The semiclassical self-consistent-field method for polyatomic vibrations: Use of hyperspherical coordinates for H₂O and CO₂

The use of hyperspherical coordinates within the semiclassical self-consistent-field model (SCSCF) is investigated for two-mode models, corresponding to nonbending CO₂ and H₂O. The hyperspherical coordinate set is highly collective; since the screening which is characteristic of collective coordinates should result in increased accuracy of SCF methods, it might be expected that these coordinates would lead to very good SCF results. Numerical tests show that indeed the hyperspherical SCF results are accurate and superior to SCF either in local- or in normal-mode coordinates, the improvement being larger for CO₂ than for H ₂O. These calculations show as does recent work on HCN that proper choice of the coordinate system can lead to much improved SCF results.