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Electron-hole interaction is an important factor that determines the
optical response of semiconductors and insulators. One of the approach
that allows to include this effect into the DFT formalism is based on
a solution of the Bethe-Salpeter equation (BSE). The BSE in a strict
sense describes the evolution of two particle Green function. However
when combined with DFT it is usually simplified into an eigenvalue
equation of the electron-hole Hamiltonian, where the electron-hole
electrostatic interaction is statically screened within the random
phase approximation. The BSE-DFT formalism has been successfully used
for calculating frequency dependent macroscopic dielectric function as
well as the excitation edge. In the present talk I will focus mainly
on discussion of method to calculate and the properties of lowest
excitions in AlN and others wurtzite semiconductors. In AlN due to
large and negative crystal-field splitting the excitation edge is
determined by transition between only single valence and single
conduction bands around the center of the BZ. Therefore this case is a
perfect candidate to demonstrate the Elliott like behavior of the
lowest excitons.