Proton-driven many-body interactions and structural organization in He _n H⁺ clusters

We present a systematic description of the interactions governing He _n H⁺ clusters, derived from gold-standard ab initio data. Two-, three-, and four-body potential contributions generated using CCSD(T)/CBS calculations and a kernel-based machine learning approach are integrated within a many-body expansion formalism. Benchmark tests show that inclusion of up to four-body terms is required to achieve consistent accuracy for larger clusters. Using the validated potential, global minimum searches reveal that structural organization proceeds through sequential binding of He atoms to a rigid linear HeH⁺He core, with formation of well-defined solvation motifs, while the more weakly bound He atoms display increasing degrees of delocalization. Zero-point-corrected energetics reproduce the experimentally reported stability patterns for n ≤ 13 clusters, while the onset of pronounced He delocalization, associated with microscopic superfluid-like behavior, introduces nontrivial quantum effects that influence stability trends for larger clusters. From a computational perspective, these results establish the central importance of higher-order many-body effects and quantum contributions in accurately describing proton microsolvation in He, while providing a reliable and comprehensive framework for interpreting experimental stability trends in proton-bound noble-gas clusters.