The He-H₃ ⁺ complex. I. Vibration-rotation-tunneling states and transition probabilities

With a He-H₃ ⁺ interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v₂ = 1 excited state of H₃ ⁺. The potential has three equivalent global minima with depth D_e = 455.3 cm^-1 for He in the plane of H₃ ⁺, three equatorial saddle points that separate these minima with barriers of 159.5 cm^-1, and two axial saddle points with energies of 243.1 cm^-1 above the minima. The dissociation energies calculated for the complexes of He with ortho-H₃ ⁺ (oH₃ ⁺) and para-H₃ ⁺ (pH₃ ⁺) are D₀ = 234.5 and 236.3 cm^-1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the j_k = 1₀ and 1₁ rotational ground states of oH₃ ⁺ and pH₃ ⁺, with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 3₃ in He-oH₃ ⁺, and 2₂ and 2₁ in He-pH₃ ⁺. The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v₂ = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He-H₃ ⁺ interaction potential and of the ensuing calculations of the VRT states.