Investigations of surface potentials

Abstract

The potential energy at the surface of materials, like graphene, might be able to trap atoms and molecules. In order to probe this possibility, the theoretical foundations of Density Functional Theory are studied, and the need for numerical calculations is understood. Iterative methods to solve numerical calculations are presented. Quantum ESPRESSO, a Linux package used for numerical calculations is examined, and its important features are explained. Simple simulations involving Aluminium, and Silicon are carried out. The accuracy of quantum ESPRESSO is verified using the Hydrogen molecule, for which we have the analytical solution. Four different attempts at modeling graphene are then presented. The system of a single hydrogen molecule and a graphene sheet, is then studied. Finally, the notion of accuracy in numerical calculations is analyzed in light of the simulations that have been run.