Nanomaterials design for super-degenerate electronic state beyond the limit of geometrical symmetry

Abstract

Spherical atoms have the highest geometrical symmetry. Due to this symmetry, atomic orbitals are highly degenerate, leading to closed-shell stability and magnetism. No substances with greater degrees of degeneracy are known, due to geometrical limitations. We now propose that realistic magnesium, zinc, and cadmium clusters having a specific tetrahedral framework possess anomalous higher-fold degeneracies than spherical symmetry. Combining density functional theory calculations with simple tight-binding models, we demonstrate that these degeneracies can be attributed to dynamical symmetry. The degeneracy condition is fully identified as an elegant mathematical sequence involving interatomic parameters. The introduction of dynamical symmetry will lead to the discovery of a novel category of substances with super-degenerate orbitals.

Periodicity of molecular clusters based on symmetry-adapted orbital model

“…It was confirmed that all the obtained structures have no imaginary frequencies. A small part of the present clusters has also been discussed in our recent paper 41 , including Mg 4 , Mg 10 , Mg 20 , Zn 4 , Zn 10 , Zn 20 , Cd 4 , Cd 10 , Cd 20 , Si 10 , Ge 10 , Sn 10 , Pb 10 , Al 6 Sn 4 , Ga 6 Sn 4 , and In 6 Sn 4 .…”

Recent advances in atomic cluster synthesis: a perspective from chemical elements

“…This tendency is rationalized by the thermodynamic stability based on the electronic configurations unique to clusters typified by superatoms. [6][7][8]25,32,36,47,90 These clusters generally have relatively rigid structures with large bond angles of up to 90°originating from p-electrons and the ability to contain a few atoms of other group elements in electronically stabilized skeletons. In particular, the endohedral structures typified by stannaspherenes mentioned in the gas-phase synthesis section enable the incorporation of other groups of elements without ligands.…”

“…[1][2][3] On the other hand, their electronic states of clusters resemble more closely those of molecules than bulk materials (including nanoparticles), leading to their unique characteristics. [4][5][6][7][8] Such clusters contribute to the manifestation of highly efficient and sophisticated biological functions in nature, such as water oxidation in photosynthesis, electron transfer, nitrogen fixation, and breathing. [9][10][11][12][13] Moreover, clusters possess various structural characteristics that are not observed in other chemicals, including the number of constituent atoms, types of constituent elements, elemental ratios, atomic arrangements, and geometrical symmetry.…”

Highly Accurate Synthesis of Quasi‐sub‐nanoparticles by Dendron‐assembled Supramolecular Templates

“…[1][2][3][4][5] Particularly, atomic clusters, which are ultrasmall substances up to sub-nanosize scale ( � 1 nm), have attracted attention because they possess unusual properties not found in general NPs. [6][7][8][9][10][11] In contrast to NPs whose properties are dependent on particle size, [4,12] sub-nanoparticles (SNPs), including the clusters, can also be regarded as inorganic molecules because their properties are determined by quantum chemical factors such as molecular orbitals and structural symmetry [11,[13][14][15] and differ dramatically depending on the number of constitutive atoms. [16][17][18] Although the origins of the properties of NPs (> 3 nm) and SNPs ( � 1 nm) are different, their border, which exists in the quasi-sub-nano region (1-3 nm, 60-1000 constitutive atoms), [18] has not been clarified.…”