From atoms to extended structures via ab-initio and multi-scale simulations

This thesis deals with the theoretical and computational modelling of materials by using a variety of ab-initio approaches to accurately predict the properties of realistic structures. A number of known and novel carbon-based materials are studied, exploiting the unique versatility of carbon to bind into several bonding configurations, with the aim of tailoring their electronic and mechanical characteristics. In this regard, the methods used to carry out electronic structure simulations depend on the system size: from the Dirac-Hartree-Fock approach to model molecular properties, to Density Functional Theory used for periodic solids, such as diamond and graphene-related materials composed by a few to some hundred of atoms, to Density Functional Tight Binding or plane Tight Binding to study nanowires or Beltrami pseudospheres, which are composed by some hundreds to a few millions atoms. The details of these methods are introduced in the chapters where they are used. The criterion used to present these concepts is to organize the chapters, with the exception of the last one, according to the increasing dimension of the systems. More in details, the first chapter uses the Dirac-Hartree-Fock approach to simulate atoms and molecules, such bromotrifluoromethane; the second chapter deals with periodic systems characterized by unit cells with a relatively small number of atoms, such as diamond and graphite; the third one discusses graphene and graphene-related materials with lower density; the fourth one present a new computational and experimental model of silicon carbide nanowires coated with silicon dioxide shell; the fifth chapter is focused on the study of sp2-hybridized carbon atoms, arranged on a Beltrami surface. The latter topic spans different research fields such as geometrical topology, physics and mechanical engineering. Finally, the last chapter is dedicated to an on going work which deals with the Non-Adiabatic Molecular Dynamics simulation of amorphous silica samples where we couple the nuclear dynamic of the system to the electronic structure