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We develop a scheme for building the scalar exchange-correlation (xc) kernelof time-dependent density functional theory (TDDFT) from the tensorial kernelof time-dependent {\em current} density functional theory (TDCDFT) and theKohn-Sham current density response function. Resorting to the localapproximation to the kernel of TDCDFT results in a nonlocal approximation tothe kernel of TDDFT, which is free of the contradictions that plague thestandard local density approximation (LDA) to TDDFT. As an application of thisgeneral scheme, we calculate the dynamical xc contribution to the stoppingpower of electron liquids for slow ions to find that our results are inconsiderably better agreement with experiment than those obtained using TDDFTin the conventional LDA.

physical review. b, condensed matter and materials physics

Including nonlocality in exchange-correlation kernel from time-dependent  current density functional theory: Application to the stopping power of  electron liquids