Non-adiabatic effects in the H₃⁺ spectrum

The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm^-1 for H₃⁺ and must be included in high-accuracy calculations. Different strategies to obtain the corresponding energy shifts are reviewed in the article. A promising way is to introduce effective vibrational reduced masses that depend on the nuclear configuration. A new empirical method that uses the stockholder atoms-in-molecules approach to this effect is presented and applied to H₃⁺. Furthermore, a highly accurate potential energy surface for the D₃⁺ isotopologue, which includes relativistic and leading quantum electrodynamic terms, is constructed and used to analyse the observed rovibrational frequencies for this molecule. Accurate band origins are obtained that improve existing data. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H₃⁺, H₅⁺ and beyond'.