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

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.

Figure 1

Electron density $n(k;r)$ in the Hookean atom with four electrons in the ${}^5{S}_u$ state for force constants $k=0.25$ (a), $k=0.0012$ (b), and $k=0.0001$ (c) in the external potential given in Eq. (1), derived from VMC simulations. Curves (b) and (c) have been multiplied by 100 and 500, respectively, for comparison purposes. Density and length are in atomic units.