Document Type : Research Article


1 Molecular Engineering Laboratory, Department of Physics, University of Patras, Patras, 26500, Greece Institute of Electronic Structure and Laser, Foundation for Research &Technology Hellas, Vassilika Vouton, P.O. Box 1385, Heraklion, Crete, 71110, Greece

2 Molecular Engineering Laboratory, Department of Physics, University of Patras, Patras, 26500, Greece Department of Physics University of Sargodha, Sub-campus Bhakkar, 30000, Pakistan


We demonstrate that a suitable atomistic method with judicially selected nanoclusters/ nanocrystals (in real space) supplemented with general symmetry and dimensionality arguments, can give surprisingly good results for macroscopic properties of the infinite crystalline solid, such as bandgaps, cohesive energies, as well as aromaticity (if any), at minimal computational cost and maximum physical insight. For graphene on top of these properties the present approach can successfully describe in real space and illuminate many of its exotic properties, which are usually introduced in k-space, such as Dirac points or topological insulators. An early version of this 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.

Graphical Abstract

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


Main Subjects