Recent advances in computational physics and chemistry have lead to greater understanding and predictability of the electronic and optical properties of materials. This understanding can be used to impact directly the development of future devices (whose properties depend on the underlying materials) such as light-emitting diodes (LEDs) and photovoltaics. In particular, density functional theory (DFT) has become the standard method for predicting the ground-state properties of solid-state systems, such-as total energies, atomic configurations and phonon frequencies. In the same period, the so called many-body perturbation theory techniques based on the dynamics of the single-particle and two-particle Green's function have become one of the standard methods for predicting the excited state properties associated with the addition of an electron, hole or electron-hole pair into a material. The GW and Bethe-Salpeter equation (GW-BSE) technique is a particularly robust methodology for computing the quasiparticle and excitonic properties of materials.

The challenge over the last several years has been to apply these methods to increasingly complex systems. Nano-materials are materials that are very small (on the order of a nanometer) in at least one dimension (e.g. molecules, tubes/rods and sheets). These materials are of great interest for researchers because they exhibit new and interesting physical and electronic properties compared to those of conventional bulk crystals. These physical properties can often be tuned by controlling the geometry of the materials (for example the chiral angle of a nanotube). Various DFT computer packages have been optimized to compute the ground-state properties of large systems and nano-materials. However, the application of the GW-BSE methodology to large systems and large nano-materials is often thought to be too computationally demanding.

In this work, we will discuss research towards understanding the electronic and optical properties of nano-materials using (and extending) first-principles computational techniques, namely the GW-BSE technique for applications to large systems and nano-materials in particular. While, the GW-BSE approach has, in the past, been prohibitively expensive on systems with more than 50 atoms, in Chapter 2, we show that through a combination methodological and algorithmic improvements, the standard GW-BSE approach can be applied to systems of 500-1000 atoms or 100 AU x 100 AU x 100 AU unit cells. We show that nearly linear parallel scaling of the GW-BSE methodology can be obtained up to tens of thousands (and beyond) of CPUs on current and future high performance supercomputers. In Chapter 3, we will discuss improving the DFT starting point of the GW-BSE approach through the use of COHSEX exchange-correlations functionals to create a nearly diagonal self-energy matrix. We show applications of this new methodology to molecular systems. In Chapter 4, we discuss the application of the GW-BSE methodology to semiconducting single-walled carbon nanotubes (SWCNTs) and the discovery of novel many-body physics in 1D semiconductors. In Chapter 5, we discuss the application of the GW-BSE methodology to metallic SWCNTs and graphene and the discovery of unexpectedly strong excitonic effects in low-dimensional metals and semi-metals.