The (Ga<underline>1-x</underline>Zn<underline>x</underline>)(N<underline>1-x</underline>O<underline>x</underline>) solid solution (or, alloy) is a visible-light-driven photo-catalyst for water splitting. Its reduced band gap is a main advantage for harvesting solar energy. Because the synthesized samples are in the powder form, the understanding of the bulk structures and the surfaces are hindered. In this thesis, we address both the bulk and the surfaces of this material through simulations based on the density-functional theory (DFT) version of quantum electronic structure theory. The ordering of the atoms in the alloy is the key information to understand the bulk properties, especially the band gap reduction mechanism. Using the cluster expansion formalism, we construct an accurate model from DFT calculations. The subsequent Monte Carlo simulation reveals a phase diagram which has a wide miscibility gap and an x=0.5 ordered compound. The disordered phase displays strong short-range order (SRO) at synthesis temperatures. To study the influences of SRO on the lattice and electronic properties, we conduct DFT calculations on snapshots from the Monte Carlo simulation. Consistent with previous theoretical and experimental findings, lattice parameters were found to deviate from Vegard's law with small upward bowing. Bond lengths depend strongly on local environment, with a variation much larger than the difference of bond length between ZnO and GaN. The downward band gap bowing deviates from parabolic by having a more rapid onset of bowing at low and high concentrations. An overall bowing parameter of 3.3 eV is predicted from a quadratic fit to the compositional dependence of the calculated band gap. Our results indicate that SRO has significant influence over both structural and electronic properties. Recent experiments showed that the semi-polar (10<underline>1</underline>1)/(10<underline>11</underline>)surfaces dominate the powder samples. To search for stable reconstructions of these two surfaces, we use an evolutionary algorithm to explore the surface structures. To simplify the study, we only consider the pure GaN bulk with various numbers of Ga, N, and O atoms allowed to bond to surfaces. A few stable reconstructions at different Ga, N, and O chemical potentials are found. The consequences for the water splitting catalysis are discussed. In this thesis, I also include a chapter on electron transfer during a non-adiabatic process. The relevance to the water splitting project is that a photo-excited hole must transfer across the semiconductor/water interface to initiate the oxidation of water. Similarly, a photo-excited electron must transfer to the H<super>+</super> in the liquid to cause hydrogen reduction (H<sub>2</sub> formation). The transfer process is ignored in the next of the thesis. Since the Born-Oppenheimer approximation does not apply, it is a challenging problem for numerical simulations. A few approximate methods have been proposed, which greatly reduce the calculation complexity, but still take the non-adiabaticity into account. To test these methods, we study a simple model, in which the nuclei can be treated quantum mechanically. Numerically exact solutions are obtained and compared with these popular approximations. We find that these methods do produce correct trends in general. But caution must be taken since they break down in some scenarios.