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.
Highlights
Spherical atoms have the highest geometrical symmetry
We demonstrate that realistic magnesium, zinc, and cadmium clusters having a specific tetrahedral framework possess anomalous higher-fold degeneracies than spherical symmetry from first principles
The Hamiltonian, HN (N = 1, 4, 10, 20, ⋯), satisfying the degeneracy condition can be rewritten as HN 1⁄4 fε þ 3ðn À 1ÞtgI À 4t X3 ayi ai; ð3Þ
Summary
Spherical atoms have the highest geometrical symmetry Due to this symmetry, atomic orbitals are highly degenerate, leading to closed-shell stability and magnetism. As a result of this symmetry, these species possess atomic orbitals with the high degrees of degeneracy, such as d orbitals, which have a fivefold degeneracy This degeneracy in turn leads to certain properties, such as closed-shell stability and magnetism. Species having higher degrees of degeneracy than atoms have not yet been known, due to the limitations of geometrical symmetry. A superatom is analogous to an atom but with a higher-order structure: highly symmetrical metal clusters possess delocalized molecular orbitals, the shapes of which are just like those of atomic orbitals This analogy can be understood based on the three-dimensional spherical jellium model[9]. By means of simple tight-binding models and group-theoretical analyses, we elucidate that these degeneracies can be attributed to dynamical symmetry
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
