The smallest proton-bound dimer H₅⁺: theoretical progress

The protonated hydrogen dimer, H₅⁺, is the smallest system including proton transfer, and has been of long-standing interest since its first laboratory observation in 1962. H₅⁺ and its isotopologues are the intermediate complexes in deuterium fractionation reactions, and are of central importance in molecular astrophysics. The recently recorded infrared spectra of both H₅⁺ and D₅⁺ reveal a rich vibrational dynamics of the cations, which presents a challenge for standard theoretical approaches. Although H₅⁺ is a four-electron ion, which makes highly accurate electronic structure calculations tractable, the construction of ab initio-based potential energy and dipole moment surfaces has proved a hard task. In the same vein, the difficulties in treating the nuclear motion could also become cumbersome due to their high dimensionality, floppiness and/or symmetry. These systems are prototypical examples for studying large-amplitude motions, as they are highly delocalized, interconverting between equivalent minima through internal rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the computational vibrational spectroscopy of the H₅⁺ cation and its isotopologues are reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H₃⁺, H₅⁺ and beyond'.