Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior

TL;DR

This paper derives an exact frequency-dependent exchange kernel for insulators in TD-DFT, addressing long-wavelength divergence issues and improving response property calculations over traditional approximations.

Contribution

It provides an exact expression for the Kohn-Sham exchange kernel in insulators, capturing its long-wavelength behavior and comparing it with GW-BSE methods.

Findings

The EXX kernel exhibits the correct long-wavelength divergence.

It improves upon adiabatic local-density and GGA kernels.

Comparison shows consistency with GW-BSE approach.

Abstract

We present an exact expression for the frequency-dependent Kohn-Sham exact-exchange (EXX) kernel for periodic insulators, which can be employed for the calculation of electronic response properties within time-dependent (TD) density-functional theory. It is shown that the EXX kernel has a long-wavelength divergence behavior of the exact full exchange-correlation kernel and thus rectifies one serious shortcoming of the adiabatic local-density approximation and generalized-gradient approximations kernels. A comparison between the TDEXX and the GW-approximation-Bethe-Salpeter-equation approach is also made.