Frequency‐Dependent Exchange Correction to the Dielectric Function of the Electron Gas

Abstract

The equation of motion of the Wigner distribution function in the homogeneous electron gas is decoupled using the Hartree-Fock prescription. After linearization, the variational procedure, used by Rajagopal and Jain and by Langreth is applied. The transverse and the longitudinal dielectric functions in the Hartree-Fock approximation are derived, and the consistency of the equations for the charge density and the current density is examined. Several limits are calculated. The slope of the plasmon mode is substantially lowered by the exchange interactions, and the damped acoustic mode disappears for the densities that give a negative bulk modulus in the Hartree-Fock approximation. The exchange interaction only slightly influences the dispersion of the transverse collective modes.Mittels der Hartree-Fock-Vorschrift wird die Bewegungsgleichung der Wigner-Verteihngsfunktion im homogenen Elektronengas entkoppelt. Nach Linearisierung wird die von Rajagopal und Jain sowie von Langreth benutzte Variationsmethode angewendet. Es werden die transversalen und longitudinalen dielektrischen Funktionen in der HartreePock-Naherung abgeleitet und die Konsistenz der Gleichungen fur die Ladungsdichte und Stromdichte untersucht. Einige Grenzfille werden berechnet. Der Anstieg der PlasmonMode wird durch die Austauschwechselwirkungen wesentlich verringert, und die gediimpfte akustische Mode verschwindet fur die Dichten, die einen negativen Kompressionsmodul in der Hartree-Fock-Niherung liefern. Die Austauschwechselwirkung beeinflul3t die Dispersion der kollektiven transversalen Moden nur wenig.

The Pair Correlation Function and the Dielectric Response in the Homogeneous Electron Gas

“…If only exchange is taken into account, the "exchange decoupling method" as discussed in Section 5 (and reference [ 141) satisfies both the consistency requirements ( l l a ) and ( l l b ) . As far as we know, this is the only existing method to do so.…”

Simple dynamic exchange-correlation kernel of a uniform electron gas

“…16 The xc kernel f xc ͑n ; q , ͒ ͓or, equivalently, the so-called local-field factor G͑n ; q , ͒ =−͑q 2 /4͒f xc ͑n ; q , ͔͒ of the uniform electron gas has been investigated by many authors, since the early static local-field factor introduced by Hubbard 17 by summing all the exchange ladder diagrams entering the evaluation of the density-response function. Nowadays, diffusion Monte Carlo ͑DMC͒ calculations of the localfield factor of the uniform electron gas are available, 18,19 which have been parametrized by Corradini et al 20 Calculations of the frequency dependence of the local-field factor were carried out by Brosens and co-workers, 21,22 and, more recently, by Richardson and Ashcroft. 23 Figure 1 compares the static form of our xc kernel f xc ͑n ; q , ͒, which we have obtained from Eq.…”

Theory of inelastic lifetimes of surface-state electrons and holes at metal surfaces

“…Calculations of the frequency dependence of the xc kernel of a homogeneous electron gas have been carried out mainly in the limit of long wavelengths [72,73,74,75,76,77], but work has also been done for finite wave vectors [78,79,80,81]. Approximate expressions for the frequency-dependent xc kernel of inhomogeneous systems have been reported in Refs.…”