Time-dependent current-density functional theory for the friction of   ions in an interacting electron gas
  Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',\omega)$ the {\em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an interacting electron gas (EG) for ions tends to give a too large value of Q for heavy ions in the medium- and low-density EG, if we adopt the local-density approximation (LDA) to $f_{xc}({\bf r},{\bf r}',\omega)$, even though the formula itself is formally exact. We have rectified this unfavorable feature by reformulating the formula for Q in terms of the {\em tensorial} xc kernel of the time dependent current-density functional theory, to which the LDA can be applied without intrinsic difficulty. Our numerical results find themselves in a considerably better agreement with the experimental stopping power of Al and Au for slow ions than those previously obtained within the LDA to the TDDFT. 
V. U. Nazarov, J. M. Pitarke, Y. Takada, G. Vignale, Y.-C. Chang