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), the exact exchange-correlation (xc) kernel f xc (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 f xc (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 f xc 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, lim q→0 f xc (n, q, ω) = -α(ω)e 2 /q 2 , 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.