From Spheres to Cones: Structural Instabilities and Acidity at Conical Regions in Trivalent Metal Ion Nano-clusters

Sub-nanometer aqueous clusters containing a single trivalent metal cation can exhibit charge-induced structural instabilities. Here, we present computational evidence that clusters containing a single \ce{Fe^{3+}}, \ce{Lu^{3+}}, or \ce{La^{3+}} ion undergo continuous geometric transformations as a consequence of this instability. These clusters dynamically evolve across their potential energy landscape, adopting triangular, elongated two-point, single-point, and more spherical configurations often with distinct conical surface protrusions. The manifestation of this instability differs from that observed in mesoscopic and microscopic droplets containing macroions, where stable ``star-like'' structures form, characterized by a specific number of conical protrusions that varies with the droplet size. In the present study, we find that the orientation of the \ce{H2O} molecules surrounding the metal ion is influenced not only by the electric field of the trivalent ion but also by the local conical protrusions. To further investigate the local acidity in the conical protrusions, we employ a proxy model system consisting of an aqueous nano-cluster containing three \ce{H3O+} ions, simulated using ab initio molecular dynamics. Within the conical regions of the cluster, protons exhibit diffusion across several water molecules, in contrast to the more localized proton delocalization observed in the compact body of the cluster. These findings suggest that local geometry can significantly modulate acidity in highly charged nano-clusters, with potential implications for understanding charge-transfer and ionization mechanisms in techniques such as electrospray ionization mass spectrometry. Additionally, the structural motifs and solvent organization reported here provide a molecular-level framework that can complement interpretations from infrared spectroscopic data.