A theoretically well-founded theory of two-photon absorption using the free electron-gas model of dye molecules 50> is to be found in 49>. [Pg.20]

The theory fails to explain the molar specific heat of metals since the free electrons do not absorb heat as a gas obeying the classical kinetic gas laws. This problem was solved when Sommerfeld (1) applied quantum mechanics to the electron system. [Pg.27]

In the electron theory of metals no accurate allowance has hitherto been made for the effects of the conduction electrons on each other. Drude and Lorentz even went the length of assuming that to a first approximation the mutual action of the electrons and ions may be neglected, and accordingly spoke of a gas of free electrons. [Pg.63]

Space-coordinate density transformations have been used by a number of authors in various contexts related to density functional theory [26,27, 53-64, 85-87]. As the free-electron gas wavefunction is expressed in terms of plane waves associated with a constant density, these transformations were introduced by Macke in 1955 for the purpose of producing modified plane waves that incorporate the density as a variable. In this manner, the density could be then be regarded as the variational object [53, 54]. Thus, explicitly a set of plane waves (defined in the volume V in and having uniform density po = N/V) [Pg.173]

Optical properties of metal nanoparticles embedded in dielectric media can be derived from the electrodynamic calculations within solid state theory. A simple model of electrons in metals, based on the gas kinetic theory, was presented by Drude in 1900 [9]. It assumes independent and free electrons with a common relaxation time. The theory was further corrected by Sommerfeld [10], who incorporated corrections originating from the Pauli exclusion principle (Fermi-Dirac velocity distribution). This so-called free-electron model was later modified to include minor corrections from the band structure of matter (effective mass) and termed quasi-free-electron model. Within this simple model electrons in metals are described as [Pg.80]

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 [Pg.259]

The general Jacobian problem associated with the transformation of a density Pi(r) into a density p2(r) (where these densities differ from that of the free-electron gas) was discussed by Moser in 1965 [58]. This work was not performed in the framework of orbital transformations - which might have interested chemists, nor was it done in the context of density functional theory - which might have attracted the attention of physicists. It was a paper written for mathematicians and, as such, it remained unknown to the quantum chemistry community. In the discussion that follows, we use the more accessible reformulation of Bokanowski and Grebert (1995) [65] which relies heavily on the work of Zumbach and Maschke (1983) [61]. Let us define as ifjy = the space of [Pg.175]

Another important accomplislnnent of the free electron model concerns tire heat capacity of a metal. At low temperatures, the heat capacity of a metal goes linearly with the temperature and vanishes at absolute zero. This behaviour is in contrast with classical statistical mechanics. According to classical theories, the equipartition theory predicts that a free particle should have a heat capacity of where is the Boltzmann constant. An ideal gas has a heat capacity consistent with tliis value. The electrical conductivity of a metal suggests that the conduction electrons behave like free particles and might also have a heat capacity of 3/fg, [Pg.128]

Note that the exchange term is of the form / y(r,r ) h(r )dr instead of the y (r) (r) type. Equation (1.12), known as the Hartree-Fock equation, is intractable except for the free-electron gas case. Hence the interest in sticking to the conceptually simple free-electron case as the basis for solving the more realistic case of electrons in periodic potentials. The question is how far can this approximation be driven. Landau s approach, known as the Fermi liquid theory, establishes that the electron-electron interactions do not appear to invalidate the one-electron picture, even when such interactions are strong, provided that the levels involved are located within kBT of Ep. For metals, electrons are distributed close to Ep according to the Fermi function f E) [Pg.59]

Several other studies have appeared that are worthy of note. In a series of works by Keller [89-94] and Apell [95], the nonlocal nonlinear response for free-elec-tron-like metals have been examined using various theoretical approaches which are basically extensions of linear theories on the optical response of metals. The results [92] reduce to those obtained by Rudnick and Stern [26] using a similar approach when the free-electron gas is considered to be homogeneous. [Pg.154]

The mechanism by which equilibrium is attained can only be visualized in terms of microscopic theories. In the kinetic sense, equilibrium is reached in a gas when collisions among molecules redistribute the velocilies lor kinetic energies) of each molecule until a Maxwellian distribution is reached for the whole bulk. In the case of the trend toward equilibrium for two solid bodies brought into physical contact, we visualize the transfer of energy by means of free electrons and phonons (lattice vibrations). [Pg.581]

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. [Pg.164]

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. [Pg.104]

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