Systematic approach to Density Functional Theory

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Kieron Burke of the University of California-Irvine is supported by an award from the Chemical Theory, Models and Computational Methods program to develop methods that improve the accuracy and reliability of electronic structure calculations. Modern chemical and materials research increasingly relies on electronic structure calculations, i.e., solving the equations of quantum mechanics for electrons to predict or understand physical and chemical properties. Burke's method uses very fundamental properties of quantum mechanics to derive improved approximations in a highly systematic fashion. The intellectual value is to understand the quantum nature of electrons more deeply than before, in a way that significantly reduces errors. The impact could be significant, as it could improve electronic structure calculations for thousands of scientific papers each year, including those related to drug discovery, and to the identification of new catalysts, and new phases of matter. There is also a broad-based educational component, as graduate, undergraduate, and high school students are involved in the research.Burke and his research group combine theoretical methods from three different disciplines. A systematic non-empirical approach to density functional approximation is used, via an asymptotic expansion in powers of Planck's constant, the fundamental quantity that determines the strength of quantum effects. For model systems, the approximations can be found explicitly, and yield far more accurate results than previous formulas. For realistic systems (molecules and materials), the general forms can be used to deduce asymptotically exact approximations that significantly improve on those in use today, and constrain more sophisticated approaches. The methods are also applied to the problem of orbital-free electronic structure calculations, which holds the promise of making much larger distance and time scales accessible to density functional theory (DFT) calculations. The work includes an alternative strategy to the DFT framework in use today, called potential functional theory. A natural connection with thermal DFT has the potential to lead to useful applications in the time-dependent density functional theory of molecules and of warm dense matter.