The rotational-vibrational spectrum of symmetric non-rigid triatomics in hyperspherical coordinates: the H+ 3 molecule

Theoretical methods are described for the calculation of rovibrational levels of symmetric non-rigid triatomics using the symmetric hyperspherical coordinates of Smith and Whitten. An adiabatic separation of radial and angular motion is shown to be valid for H+ 3. The adiabatic angular functions are chosen as a linear combination of products of angular-momentum eigenfunctions and specially developed hyperspherical basis functions. Corrections to the adiabatic approximation are included by Brillouin-Wigner perturbation theory. Results are given for the H+ 3 system. The present approach has the advantage that all symmetric arrangements are treated equivalently.