A new tutorial on phonon-assisted luminescence by finite atomic displacement is available in the wiki web-page.
In this tutorial we explain step-by-step how to calculate the luminescence spectra taking into account phonon vibration. The present approach can applied to indirect and direct band gap semiconductors where coupling with phonons play an important role. An example for hexagona-boron nitride is provided in the tutorial. Notice that this kind of calculations are quite involved and they have a large computational cost, therefore at present they are limited to not too complex materials.