We develop advanced theory, algorithms and code for applications to predict, explain and explore the properties, structure, and behavior of materials. We focus mainly on first-principles-based methods and algorithms in computational materials science to explain advanced characterization experiments. However, we also developing new model and new algorithms to utilize scalar and parallel computer architectures. Areas include: electronic and thermodynamic properties of long-range, partially long-range, or short-range ordered alloys, new electronic-structure algorithms, mechanical properties of alloys and the role of solute and defects, properties of nanoassemblies, multiscale modeling for spatial and temporal scales, and properties of alloys and molecular solids for hydrogen-storage.