  We calculate the "head" element or the (0,0)-element of the wave-vector and
frequency-dependent dielectric matrix of bulk crystals via first-principles,
all-electron Kohn-Sham states in the integral of the irreducible polarizability
in the random phase approximation. We approximate the macroscopic "head"
element of the inverse matrix by its reciprocal value, and integrate over
frequencies and momenta to obtain the electronic energy loss of protons at low
velocities. Numerical evaluation for diamond targets predicts that the band gap
causes a strong non-linear reduction of the electronic stopping power at ion
velocities below 0.2 atomic units.
