[6]. He clearly formulated the basic idea that the transfer of an electron from a metal to an ion in solution (or in the reverse direction) can be accomplished only when the energy levels of the initial and the final states turn out to be virtually identical (for example, an electron on the Fermi level in a metal + a singly-charged ion in solution is the initial state and an electron + an ion, i.e. the atom in solution is the final state). 

The beginnings of the enormous field of solid-state physics were concisely set out in a fascinating series of recollections by some of the pioneers at a Royal Society Symposium (Mott 1980), with the participation of a number of professional historians of science, and in much greater detail in a large, impressive book by a number of historians (Hoddeson et al. 1992), dealing in depth with such histories as the roots of solid-state physics in the years before quantum mechanics, the quantum theory of metals and band theory, point defects and colour centres, magnetism, mechanical behaviour of solids, semiconductor physics and critical statistical theory. 

In the above-mentioned 1980 symposium (p. 8), the historians Hoddeson and Baym outline the development of the quantum-mechanical electron theory of metals from 1900 to 1928, most of it in the last two years of that period. The topic took off when Pauli, in 1926, examined the theory of paramagnetism in metals and proved, in a famous paper (Pauli 1926) that the observations of weak paramagnetism in various metals implied that metals obeyed Fermi-Dirac statistics - i.e., that the electrons in... 

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