Hookean atom with four electrons: On the formation of a tetrahedral Wigner molecule in the weak trapping limit

Abstract

Numerical results are presented on states ${}^{5}{S}_{u}$ and ${}^{3}{P}_{g}$ of the Hookean atom with four electrons. Using standard ab initio quantum chemistry methods, the quintet configuration is shown to be the ground state for the weak harmonic trapping constant $k$. For large $k$ values, there is a crossover to the triplet ${}^{3}{P}_{g}$ ground state. Finally, it is concluded that the Coulombic potential energy approaches the localized electron limit of a tetrahedral Wigner molecule as the harmonic force constant $k$ tends to zero.