It seems paradoxical but tetrahedral nanostructures of certain metals can show a higher degree of symmetry than a “spherical” atom, according to work published by a team from Tokyo Institute of Technology. [N. Haruta *et al., Nature Commun*, 2018, 9 (1) DOI: 10.1038/s41467-018-06244-8]

Symmetry is a fundamental concept in physics and chemistry but new discoveries are few and far between. Finding a seeming paradox in the symmetry of clusters could not only open up a new understanding of the laws of physics but could lead to new discoveries in electrical and magnetic properties that arise from a new kind of symmetry.

It seems obvious, an atom must naturally have the greatest degree of geometrical symmetry, represented as it is as a tiny sphere. However, that does not take into account degeneracy wherein quantum energy levels might correspond simultaneously to two or more different states in a quantum system. Degeneracy, of course, leads to interesting properties such as high conductivity and magnetism. It is not possible to make a material with a higher degree of degeneracy than a spherical atom. But a different type of symmetry might lead to a higher degree of degeneracy.

The Tokyo team hoped to demonstrate that some metals, such as zinc and magnesium, might be combined to produce a particular symmetry in an inflated tetrahedral structure. The symmetry of these structures arises not in the conventional geometric sense of symmetry but through the dynamic characteristics of the system. "We have demonstrated that realistic magnesium, zinc, and cadmium clusters having a specific tetrahedral framework possess anomalous higher-fold degeneracies than spherical symmetry," explains team leader Kimihisa Yamamoto.

The researchers used a tight-binding model analysis, which they then validated with density functional theory (DFT) calculations, in order to identify the general condition regarding the bonding interactions between atoms, what they refer to as the "transfer integrals". These give rise to the predicted dynamic symmetry. "Surprisingly, the degeneracy condition can be represented as an elegant square-root mathematical sequence involving the ratios of the transfer integrals," Yamamoto explains. "It is also impressive that this sequence has already been discovered by Theodorus in ancient Greece, independently of materials science," he adds.

"The degeneracy condition is fully identified as an elegant mathematical sequence involving interatomic parameters," the team writes. "The introduction of dynamical symmetry will lead to the discovery of a novel category of substances with super-degenerate orbitals."

*David Bradley blogs at Sciencebase Science Blog and tweets @sciencebase. His popular science book *Deceived Wisdom* is now available.*