In this thesis a new method based on the Tight-Binding Linear Muffin Tin Orbital (TB-LMTO) formalism and the Quasiparticle Self-consistent GW (QSGW) approximation is proposed. The method is capable of generating accurate electronic bands structure of large supercells necessary to model alloys structures. The strategy consist in building simple and small hamiltonian from linear Muffin-tin-orbitals (LMTO). Parameters in this hamiltonian are then used to fit the difference in QSGW self-energies and LDA exchange-correlation potentials. The parameter are assumed to transfer to new environments --- a procedure we check carefully by comparing our predicted band to QSGW bands for small supercells. The method possess both the accuracy of the QSGW approximation, (which is the most reliable way to determine energy bands accurately, and yet too expensive for the large supercells required here), and the efficiency of the TB-LMTO method. The accurate and highly efficient hamiltonian is used to predict the electronic and optical transitions of Si1-xGex alloys and SnxSiyGe1-x-y alloys. The goal is to engineer direct band gap material compatible with the silicon technology. The results obtained are compared to available experimental data.

The nucleon resonance spectrum consists of many overlapping excitations. Polarization observables are an important tool for understanding and clarifying these spectra. While there is a large data base of differential cross sections for the process, very few data exist for polarization observables. A program of double polarization experiments has been conducted at Jefferson Lab using a tagged polarized photon beam and a frozen spin polarized target (FROST). The results presented here were taken during the first running period of FROST using the CLAS detector at Jefferson Lab with photon energies ranging from 329 MeV to 2.35 GeV. Data are presented for the E polarization observable for eta meson photoproduction on the proton from threshold (W=1500 MeV) to W=1900 MeV. Comparisons to the partial wave analyses of SAID and Bonn-Gatchina along with the isobar analysis of eta-MAID are made. These results will help distinguish between current theoretical predictions and refine future theories.