Coordination-driven magic numbers in protonated argon clusters

Charged atom clusters give a way to study charged-neutral interactions at the borderline between few-body and many-body physics. Protonated argon clusters Ar_nH⁺ have been one of the more difficult systems to explain. In this talk, we present a theoretical quantum mechanical study of protonated argon clusters [1], successfully predicting all the Ar_nH⁺ magic numbers, agreeing with the latest experimental data. Assuming that 2 argon atoms very close to the proton form a fixed linear "core" Ar₂H⁺, we employ a 4-body potential energy surface fit from accurate quantum chemistry calculations which includes 2-body Ar-Ar interaction terms, and 4-body terms for other Ar atoms interacting with the core. We use conformational space annealing to find the optimal geometries of the clusters for this potential, and diffusion MC and path integral MC to account for zero-point vibrational energy and temperature. We find that fixing the core introduces a significant many-body effect on magic numbers less than 34-39, where Ar atoms form pentagonal rings around a central Ar₁₉H⁺ structure, while for clusters larger than Ar₃₉H⁺, a 2-body potential is sufficient to describe the transition to icosahedral packing of Ar atoms. 

[1] Saajid Chowdhury, María Judit Montes de Oca-Estévez, Florian Foitzik, Elisabeth Gruber, Paul Scheier, Pablo Villarreal, Rita Prosmiti, Tomás González-Lezana, and Jesús Pérez-Ríos (2026). “Coordination-driven magic numbers in protonated argon clusters”. (Under review).