Quantum microsolvation and size-resolved energetics of He-solvated H₂⁺ and D₂⁺ cations

Helium nanoclusters provide a highly quantum solvent environment in which light ions experience pronounced zero-point motion and delicate competition between ion-solvent and solvent-solvent interactions. We report quantum diffusion Monte Carlo (DMC) calculations for protonated hydrogen cations embedded in helium clusters, H₂⁺@He_N and D₂⁺@He_N, quantifying ground-state energetics, evaporation energies, and microsolvation motifs up to medium-size N = 30 systems. Using CCSD(T)/CBS-quality interaction potentials augmented by short-range nonadditivity and correct long-range behavior, we analyze size-resolved stabilization patterns, aiming to identify possible shell-closure signatures governed by the balance of anisotropic cation-He forces and weak He-He binding. The resulting DMC probability densities reveal heterogeneous quantum microsolvation patterns, exhibiting both solidlike and liquidlike characteristics. Quantum effects are substantial, with the first two helium atoms found well localized, and as the cluster size increases, inner helium layers retain partial solidlike character, while pronounced quantum delocalization and He-exchange dominate the outer shells. As a consequence, no clear, well-defined shell-closure ("magic" N) could be identified, although the D₂⁺He_N clusters show a more compact, well-formed central ring around the [He-H-H-He]⁺ core for N ≥ 10 compared to the H₂⁺He_N ones. The computed evaporation energy trends rationalize experimentally observed ion-yield anomalies and delineate where semiclassical Feynman-Hibbs corrections deviate from exact ground-state sampling. Overall, this work establishes a benchmark quantum description for protonated He clusters and offers microscopic insight into the interplay of nuclear quantum effects, many-body interactions, and isotopic substitution in He-solvated ionic complexes, with implications for ion spectroscopy and low-temperature cluster physics.