A grand challenge for science today is to bridge the time and length scales from the electronic scale to the macroscopic properties of real, complex materials and systems. At the electronic scale, understanding of the interacting many-body system of electrons presents many of the most challenging problems in physics and chemistry. Density functional theory (DFT) has made possible the great advances in theory and computational methods that enable predictions of properties of materials from fundamental equations. In wide classes of materials, predictions are in very good agreement with experiment and the calculations reveal information far beyond what is measure by the experiments. In many cases reliable predictions can be made in advance of experiments and simulations are becoming tools for theorists and experimentalists alike. DFT is the basis for essentially all “first-principles” (Car-Parrinello) molecular dynamics, and methods under development are allowing direct calculations on large length scales. Nevertheless, many of the most interesting problems are on length (and especially time) scales far beyond the reach of present simulations. Developing new methods to reach from the electronic scales to much longer scales is a set of great challenges in many fields of science. This lecture is an introduction to DFT, the simple ideas upon which the theory is based and the remarkable power of the Kohn-Sham approach. The goal is to bring out 1) the role of DFT in providing fundamental information on many properties of materials, 2) the sense in which DFT provides a basis for development of reliable methods at long length and time scales, and 3) caution that all current DFT methods involve approximations that must be tested and used with care.
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