Measuring the kernel of time-dependent density functional theory with   X-ray absorption spectroscopy of 3d transition metals
  The 2p-3d core hole interaction in the L2,3 absorption spectra of the 3d transition metals is treated within time-dependent density functional theory (TDDFT). A simple three-level model explains the origin of the strong deviations from the one-particle branching ratio and yields matrix elements of the unknown exchange-correlation (XC) kernel directly from experiment. 
A. Scherz, E.K.U. Gross, H. Appel, C. Sorg, K. Baberschke, H. Wende,   K. Burke