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Center for Nonlinear Studies |
In 1929 Dirac pointed out that with the Dirac/Schrödinger equation as a newly found fundamental physical law of nature, it was only a matter of solving this equation in order to know all the properties of a system. However, to this day there is no method for directly solving engineering problems, such as mechanical strength and radiation damage, using this equation. Instead methods bridging the length scales between the Ångström scale of the Dirac/ Schrödinger equation and the millimeter and larger engineering scales are needed. An important step in this multi-scale chain is the Nobel Prize winning [1] Density Functional Theory (DFT), formulated and made into a practical scheme in two foundational papers by Hohenberg and Kohn [2], and Kohn and Sham[3] in 1964 and 1965. I will present the fundamentals of DFT and connect this theory both down the scales to the Dirac/Schrödinger equation, and up to engineering scale applications. In particular, I will discuss the exchange-correlation (xc) functional, the part of DFT that connects to the Dirac/Schrödinger equation. The approximations to the unknown, exact or ‘divine’ [4], xc functional decides the achievable accuracy with DFT. In creating more accurate approximations for this unknown xc functional, there is crucial need for dialogue between Theoretical Condensed Matter Physicists and functional developers. [1] Walter Kohn, 1998, http://nobelprize.org/nobel_prizes/chemistry/laureates/1998/ [2] Inhomogeneous Electron Gas, P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). [3] Self-Consistent Equations including Exchange and Correlation Effects, W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). [4] In Pursuit of the "Divine" Functional, Ann E. Mattsson, Science 298, 759 (25 October 2002).
Host: John Wills, T-1