Kohn-Sham scheme for frequency dependent linear response

Abstract

We study the Kohn-Sham scheme for the calculation of the steady state linear response to a harmonic perturbation that is turned on adiabatically. Although in general the exact time dependent exchange-correlation potential cannot be expressed as the functional derivative of a universal functional due to the so-called causality paradox, we show that for a harmonic perturbation the exchange-correlation part of the first-order Kohn-Sham potential $v_s^{(1)}(r)\cos (\omega t)$ is given by $v_{xc}^{(1)}(r)=\delta K_{xc}^{(2)}/\delta n^{(1)}(r)$. $K_{xc}^{(2)}$ is the exchange-correlation part of the second-order quasienergy $K_v^{(2)}$. The Frenkel variation principle implies a stationary principle for the second-order quasienergy. We also find an analogous stationary principle and KS scheme in the time dependent extension of one-matrix functional theory, in which the basic variable is the one-matrix (one-body reduced density matrix).

11 pages; minor corrections; details added

References in corpus (3)

• On the "Causality Paradox" of Time-Dependent Density Functional Theory
• The Kohn-Sham system in one-matrix functional theory
• Comment on "Critique of the foundations of time-dependent density functional theory" [Phys. Rev.A. 75, 022513 (2007)]