  A LMTO implementation of Aversa and Sipe's length-gauge formalism for
calculating the full frequency dependent second-harmonic generation in the
independent particle approximation is presented. It is applied to GaAs, GaP,
3C-SiC, c-BN and wurtzite and zincblende GaN and AlN. The use of the scissor's
operator for correcting LDA errors is discussed and compared to an alternative
approach in which the Hamiltonian is corrected. The latter is found to be
superior. Decomposition in omega and 2 omega resonances and in intra- and
inter-band contributions and in specific band-to-band contributions are
presented.
