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Testing Koopmans spectral functionals on the analytically-solvable Hooke's atom

Yannick Schubert1,2*, Nicola Marzari3,4, Edward Linscott3*

1 Department of Physics, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland,

2 Now at: Department of Chemistry, University of Zurich, 8057 Zurich, Switzerland

3 Theory and Simulations of Materials (THEOS), École polytechnique fédérale de Lausanne, 1015 Lausanne, Switzerland

4 National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne, 1015 Lausanne, Switzerland

* Corresponding authors emails:,
DOI10.24435/materialscloud:mc-xr [version v2]

Publication date: Feb 23, 2023

How to cite this record

Yannick Schubert, Nicola Marzari, Edward Linscott, Testing Koopmans spectral functionals on the analytically-solvable Hooke's atom, Materials Cloud Archive 2023.29 (2023),


Koopmans spectral functionals are a class of orbital-density-dependent functionals designed to accurately predict spectroscopic properties. They do so markedly better than their Kohn-Sham density-functional theory counterparts, as demonstrated in earlier works on benchmarks of molecules and bulk systems. This work is a complementary study where --- instead of comparing against real, many-electron systems --- we test Koopmans spectral functionals on Hooke's atom, a toy two-electron system that has analytical solutions for particular strengths of its harmonic confining potential. As these calculations clearly illustrate, Koopmans spectral functionals do an excellent job of describing Hooke's atom across a range of confining potential strengths. This work also provides broader insight into the features and capabilities of Koopmans spectral functionals more generally.

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Preprint (Preprint where the data is discussed)


Hooke's atom Koopmans spectral functionals Orbital-density dependent functionals Electronic structure