Vibration spectrum of H3+: A model hamiltonian

A Numerical Variational Method for Calculating Accurate Vibrational Energy Separations of Small Molecules and Their Ions

“…As has been pointed out by us elsewhere (see Burton et al 1984a), there is an ellipse of singularities associated with large amplitude of vibrations which manifest themselves in the Watson term of the normal coordinate Hamiltonian. By considering only small vibrational amplitudes, we have demonstrated that the Watson term can be effectively replaced by a third-order perturbation expression (see Burton et al 1984a).…”

“…Both are ab initio methods and have yielded excellent results for the vibrational spacings of small triatomic ions. The present investigation details and extends our solution algorithm which we have successfully applied to the investigation of the vibrational spacings of small D3h molecular ions (see Burton et al 1984aBurton et al , 1984bBurton et al , 1985 where Ta is the kinetic energy operator, T t the vibrational angular momentum operator, U w the Watson operator and V the total electronic pot~ntialoperator. Our adoption of this Hamiltonian [in preference to (Rl' R 2 ,R 3 ) or (R, (T, 8) representations] was due to our initial interest in accurately modelling the low lying vibrational states.…”

“…For the multi-dimensional vibrational problem the two reported numerical Rayleigh-Ritz variation algorithms are the finite difference algorithm of Cropek and Carney (1984) and the finite element method of Burton et al (1984aBurton et al ( , 1984bBurton et al ( , 1985. Both are ab initio methods and have yielded excellent results for the vibrational spacings of small triatomic ions.…”

“…By considering only small vibrational amplitudes, we have demonstrated that the Watson term can be effectively replaced by a third-order perturbation expression (see Burton et al 1984a). The expression used for U w is given by …”

“…Correct to second order, the Watson term has no inter-mode coupling (see Burton et al 1984a). Its inclusion in equation (8) would only marginally alter the onedimensional eigenvalues, since for the three-dimensional problem Hi the Watson term generally increases the vibrational energy level by 27 ·46 cm-1 .…”