First principles calculations of Raman spectra for nanostructures and improved high order forces

Advances in computing technology coupled with theoretical developments on the electronic structure problem have laid the foundation for the rapidly growing field of computational materials science. Modern supercomputers are able to perform ab initio calculations of realistic systems containing thousands of atoms. This is an important step forward in the maturation of the field because computational insight can be used to make predictions about or predict experimental data.

This dissertation aims to address contemporary theory and practice of solving the electronic structure problem for a variety of nanoscale systems, most of which are of interest for energy application such as photovoltaics or Li-ion batteries. Our calculations are performed within density functional theory using real-space pseudopotentials. In the first part, we examine nanocrystals. We calculate size-dependent properties for ZnO nanocrystals with Al and Ga dopants. Next, we calculate Raman spectra for Si nanocrystals with Li impurities and Si-Ge core-shell structures, which gives us insight into the structure of these nanocrystals. In the second portion, we examine in depth the calculation of interatomic forces within density functional theory and propose a new integration scheme which we demonstrate calculates more accurate bond lengths and vibrational frequencies and improves the stability of molecular dynamics simulations.