Electron gas, behavior

Fukui function represents the deviation of the system s response to adding or subtracting electrons from electron gas behavior. 

The enhancement factor Fy(s) describes deviations from homogeneous electron gas behavior. For PBE, it is written as... 

An entirely different approach to the correlation problem is taken in the plasma model (Bohm and Pines 1953, Pines 1954, 1955), in which the electrons in a metal are approximated by a free-electron gas moving in a uniform positive background. According to classical discharge theory, such a plasma is characterized by an oscillatory behavior having a frequency... 

The free-electron gas was first applied to a metal by A. Sommerfeld (1928) and this application is also known as the Sommerfeld model. Although the model does not give results that are in quantitative agreement with experiments, it does predict the qualitative behavior of the electronic contribution to the heat capacity, electrical and thermal conductivity, and thermionic emission. The reason for the success of this model is that the quantum effects due to the antisymmetric character of the electronic wave function are very large and dominate the effects of the Coulombic interactions. 

Many-body perturbation theory (MBPT) for periodic electron systems produces many terms. All but the first-order term (the exchange term) diverges for the electron gas and metallic systems. This behavior holds for both the total and self-energy. Partial summations of these MBPT terms must be made to obtain finite results. It is a well-known fact that the sum of the most divergent terms in a perturbation series, when convergent, leads often to remarkably accurate results [9-11]. 

The outer electrons in metals such as Li and Na have a very low ionization energy, and are largely delocalized. Such electrons are described as constituting a nearly free electron gas. It may be noted, though, that this description is somewhat misleading as the behavior of the electrons is dominated by the exclusion principle, while the molecules in normal gases can be described by classical statistical mechanics. 

The surface states observed by field-emission spectroscopy have a direct relation to the process in STM. As we have discussed in the Introduction, field emission is a tunneling phenomenon. The Bardeen theory of tunneling (1960) is also applicable (Penn and Plummer, 1974). Because the outgoing wave is a structureless plane wave, as a direct consequence of the Bardeen theory, the tunneling current is proportional to the density of states near the emitter surface. The observed enhancement factor on W(IOO), W(110), and Mo(IOO) over the free-electron Fermi-gas behavior implies that at those surfaces, near the Fermi level, the LDOS at the surface is dominated by surface states. In other words, most of the surface densities of states are from the surface states rather than from the bulk wavefunctions. This point is further verified by photoemission experiments and first-principles calculations of the electronic structure of these surfaces. 

Jerome [48] proposed that the -behavior of pA(I) could be caused by electron-spin fluctuation scattering. This approach can be viewed as an extension of electron-electron scattering to larger effective interaction strengths, which are perhaps caused by the lower dimensionality. The dominant process is scattering of electrons by collective excitations of the electron gas (the spin fluctuations) rather than first-order electron-electron scattering. 

Finally, one should not forget the purely one-dimensional models, such as calculation of the conductivity of the one-dimensional interacting electron gas [50]. Such a model also gives a power law for the resistivity. For an attractive long-range electron-electron interaction there is an enhancement of ah and a different power law from that expected for (say) phonon scattering. However, it is not clear whether such a model applies to the compounds in Fig. 1, which have different ground states, yet still show similar resistivity behavior. 

Spin and charge excitations are thus decoupled by coulombic interactions in the one-dimensional electron gas. However, the one-dimensional Fermion system is not a Fermi liquid, as indicated by the behavior of the momentum distribution function, which does not exhibit a Fermi step at kF and presents a single-particle density of states vanishing according to a power law singularity at EF. This is a Luttinger liquid [29] with... 

Cohen, A. J., and R. G. Gordon (1976). Modified electron-gas study of the stability, elastic properties, and high-pressure behavior of MgO and CaO crystals. Phys. Rev. B14, 4593-605. 

As shown in Fig. 12, another regime of relaxation is reached at very low temperature (7 <8 K), where a behavior l/T, oc Tis recovered [51, 69, 70, 144]. The low temperature regime looks like a Korringa law with an enhancement factor of the order 10 with respect to the regime r>30 K. It has been first proposed that this change in behavior for the enhancement originates in the dimensionality cross-over of one-particle coherence and the restoration of a Fermi liquid component in two directions. It is still an open problem to decide whether the Fermi liquid properties recovered below 8 K are those of a 2-D or 3-D electron gas. Furthermore the intermediate temperature regime 8 K ... 

As shown by Sommerfeld (1.), the electron gas Is a degenerate Fermi-Dirac gas and Its properties will differ from the classical (Boltzmann) gas. These deviations will increase as the temperature decreases or as the density increases (2,2) Due to the low mass of the electron, these departures from classical behavior will persist to higher temperatures and lower densities than for atomic systems. Under conditions of 1 atm pressure, Gordon (3) showed that the deviation of the Fermi-Dirac gas from the... 

The halogens (except fluorine) exhibit both electron-accepting and electron-releasing behaviors. Since they resemble the noble gas elements only in regard to electron-releasing, this aspect of the chemistry of the two families will be discussed first. The more familiar acceptance of electrons by halogens is discussed later in the chapter. 

The LDA or its spin-polarized generalization, the local spin density (LSD) approximation provides a means of folding exchange and correlation effects, calculated on the basis of the local behavior of a uniform electron gas, into a set of self-consistent Hartree-like equations which contain only local operators for the potential. This procedure is represented schematically in Fig. 1. 

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