A kernel-based machine learning potential and quantum vibrational state analysis of the cationic Ar hydride (Ar₂H⁺)

One of the most fascinating discoveries in recent years, in the cold and low pressure regions of the universe, was the detection of ArH⁺ and HeH⁺ species. The identification of such noble gas-containing molecules in space is the key to understanding noble gas chemistry. In the present work, we discuss the possibility of [Ar₂H]⁺ existence as a potentially detectable molecule in the interstellar medium, providing new data on possible astronomical pathways and energetics of this compound. As a first step, a data-driven approach is proposed to construct a full 3D machine-learning potential energy surface (ML-PES) via the reproducing kernel Hilbert space (RKHS) method. The training and testing data sets are generated from CCSD(T)/CBS[56] computations, while a validation protocol is introduced to ensure the quality of the potential. In turn, the resulting ML-PES is employed to compute vibrational levels and molecular spectroscopic constants for the cation. In this way, the most common isotopologue in ISM, [³⁶Ar₂H]⁺, was characterized for the first time, while simultaneously, comparisons with previously reported values available for [⁴⁰Ar₂H]⁺ are discussed. Our present data could serve as a benchmark for future studies on this system, as well as on higher-order cationic Ar-hydrides of astrophysical interest.