Theoretical methods for the rotation–vibration spectra of triatomic molecules: distributed Gaussian functions compared with hyperspherical coordinates

ABSTRACT An approximate variational method based in the use of distributed Gaussian functions (DGF) and bond-length coordinates has been applied to study the rotation–vibration spectra of different triatomic molecules. In addition, an approach which employs hyperspherical coordinates and a basis set of hyperspherical harmonics constitutes a valid benchmark to test its capabilities. This work describes the technical details of both methods to provide the energies and symmetry of the corresponding rovibrational states and reviews their application to three different systems: For Ar and Ne the DGF technique exhibits a particularly good performance, but some limitations are observed for a more demanding scenario such as the H ion. The possible origin of these deficiencies are also discussed in detail.