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Thermal Density Functional Theory in Context

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Frontiers and Challenges in Warm Dense Matter

Abstract

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. This review emphasizes thermal DFT’s strengths as a consistent and general framework.

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Notes

  1. 1.

    See Refs. [24] or [25] for quantum mechanical background that is useful for this chapter.

  2. 2.

    In this work, we discuss only spin-unpolarized electrons.

  3. 3.

    Here and in the remainder of the chapter, we restrict ourselves to square-integrable wavefunctions over the domain \({\mathbb{R}}^{3N}\).

  4. 4.

    For a more extended discussion of these topics, see Ref. [60].

  5. 5.

    Note that, we eventually choose to work in a system of units such that the Boltzmann constant is k B  = 1, that is, temperature is measured in energy units.

  6. 6.

    The interested reader may find the extension of the Hohenberg-Kohn theorem to the thermal framework in Mermin’s paper.

  7. 7.

    Uniform coordinate scaling may be considered as (very) careful dimensional analysis applied to density functionals. Dufty and Trickey analyze non-interacting functionals in this way in Ref. [15].

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Acknowledgements

We would like to thank the Institute for Pure and Applied Mathematics for organization of Workshop IV: Computational Challenges in Warm Dense Matter and for hosting APJ during the Computational Methods in High Energy Density Physics long program. APJ thanks the U.S. Department of Energy (DE-FG02-97ER25308), SP and KB thank the National Science Foundation (CHE-1112442), and SP and EKUG thank European Community’s FP7, CRONOS project, Grant Agreement No. 280879.

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Correspondence to Aurora Pribram-Jones .

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Pribram-Jones, A., Pittalis, S., Gross, E.K.U., Burke, K. (2014). Thermal Density Functional Theory in Context. In: Graziani, F., Desjarlais, M., Redmer, R., Trickey, S. (eds) Frontiers and Challenges in Warm Dense Matter. Lecture Notes in Computational Science and Engineering, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-04912-0_2

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