Equitable Partitions in Inorganic Nanoclusters

Introduction. Graph-theoretical concepts allow an alternative understanding of the role of symmetry in inorganic nanomaterials and offer a fine-grained look at the relative importance of their constituent atoms. Here, a link is shown between the concept of Equitable Partitions (EPs) of chemical graphs [1–3] and the distribution of local properties of nanoparticles.

Methods. The study focused on the geometrical and physical properties of idealised spherical and polyhedral nanoclusters of iron and cobalt. Clusters extracted from bulk lattices of the corresponding chemical elements were modeled as graphs based on nearest-neighbor adjacency, and their EPs were determined. The clusters were subjected to classical force-field modeling, as well as DFT calculations using the SIESTA software package [4].

Results. The following properties were determined: atom radial distances from the cluster center; a measure of forces on atoms; local charge densities; and local magnetic moments. Their values were found to be distributed according to the graph’s equitable partition; in other words, all atoms in a given partition cell share the exact same properties.

Conclusions. Our method sheds new light on the symmetries of inorganic nanomaterials and the role of individual atoms therein. Our findings can have implications in the understanding, design, and engineering of magnetic nanoparticles, catalyst materials, and other applications at the nanoscale.

References

1. I. Michos, V. Raptis. Graph Partitions in Chemistry. Entropy 2023, 25, 1504.

2. V. Raptis, A. Kaltzoglou. Graph Theoretical Analysis as an Aid in the Elucidation of Structure-Property Relations of Perovskite Materials. AIP Conf Proc 2024, 3030, 110005.

3. V. Raptis, I. Michos. Chemical Equitable Partitions: A new Perspective on Molecular Symmetries and Its Implications for the Study of Structure–Property Relationships. MDPI Proceedings 2025, 123, 6.

4. José M. Soler et al. The SIESTA method for ab initio order-N materials simulation. J. Phys.: Condens. Matter 2002, 14, 2745.