  We express the high-frequency (anti-adiabatic) limit of the
exchange-correlation kernels of an inhomogeneous electron gas in terms of the
following equilibrium properties: the ground-state density, the kinetic stress
tensor, the pair-correlation function, and the ground-state
exchange-correlation potential. Of these quantities, the first three are
amenable to exact evaluation by Quantum Monte Carlo methods, while the last can
be obtained from the inversion of the Kohn-Sham equation for the ground-state
orbitals. The exact scalar kernel, in this limit, is found to be of very long
range in space, at variance with the kernel that is used in the standard local
density approximation. The anti-adiabatic xc kernels should be useful in
calculations of excitation energies by time-dependent DFT in atoms, molecules,
and solids, and provides a solid basis for interpolation between the low- and
high-frequency limits of the xc kernels.
