| Sumario: | According to time-dependent density functional theory, the exact exchange-correlation kernel fxc(n,q,ω) for wave vector q and frequency ω determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear density response of an electron gas of uniform density n=3/(4πrs3). Here we propose a parametrization of this function based upon the satisfaction of exact constraints. For the static (ω=0) limit, we modify the model of Constantin and Pitarke to recover at small q the known second-order gradient expansion, and to correct its approach to the large q limit. For all ω at q=0, we use the model of Gross, Kohn, and Iwamoto. A Cauchy integral extends this model to complex ω. Scaling relations are identified. We then combine these ingredients, damping out the ω dependence at large q. Away from q=0 and ω=0, the correlation contribution to the kernel becomes dominant over exchange, even at rs=4. The resulting correlation energies for 1≤rs≤10 from integration over imaginary ω are essentially exact. The plasmon pole of the density response function is found by analytic continuation of fxc to ω just below the real axis, and the resulting plasmon lifetime at rs= 4 is found for q<kF. A static charge-density wave is found for rs>69, and shown to be associated with softening of the plasmon mode.
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