Abstract
The periodic table has always contributed to the discovery of a number of elements. Is there no such principle for larger-scale substances than atoms? Many stable substances such as clusters have been predicted based on the jellium model, which usually assumes that their structures are approximately spherical. The jellium model is effective to explain subglobular clusters such as icosahedral clusters. To broaden the scope of this model, we propose the symmetry-adapted orbital model, which explicitly takes into account the level splittings of the electronic orbitals due to lower structural symmetries. This refinement indicates the possibility of an abundance of stable clusters with various shapes that obey a certain periodicity. Many existing substances are also governed by the same rule. Consequently, all substances with the same symmetry can be unified into a periodic framework in analogy to the periodic table of elements, which will act as a useful compass to find missing substances.
Highlights
The periodic table has always contributed to the discovery of a number of elements
The spherical jellium model is a candidate for such a theory; most clusters do not have quasi-spherical Ih symmetry[14,15], because their atomicities are inappropriate for the construction of Ih symmetry structures
We have focused on the violation of the spherical jellium model to extend the theory for the prediction of clusters
Summary
According to the first-order perturbation theory, the jellium orbitals that overlap the nuclear charge distribution are selectively stabilized, depending on each structural symmetry, as compared with the spherical jellium model[19]. When the split orbitals are filled with a suitable number of valence electrons, structural symmetry is maintained without any Jahn–Teller distortion[16]. According to the SAO model, in the case of four-atom clusters (E4), only the elements having 2, 4, and 5 valence electrons fill the split orbitals. The optimized geometries and molecular orbitals of Cd4, Sn4, and Sb4, which constitute elements in the same period, are shown in Fig. 4b (see Supplementary Fig. 5 for reference). The optimized geometries and molecular orbitals of Si4, Ge4, Group
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