LAUSR

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