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

TL;DR

This paper evaluates Koopmans spectral functionals on Hooke's atom, a solvable two-electron model, demonstrating their accuracy and providing insights into their broader applicability for spectroscopic predictions.

Contribution

It is the first to test Koopmans spectral functionals on an analytically solvable model, revealing their effectiveness beyond complex many-electron systems.

Findings

Koopmans functionals accurately describe Hooke's atom across various potentials.

They outperform traditional Kohn-Sham density-functional theory in this model.

The study offers insights into the capabilities of Koopmans spectral functionals.

Abstract

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.