The development of modern materials science has led to a growing need to understand the phenomena determining the properties of materials and processes on an atomistic level. The interactions between atoms and electrons are governed by the laws of quantum mechanics; hence, accurate and efficient techniques for solving the basic quantum-mechanical equations for complex many-atom, many-electron systems must be developed. Density functional theory (DFT) marks a decisive breakthrough in these efforts, and in the past decade DFT has had a rapidly growing impact not only on fundamental but also industrial research. This article discusses the fundamental principles of DFT and the highly efficient computational tools that have been developed for its application to complex problems in materials science. Also highlighted are state-of-the-art applications in many areas of materials research, such as structural materials, catalysis and surface science, nanomaterials, and biomaterials and geophysics.

Solid surfaces are used extensively as catalysts throughout the chemical industry, in the energy sector, and in environmental protection. Recently, density functional theory has started providing new insight into the atomic-scale mechanisms of heterogeneous catalysis, helping to interpret the large amount of experimental data gathered during the last decades. This article shows how density functional theory can be used to describe the state of the surface during reactions and the rate of catalytic reactions. It will also show how we are beginning to understand the variation in catalytic activity from one transition metal to the next. Finally, the prospects of using calculations to guide the development of new catalysts in industry will be discussed.

Although density functional theory (DFT) calculations have been widely used in many areas of the geosciences for the last 15 years, arguably the most successful application of these methods has been when they are used to understand the properties of minerals and melts in the Earth's pressures of the Earth's 6000 K and 360GPa) are so extreme that experiments under these conditions are very difficult. DFT calculations have been used to provide invaluable estimates of physical parameters that are fundamental to understanding the dynamics and evolution of the Earth. In particular, DFT calculations have helped provide estimates of the mineralogy and chemistry of the Earth's core, the high-temperature and pressure elasticity of the stable crystal phases in the mantle, the effect of defects on physical properties of mantle minerals, and, most recently, the discovery of a new phase of (Mg, Fe)SiO3 just above the core. These and other applications of DFT in the geosciences are described and their implications discussed.

The development of materials and devices at the nanoscale presents great challenges, from synthesis to assembly to characterization. Often, progress can only be made by complementing experimental work with electronic-structure modeling, harnessing the efficiency, predictive power, and atomic resolution of density functional theory to describe molecular architectures exactly at those scales (hundreds or thousands of atoms) where the most promising and undiscovered properties are to be engineered. Some of the next-generation technologies that will benefit first from first-principles simulations encompass areas as diverse as energy and information storage and retrieval, detection and sensing of biological and foreign contaminants, nanostructured catalysts, nanomechanical devices, hybrid organic-inorganic and biologically inspired materials, and novel computer technologies based on integrated optical and electronic platforms. This article reviews some of the recent successes and insights gained by electronic-structure modeling, ranging from carbon nanotubes to semiconducting nanoparticles, quantum dots, and self-assembled monolayers.

As an example of the application of density functional theory (DFT) to materials design, we describe our use of ab initio calculations based on DFT to develop a new structural material: Gum MetalTM, a novel, multifunctional titanium alloy with a low Young's modulus and high strength. We first carried out calculations on elastic constants in several Ti-X binary alloys to obtain the basic principles on which to determine the compositional limitations of an alloy with a low modulus. The elastic properties in the Ti-based binary alloys were successfully estimated by ab initio calculations, with the result implying absolute elastic softening at the valence electron number per atom, e/a, of 4.24. We also studied the effects of additional elements experimentally and, by comparison with electronic-structure calculations, found two more key parameters (approximately representing bond strength and electronegativity), critical for the design of practical elastic properties. We discuss dislocation-free plastic deformation of Gum Metal and its relation to the absolute elastic softening at an e/a value of 4.24, and finally we discuss the prospects for future applications of DFT in structural materials.