A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a stringent validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising some standard set, the present approach not only uncovers the flaws and patent failures of the functionals but, even more importantly, also allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming and thus is particularly suitable for rapid screening of new functionals.
Due to the real-valuedness of the natural orbitals in question, no distinction is made in this paper between the exchange and the so-called L integrals.
Strictly speaking, UGU is not a genuine 1-matrix functional as it is not invariant to unitary transformations among NOs with degenerate occupation numbers.
Like UGU, these expressions are not invariant to unitary transformations among NOs with degenerate occupation numbers.
This expression shares the aforementioned invariance problem with UGU, UBBC1, and UBBC2.