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These doubly excited states matter in polyenes, carotenoids and many photochemical pathways.","posed_since":"","precise":"In linear-response TDDFT with a frequency-independent (adiabatic) exchange-correlation kernel $f_{\\mathrm{xc}}$, states of dominant double-excitation character are absent from the spectrum. Construct a frequency-dependent kernel $f_{\\mathrm{xc}}(\\omega)$ applicable to general molecules at cost comparable to hybrid TDDFT that reproduces the 2 1Ag- states of butadiene, hexatriene and octatetraene and the doubly excited states of the QUEST benchmark (a database of near-exact molecular excitation energies) within $0.2\\ \\mathrm{eV}$. An answer is such a kernel with benchmarks, or a proof that no kernel in a stated class can do it.","problem_ref":null,"references":"","settled_by":"Benchmarks of the kernel against near-exact excitation energies for doubly excited states of polyenes and the QUEST set.","status_note":"Dressed kernels introduced in 2004 (Maitra, Zhang, Cave, Burke, J. Chem. Phys., https://doi.org/10.1063/1.1651060) treat isolated doubles; no general-purpose kernel exists.","title":"A practical TDDFT kernel that captures double 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