Superatom Orbitals, Orbital Splitting and Structure Prediction of Pure Alkali Metal Clusters

Jellium model achieved great success in predicting stable clusters with closed electronic shells and zero spin. In order to explain the stability of open shell clusters, it is necessary to consider the case of non-degenerate energy levels. In this paper the energy levels in nine low-lying Li$_{19}$ clusters are analysed systematically through superatomic orbital splitting effect. It is found that for originally degenerate orbitals like five 1D orbitals, the more the orbital extends in the direction of the cluster extension, the lower the energy of the orbital becomes. So oblate Li$_{19}$ clusters have the orbital sequence of $1\mathrm{S}^2-1\mathrm{P}_{x/y}^{4}-1\mathrm{P}_{z}^{2}-1\mathrm{D}_{xy/x^2-y^2}^{4}-2\mathrm{S}^2-1\mathrm{D}_{xz/yz}^{4}-1\mathrm{D}_{z^2}^{1}$, while prolate Li$_{19}$ clusters have the sequence of $1\mathrm{S}^2-1\mathrm{P}_{z}^{2}-1\mathrm{P}_{x/y}^{4}-1\mathrm{D}_{z^2}^{2}-1\mathrm{D}_{xz/yz}^{4}-1\mathrm{D}_{xy/x^2-y^2}^{4}-2\mathrm{S}^1$. This electron configuration is applied to predict the shape and magnetic moment of the alkali metal Li$_{n}$ clusters. The stability of the Li$_{14}$ cluster can be successfully interpreted in the framework of orbital splitting effect without resorting to the super valence bond (SVB) model, indicating a non-spherical cluster can achieve good stability without meeting the magic number. It is also proposed that the orbital splitting can be used to predict the shape (prolate, oblate or sphere) and magnetic moment of clusters. 11 out of 16 predicted shapes of Li$_n(n=3-18)$ are consistent with the results obtained by the principle of minimum energy.