Performance of the NOF Theory in the Description of the Four-Electron Harmonium Atom in the Singlet State

Abstract: In recent years, the natural orbital functional (NOF) theory has emerged as an alternative approach to both density functional theory (DFT) and wave-function (WFN) methods for electronic structure investigations. Several NOFs have been proposed, for which validation is necessary. A well-known tool for calibration, testing, and benchmarking of an approximate electronic structure method is the harmonium atom. In this model system, the electron-nucleus potential is replaced by a harmonic confinement, but the electron-electron Coulomb interaction remains. By varying the strength of the harmonic potential, the correlation regime can be tuned, making possible the transition from the weakly to the strongly correlated regime. Accordingly, the harmonium stands as an adequate system for studying the behavior of approximate NOFs, since it is possible to contrast them with their exact counterparts obtained from the analytic solution. In this presentation, the comparison between the quasi-exact and approximate electron-electron repulsion energy provided by eight known NOFs, in the singlet state of the four-electron harmonium atom with varying confinements, is analyzed in some detail. The present approach, which will appear soon in the Journal of Chemical Physics 143 (arXiv:1511.06564 [physics.chem-ph]), not only reveals the failures of the functionals but also pinpoints the causes. In general, the functional PNOF6 shows the most consistent behavior, wit