Since the experimental obtention of graphenen in 2004, the two dimensional crystalline systems was a study subject of strong analysis from theoretical and experimental point of view. The analytical methods goes from tight binding, Dirac equations for K and K’ points to functional density theories. The present work is an initial study of the electronic structure and the phonon frequencies spectra of 2D crystalline systems using functional density theory. We use the Exciting Fortran 90 code and GPAW Python code. The results of electronic structure for some 2D lattices are shown and also the graphene phonon frequencies spectra.