Progress towards understanding ultranonlocality through the wave-vector and frequency dependence of approximate exchange-correlation kernels

In the framework of time-dependent density functional theory (TDDFT), exact exchange-correlation (xc) kernel $f_{xc}(n,q,\omega)$ determines ground-state energy, excited-state energies, lifetimes, and linear response any many-electron system. The recently developed MCP07 xc A. Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) energies plausible plasmon lifetimes. As is constructed to describe $f_{xc}$ UEG, it cannot capture optical properties real materials. To verify this claim, we follow Nazarov Lett. 102, 113001 (2009)] construct long-range, dynamic kernel, $\lim_{q\to 0}f_{xc}(n,q,\omega) = -\alpha(\omega)e^2/q^2$, a weakly inhomogeneous gas, using other common kernels. strong wavevector frequency dependence "ultranonlocality" coefficient $\alpha(\omega)$ demonstrated for variety simple metals semiconductors. We examine how imposing constraints on an approximate shapes $\alpha(\omega)$. Comparisons kernels derived from correlated-wavefunction calculations are drawn.