Theory of the Inhomogeneous Electron Gas

Theory of the Inhomogeneous Electron Gas

Author: Stig Lundqvist

Publisher: Springer Science & Business Media

ISBN: 9781489904157

Category: Science

Page: 396

View: 346

The theory of the inhomogeneous electron gas had its origin in the Thomas Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

Many-body Theory of a Rapidly Varying Inhomogeneous Electron Gas

Many-body Theory of a Rapidly Varying Inhomogeneous Electron Gas

Author: John William Gadzuk

Publisher:

ISBN: UIUC:30112106631580

Category: Electron gas

Page: 93

View: 440

The case of an inhomogeneous electron gas within which the density variation is significant over a spatial range of the order of a Fermi wave-length is considered in this report. It is seen that for most systems of physical interest, this sort of non-uniformity is a result of diffraction effects. This is a fundamentally different phenomenon than can reasonably be treated by the density gradient method of Kohn for slowly varying inhomogeneous electron gases. Several sample cases are treated. The first considerations are directed towards the problem of a weak periodic potential in an interacting electron gas. The momentum-dependent self-energy is calculated for an electron propagating in the many-body medium of an electron gas plus a periodic lattice pseudo-potential. This is the equivalent of a quasi-particle energy spectrum and thus an orthogonalized plane wave energy band. It does not appear that the lattice drastically changes qualitative aspects of plane wave many-body theory. A dielectric formulation for a general inhomogeneous electron gas is presented. By introducing a new image technique, the dielectric function within the random phase approximation, which is valid in the surface region of an electron gas, is obtained. A Green's function formalism is developed for treating the static dielectric screening of a point impurity in an electron gas. The surface dielectric function is used with the impurity screening formalism to treat the problem of impurity screening in the surface region. This is an idealized model of ionic adsorption on metal surface. Screening charge densities resulting from volume polarization effects are calculated. From these results, it is seen why unjustifiable application of classical image forces in previous adsorption theories has fortunately produced reasonable results. A new method for obtaining the appropriate plasmon contribution to the electron self-energy in the surface region is developed. With these results, the electron gas surface potentials calculated by Loucks and Cutler are then improved.

Molecules in Physics, Chemistry, and Biology

Molecules in Physics, Chemistry, and Biology

Author: Jean Maruani

Publisher: Springer Science & Business Media

ISBN: 9027725985

Category: Science

Page: 460

View: 188

Volume 1: General Introduction to Molecular Sciences Volume 2: Physical Aspects of Molecular Systems Volume 3: Electronic Structure and Chemical Reactivity Volume 4: Molecular Phenomena in Biological Sciences

A New Formulation of the Inhomogeneous Electron Gas Problem

A New Formulation of the Inhomogeneous Electron Gas Problem

Author: W. Kohn

Publisher:

ISBN: OCLC:227396480

Category:

Page: 24

View: 730

A new approach to the quantum mechanical problem of the inhomogeneous electron gas is developed. The central quantities in this theory are the local electron density and various functionals of the density in which the properties of the system are incorporated. The lectures encompass the general theory and, as applications, new selfconsistent equations which are extensions of the Hartree and Hartree-Fock equations, as well as a discussion of elementary excitations. Preliminary numerical results also are presented. (Author).

Electrons In Metals And Alloys

Electrons In Metals And Alloys

Author: J. A. Alonso

Publisher: Academic Press

ISBN: 9780080984490

Category: Technology & Engineering

Page: 603

View: 502

This book is a broad review of the electronic structure of metals and alloys. It emphasises the way in which the behavior of electrons in these materials governs the thermodynamic and other properties of these conducting materials. The theoretical treatment proceeds from a wave mechanics approach to more sophisticated techniques for the description of the properties of metals and alloys.