Microsolvation of a Proton by Ar Atoms: Structures and Energetics of Ar_nH⁺ Clusters

We present a computational investigation on the structural arrangements and energetic stabilities of small-size protonated argon clusters, Ar nH +. Using high-level ab initio electronic structure computations, we determined that the linear symmetric triatomic ArH +Ar ion serves as the molecular core for all larger clusters studied. Through harmonic normal-mode analysis for clusters containing up to seven argon atoms, we observed that the proton-shared vibration shifts to lower frequencies, consistent with measurements in gas-phase IRPD and solid Ar-matrix isolation experiments. We explored the sum-of-potentials approach by employing kernel-based machine-learning potential models trained on CCSD(T)-F12 data. These models included expansions of up to two-body, three-body, and four-body terms to represent the underlying interactions as the number of Ar atoms increases. Our results indicate that the four-body contributions are crucial for accurately describing the potential surfaces in clusters with n> 3. Using these potential models and an evolutionary programming method, we analyzed the structural stability of clusters with up to 24 Ar atoms. The most energetically favored Ar nH + structures were identified for magic size clusters at n = 7, 13, and 19, corresponding to the formation of Ar-pentagon rings perpendicular to the ArH +Ar core ion axis. The sequential formation of such regular shell structures is compared to ion yield data from high-resolution mass spectrometry measurements. Our results demonstrate the effectiveness of the developed sum-of-potentials model in describing trends in the nature of bonding during the single proton microsolvation by Ar atoms, encouraging further quantum nuclear studies.