Kohn-Sham scheme for frequency dependent linear response

TL;DR

This paper develops a Kohn-Sham scheme for calculating the linear response of quantum systems to harmonic perturbations, addressing causality issues and extending to one-matrix functional theory.

Contribution

It introduces a stationary principle for the second-order quasienergy and derives a Kohn-Sham scheme for frequency-dependent linear response, including extensions to one-matrix functional theory.

Findings

Expressed the exchange-correlation potential in terms of second-order quasienergy functional

Established a stationary principle for the second-order quasienergy

Extended the Kohn-Sham scheme to time-dependent one-matrix functional theory

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).