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Climbing the ladder of density functional approximations

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Abstract

Kohn–Sham density functional theory is the most widely used method of electronic-structure calculation in materials physics and chemistry because it reduces the many-electron ground-state problem to a computationally tractable self-consistent one-electron problem. Exact in principle for the ground-state energy and electron density, it requires in practice an approximation to the density functional for the exchange-correlation energy. Common approximations fall on the rungs of a ladder, with higher rungs being more complicated to construct and use but potentially more accurate. Each rung of the ladder introduces an additional ingredient to the energy density. From bottom to top, the rungs are (1) the local spin density approximation, (2) the generalized gradient approximation (GGA), (3) the meta-GGA, (4) the hybrid functional, and (5) the generalized random phase approximation. The semi-local rungs (1–3) are important, because they are computationally efficient, they can be constructed non-empirically, they can serve as input to fourth-rung functionals, and the meta-GGA by itself can be accurate for equilibrium properties. Recent and continuing improvements to the meta-GGA are emphasized here.

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Acknowledgments

I would first like to thank the Materials Research Society for this Materials Theory Award, which was endowed by Toh-Ming Lu and Gwo-Ching Wang. I would like to thank the National Science Foundation for supporting my research over a long period. I also want to thank many collaborators; I cannot mention them all but I am especially grateful to Sy Vosko and David Langreth, who introduced me to DFT; they are no longer with us but not forgotten. I should also mention Alex Zunger, Mel Levy, Kieron Burke, Matthias Ernzerhof, Jianmin Tao, Gus Scuseria, and Adrienn Ruzsinszky. This work was supported, in part, by the National Science Foundation under Grant DMR-0854769 and, in part, by NSF EPSCoR and the Louisiana Board of Regents under the LA-SiGMA project (NSF Cooperative Agreement EPS-1003897).

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  1. Department of Physics, Temple University, USA

    John P. Perdew

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Correspondence to John P. Perdew.

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The following article is an edited transcript of the MRS Materials Theory Award presentation by John P. Perdew on November 26, 2012, at the Materials Research Society Fall Meeting in Boston. The Award “recognizes exceptional advances made by materials theory to the fundamental understanding of the structure and behavior of materials.”

To view a video of John Perdew’s presentation at the MRS 2012 Fall meeting, visit http://www.mrs.org/f12-mta-video.

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Perdew, J.P. Climbing the ladder of density functional approximations. MRS Bulletin 38, 743–750 (2013). https://doi.org/10.1557/mrs.2013.178

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