Quantum Data-Driven Modeling of Interactions and Vibrational Spectral Bands in Cationic Light Noble-Gas Hydrides: [He₂H]⁺ and [Ne₂H]⁺

Motivated by two of the most unexpected discoveries in recent years—the detection of ArH⁺ and ${\mathrm{HeH}}^{+}$ noble gas molecules in the cold, low-pressure regions of the Universe—we investigate [He₂H]⁺ and [Ne₂H]⁺ as potentially detectable species in the interstellar medium, providing new insights into their energetic and spectral properties. These findings are crucial for advancing our understanding of noble gas chemistry in astrophysical environments. To achieve this, we employed a data-driven approach to construct a high-accuracy machine-learning potential energy surface using the reproducing kernel Hilbert space method. Training and testing datasets are generated via high-level CCSD(T)/CBS[56] quantum chemistry computations, followed by a rigorous validation protocol to ensure the reliability of the potential. The ML-PES is then used to compute vibrational states within the MCTDH framework, and assign spectral transitions for the most common isotopologues of these species in the interstellar medium. Our results are compared with previously recorded values, revealing that both cations exhibit a prominent proton-shuttle motion within the infrared spectral range, making them strong candidates for telescopic observation. This study provides a solid computational foundation, based on rigorous, fully quantum treatments, aiming to assist in the identification of these yet unobserved He/Ne hydride cations in astrophysical environments.