The focus of this dissertation is the determination of the electronic structure and trans-

port properties of solids. We first review some of the theory and computational methodology

used in the calculation of electronic structure and materials properties. Throughout the dis-

sertation, we make extensive use of state-of-the-art software packages that implement den-

sity functional theory, density functional perturbation theory, and the GW approximation,

in addition to specialized methods for interpolating matrix elements for extremely accurate

results. The first application of the computational framework introduced is the determi-

nation of band offsets in semiconductor heterojunctions using a theory of quantum dipoles

at the interface. This method is applied to the case of heterojunction formed between a

new metastable phase of silicon, with a rhombohedral structure, and cubic silicon. Next, we

introduce a novel method for the construction of localized Wannier functions, which we have

named the optimized projection functions method (OPFM). We illustrate the method on a

variety of systems and find that it can reliably construct localized Wannier functions with

minimal user intervention. We further develop the OPFM to investigate a class of materials

called topological insulators, which are insulating in the bulk but have conductive surface

states. These properties are a result of a nontrivial topology in their band structure, which

has interesting effects on the character of the Wannier functions. In the last sections of the

main text, the noble metals are studied in great detail, including their electronic properties

and carrier dynamics. In particular, we investigate, the Fermi surface properties of the no-

ble metals, specifically electron-phonon scattering lifetimes, and subsequently the transport

properties determined by carriers on the Fermi surface. To achieve this, a novel sampling

technique is developed, with wide applicability to transport calculations. Additionally, the

generation and transport of hot carriers is studied extensively. The distribution of hot carri-

ers generated from the decay of plasmons is explored over a range of energy, and the transport

properties, particularly the lifetimes and mean-free-paths, of the hot carriers are determined.

Lastly, appendices detailing the implementation of the algorithms developed in the work is

presented, along with a useful derivation of the electron-plasmon matrix elements.