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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.

Periodicity of molecular clusters based on symmetry-adapted orbital model