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

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 as 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.