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In a recent article [AIP Adv. 11, 045033 (2021)], we carried out exact quantum dynamical calculations and computed ro-vibrational energy levels and wave functions for the H 3 + molecular ion up to the dissociation threshold (at J = 46) using a recently developed potential energy surface (PES) [Mol. Phys. 117, 1663 (2019)]—arguably, the most accurate to date —together with the ScalIT suite of parallel codes. In this work, we further improved the convergence accuracy and range of our ScalIT calculations for all J values up to J = 20 to a few 10 –5  cm −1 (or better). In addition, we performed an ab initio assignment of the ro-vibrational energy levels, providing vibrational ‘ v 1 , v 2 , | l |’ and rotational ‘ J , G , U , K ’ quantum labels for more than 2,200 ro-vibrational states, including every single 0 ≤ J ≤ 20 state up to and above the barrier to linearity at 10,000 cm −1 . The main underlying motivation of our work is to provide a list of reliably labeled, spectroscopically accurate energy levels in a format that can be used in spectroscopic line lists, which are based on both experimental and theoretical levels. Such line lists are of huge importance in various astrochemical and astrophysical contexts. 

H 3 + is a key player in molecular astrophysics, appearing in the interstellar medium and in the atmospheres of gas giants. It also plays an important role in star formation, and it has also been detected in supernova remnants. In theoretical chemistry, H3+ has long been a benchmark polyatomic system for high-level electronic-structure computations, as well as for quantum dynamics studies. In this work, exact quantum dynamical calculations are carried out for H3+, using the ScalIT suite of parallel codes, applied to two spectroscopically accurate potential energy surfaces. Specifically, rovibrational energy levels and wavefunctions are computed and labeled. Sixty vibrational states (for J = 0) are first determined, and then, rotational excitations for each of these “vibrational parent” states are computed up to total angular momentum J = 46, which is the highest value for which bound states of this molecule exist (D0 ∼ 35 000 cm−1). For these calculations, a very tight basis set convergence of a few 10−4 cm−1 (or less) has been achieved for almost all the computed energy levels. Where comparisons can be made, our results are found to agree well with earlier calculations and experimental data. 

The laws of physics that apply at the molecular scale are the laws of quantum mechanics. Whereas quantum electronic structure calculations are now routine for the most part, “quantum dynamics” calculations of nuclear motion are still plagued with the “curse of dimensionality.” Similar challenges may apply to the emerging field of electron dynamics. In this article, the role of recent phase- space (PS) based methods is reviewed—both individually in comparison with each other, and also collectively as an avenue for lifting the above “curse.” In addition: (a) the oldest such PS method is revamped, in order to render it suitable for extremely high accuracy applications; (b) a new PS method designed for electron dynamics is applied to a calculation of the He atom—performed in full quantum dimensionality, and treating electron correlation exactly.