First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

We propose a spatially and temporally nonlocal exchange-correlation (xc) kernel for the spin-unpolarized fluid phase of ground-state jellium, use in time-dependent density functional linear response calculations. The is constructed to satisfy known properties exact xc kernel, accurately describe correlation energies bulk frequency-moment sum rules at wide range jellium densities, including those low densities that display strong symmetry breaking. These effects are easier understand simple model than real systems. All constraints satisfied by recent MCP07 [A. Ruzsinszky, et al., Phys. Rev. B 101, 245135 (2020)] maintained new revised (rMCP07) while others added. revision $f_\mathrm{xc}^\mathrm{rMCP07}(q,\omega)$ differs from only non-zero frequencies $\omega$. Only much lower metals frequency dependence important energy jellium. As wavevector $q$ tends zero, has $-4\pi \alpha(\omega)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $\alpha(\omega)$ vanishes predicted rMCP07 be extremely small Al Na.}