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Building Kohn–Sham Potentials for Ground and Excited States

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Abstract

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density \(\rho \), there exist potentials having kth bound mixed states which densities are arbitrarily close to \(\rho \). The state can be chosen pure in dimension \(d=1\) and without interactions, and we provide numerical and theoretical evidence consistently leading us to conjecture that the same pure representability result holds for \(d=2\), but that the set of pure-state v-representable densities is not dense for \(d=3\). Finally, we present an inversion algorithm taking into account degeneracies, removing the generic blocking behavior of standard ones.

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Acknowledgements

I warmly thank Mathieu Lewin, for having advised me during this work, and Éric Cancès for useful comments. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements MDFT No 725528 and EMC2 No 810367). Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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  1. CERMICS, École des ponts ParisTech, 6 and 8 Av. Pascal, 77455, Marne-la-Vallée, France

    Louis Garrigue

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Garrigue, L. Building Kohn–Sham Potentials for Ground and Excited States. Arch Rational Mech Anal 245, 949–1003 (2022). https://doi.org/10.1007/s00205-022-01804-1

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