  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.
