The exchange-correlation potential for current-density functional theory of frequency-dependent linear response

The dynamical, long-wavelength longitudinal and transverse exchange - correlation potentials for a homogeneous electron gas are evaluated in a microscopic model based on an approximate decoupling of the equation of motion for the current - current response function. The transverse spectrum turns out to be very similar to the longitudinal one. We obtain evidence for a strong spectral structure near twice the plasma frequency due to a two-plasmon threshold for two-pair excitations, which may be observable in inelastic scattering experiments. Our results give the entire input needed to implement the time-dependent current-density functional theory scheme recently developed by G Vignale and W Kohn (1996 Phys. Rev. Lett. 77 2037), and are fitted to analytic functions to facilitate such applications.