Structural electronic and optical properties of group IV honeycomb crystals from first principles Nature has always been inspiration and resource for new technical developments that otherwise would not have been possible. Taking a close look at almost every aspect of daily life and technology it is obvious that even nowadays most of the materials are based on natural occurring raw materials and concepts. The rise of quantum mechanics which is the theory of objects compared to the size of atoms allowed an in depth understanding of the physical properties of materials and also paved the way for optimized or even tailored properties of specific technological applications. The naturally occurring graphite is a highly anisotropic allotrope of carbon. It is built from stratified atomically thin layers of carbon atoms which are strongly bonded in a honeycomb lattice within each layer. In contrast the bonding between the layers is only weak due to van der Waals interactions. The theoretical study of the electronic properties of graphite was initiated by Wallace back in the 1940s. Surprisingly the calculations also revealed remarkable electronic properties of single layer graphite which was later called graphene. In particular it was shown that due to the hexagonal symmetry of the carbon atoms within the layer the valence electrons resemble the linear dispersion of massless particles which led to a strong interest in this material. The first known extraction of a graphene layer has been achieved in 1962 by Boehm but the reliable production is possible only since 2004 due to Geim and coworkers. For this achievement Andre Geim and Konstantin Novoselov have been granted the Nobel prize of physics in 2010. Indeed very recently the large scale production of graphene by shear exfoliation has begun. Since graphene is broadly available manifold developments and predictions have been made for this new wonder material . ...