Over the past years, the scientific community has increasingly invested in the systematic curation of large-scale, flexible, and continuously updated databases to support data-driven research. In crystallography, a key reference is the Cambridge Structural Database [1], which archives all published organic and metal–organic small-molecule crystal structures characterized by single-crystal X-ray and neutron diffraction. The database currently contains over 1.3 million experimental structures, with thousands of new entries added every year. From this database we retrieved, refined, and analyzed all deposited pure Ag, pure Au, and mixed Ag–Au structures.

To analyze these atomically precise nanoclusters, we developed a framework that combines topological analysis based on graph theory with geometrical shape analysis using rotationally invariant descriptors such as asphericity and prolateness [2,3]. Each nanocluster is modeled as a graph, where atoms are represented as nodes and chemical bonds as edges. Within this framework, we compute graph-based quantities, such as node degrees and canonical graph representations [4], to characterize structural connectivity. Because graph representations do not fully capture the three-dimensional arrangement of atoms, shape descriptors quantify ellipsoidal deformations and distinguish spherical, oblate, and prolate geometries. Additionally, we employ a graph-based chirality descriptor [5] that enables a quantitative estimate of chirality. This descriptor also allows us to localize chiral features to specific regions of the cluster, namely the metallic core, the metal–ligand interface, and the ligand shell.

We present a systematic comparison of graph- and shape-based descriptors for silver, gold, and mixed silver–gold monolayer-protected clusters, highlighting key similarities and differences in their structural connectivity, chiral properties, and shape trends. In particular, the shape analysis indicates that atomically precise nanoclusters predominantly occupy a spheroidal structural regime, in which two principal axes remain essentially equivalent. These insights contribute to a deeper understanding of the topological organization of metal nanoclusters and provide a basis for rationalizing their chemical behavior.

[1] F. H. Allen,  Structural Science, 58(3):380–388, 2002.

[2] V. Blavatska, W. Janke, The Journal of chemical physics, 133(18), 2010.

[3] L. Ruddigkeit, R. V. Deursen, L. C. Blum,  J. Reymond, Journal of chemical information and modeling, 52(11):2864–2875, 2012.

[4] B. D. McKay, A. Piperno, Journal of symbolic computation, 60:94–112, 2014.

[5] E. Zerbato, T. Bürgi, A. F. Perez Mellor, The Journal of Chemical Physics, 164(7), 2026.