One-dimensional (1D) and two-dimensional (2D) models are investigated, which help to understand the unusual rovibrational energy-level structure of the astronomically relevant and chemically interesting astructural molecular ion H + 5 . Due to the very low hindering barrier characterising the 1D torsion-only vibrational model of H + 5 , this model yields strongly divergent energy levels. The results obtained using a realistic model for the torsion potential, including the computed (near) degeneracies, can be rationalised in terms of the model with no barrier. Coupling of the torsional motion with a single rotational degree of freedom is also investigated in detail. It is shown how the embedding-dependent rovibrational models yield energy levels that can be rationalised via the 2D vibrational model containing two independent torsions. Insight into the complex rovibrational energy level structure of the models and of H + 5 is gained via variational nuclear motion and diffusion Monte Carlo computations and by the analysis of the wavefunctions they provide. The modelling results describing the transition from the zero barrier limit to the large barrier limit should prove to be useful for the important class of molecules and molecular ions that contain two weakly coupled internal rotors.
IntroductionThe simplest and exactly solvable quantum chemical models that are traditionally employed to understand highresolution spectra of gas-phase molecules are based on the harmonic oscillator (HO) and rigid rotor (RR) approximations of the vibrations and the rotations, respectively. In cases when the results based on the RRHO approximation, perhaps after a slight extension based on second-order perturbation theory [1][2][3][4][5], provide a good qualitative and even a semiquantitative understanding of spectral regularities, the molecule of interest can be considered to be 'semirigid'. These are molecules for which the electronic state that is being investigated contains a single, well-defined, and relatively deep minimum. For semirigid molecules, the timescales for the vibrational and rotational motions are sufficiently different to allow their approximate separation, the vibrational spacing decreases as the vibrational excitation increases, the vibrational states have well-defined symmetries provided by the point group characterising the unique equilibrium structure, and the rotational states can be assigned to a certain vibrational state. The RRHO treatment is familiar to most chemists as excellent textbooks exist which describe slightly anharmonic molecular vibrations [6,7] as