Vibrational levels in the self-consistent-field approximation with local and normal modes. Results for water and carbon dioxide

Calculations are presented for vibrational energy levels of nonbending H₂O (at correct and linear geometries) and for linear HDO, DTO, C¹⁶O₂, and C¹⁶O¹⁸O. Results obtained from accurate numerical studies are compared to those generated by using the self-consistent-field (SCF) approximation in both normal and local coordinates. We find that for all cases except H₂O, SCF corrections systematically and considerably improve the zero-order uncoupled normal-mode eigenvalues and render them superior to the local modes even for part of the vibrational overtone region of HDO and DTO. For H₂O, the local-mode picture remains better than SCF, due partly to the small size of the Wilson coupling in local modes (or equivalently to the near-degeneracy of the normal modes). These results demonstrate the quality of the SCF as the best independent-mode approximation. Moreover, unlike the cruder decoupled-mode results, the SCF frequencies are in many cases of nearly spectroscopic accuracy.