From Zero to Infinity: Customized Atomistic Calculations for Crystalline Solids —Applications to Graphene and Diamond

methodology has been very successfully applied and extrapolated to Si, Be, BeH, CdSe, MgH, crystals and nanocrystals, with almost chemical accuracy in most cases. Here, after a pedagogical and critical review of the earlier results, we introduce a new combined and expanded approach to comparatively describe the electronic and cohesive properties of diamond and graphene. For the later a drastically enlarged sequence of “nanocrystals” of well-chosen geometries and sizes up to 1440 atoms or 8190 electrons is used to verify earlier predictions and results. We have obtained in a simple and fast way the bandgap (5.4 eV) and the cohesive energy (7.34 eV/atom) of diamond with almost chemical accuracy; and we have fully rationalized (in a different perspective and prospective) the electronic and cohesive properties of graphene, with a tentative value of cohesive energy of 7.52 eV/atom. Strangely enough this value is larger than the one for diamond and is currently under investigation. Finally, we suggest that this methodology in its current simple and transparent form can be a first-line diagnostic, functional, and inexpensive computational tool. This is particularly true for quick assessments and comparative estimates, size-dependence studies, or cases where standard k-space methods or other advanced techniques either fail or demand unavailable computational resources. We review and combine two different atomistic-calculation approaches for macroscopic solids, applying them successfully to 2D graphene, in comparison to the 3D diamond with a dual target: 1) to gain novel physical insight about the Dirac