Quantum vibrational study of the proton-bound [Ar-H-He]⁺ mixed noble-gas dimer

Proton-bound heteronuclear noble-gas complexes serve as challenging test systems for exploring proton-mediated interactions, weak intermolecular forces, and nuclear quantum effects in chemically simple yet highly anharmonic environments. In this work, we present a new three-dimensional machine-learning potential energy surface (ML-PES) for the noble-gas hydride cation [Ar-H-He]⁺, constructed within a reproducing kernel Hilbert space (RKHS) formalism and trained to high-level CCSD(T)/CBS reference energies. Particular attention is devoted to the generation, training, and validation of the PES to ensure a dense, smooth, and globally consistent representation of the interaction potential over the full configuration space relevant for quantum dynamics. The resulting ML-PES is employed in multi-configuration time-dependent Hartree (MCTDH) quantum calculations to obtain accurate vibrational energy levels for the most abundant isotopologues of [Ar-H-He]⁺. Our results reveal noticeable differences in both energies and level assignments compared to earlier theoretical studies, highlighting the importance of PES quality for reliable spectroscopic modeling. The vibrational energy levels and transition positions reported here provide spectroscopic benchmarks and may support future laboratory measurements and astrophysical observational investigations of these proton-bound noble-gas molecular systems.