We have performed calculations of the anisotropic frequency dependent
dielectric function of AlN, using the linear muffin-tin orbital method
within the atomic sphere approximation (LMTO-ASA). Our calculations s
how that the anisotropy is very small. The effect of introducing empty
spheres is to decrease the energy gap by about 20% and to make the di
electric function slightly anisotropic at higher energies. Comparisons
with experiments must await experimental results.