Toward Computational Materials Design: The Impact of Density Functional Theory on Materials Research
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Toward Computational Materials Design: The Impact of Density Functional Theory on Materials Research Jürgen Hafner, Christopher Wolverton, and Gerbrand Ceder, Guest Editors Abstract 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-ofthe-art applications in many areas of materials research, such as structural materials, catalysis and surface science, nanomaterials, and biomaterials and geophysics. Keywords: computation, density functional theory, modeling, nanoscale, simulation.
Introduction During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and atomic nuclei have had an increasingly important impact on materials science, not only in fundamental understanding but also with a strong emphasis toward materials design for future technologies. The simulations are performed with atomistic detail by solving the Schrödinger equation to obtain energies and forces, require only the atomic numbers of the constituents as input, and should describe the bonding between the atoms with high accuracy. The Schrödinger
MRS BULLETIN • VOLUME 31 • SEPTEMBER 2006
equation for the complex many-atom, many-electron system is not analytically solvable, and numerical approaches have become invaluable for physics, chemistry, and materials science. A breakthrough in these computational efforts was realized in 1964 when Walter Kohn and coworkers developed the density functional theory (DFT), a theory based on electron density, which is a function of only three spatial coordinates.1 The Kohn–Sham equations of DFT cast the intractable complexity of the electron–electron interactions into an effective single-particle potential determined by the exchange-correlation
functional. This functional (i.e., a function whose argument is another function) describes the complex kinetic and energetic interactions of an electron with other electrons. Although the form of this functional that would make the reformulation of the many-body Schrödinger equation exact is unknown, approximate functionals have proven highly successful in describing many material properties. Efficient algorithms devised for solving the Kohn–Sham equations have been implemented in increasingly sophisticated codes, tremendously boosting the a
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