Physical review. B, Condensed matter

Time-dependent Hartree-Fock formalism for the dielectric function

Nathan E. Brener, John L. Fry

Published Feb 15, 1979• 18 citations

Abstract

In this paper we derive a formula for the time-dependent Hartree-Fock dielectric function by using Green's-function theory. We develop a set of self-consistent equations for the self energy, polarization, and Green's function which can be iterated to obtain successively more accurate approximations for the polarization. In this procedure the Hartree and Hartree-Fock approximations occur naturally as the first and second steps in the iterations. As the iterations are carried out, we obtain not only the expressions for the polarization, but also the one-electron Hartree-Fock equations, so that there is no question as to which polarization formula corresponds to which equation. In this way we obtain an expression for the dielectric function which clearly and directly corresponds to the Hartree-Fock equation and which is therefore called the time-dependent Hartree-Fock (TDHF) dielectric function. In this TDHF formula for the dielectric function, the first term is the time-dependent Hartree or random-phase approximation dielectric function. We show that in order to be consistent with the theory, one should use Hartree wave functions and energies to compute random-phase approximation dielectric functions and Hartree-Fock wave functions and energies to compute TDHF dielectric functions. Numerical results are presented for the free-electron gas.

DOI: 10.1103/physrevb.19.1720

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Comments on "Time-dependent Hartree-Fock formalism for the dielectric function"

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The correct formalism for obtaining a dielectric function consistent with the Hartree-Fock approximation is outlined. It is pointed out that a recent calculation by Brener and Fry does violate Ward identities and is not a conserving approximation. To be consistent with the Hartree-Fock single-particle equation the infinite series of "ladder-bubble" diagrams must be included.

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