Semiclassical vibrational eigenvalues of triatomic molecules: Application of the FFT method to SO₂, H₂O, H₃⁺, and CO₂

We have applied a recently developed fast Fourier transform method for determining vibrational action variables to the calculation of semiclassical eigenvalues for SO₂, H₂O, H₃⁺, and CO₂ (all for zero rotational angular momenta). The results for SO₂ and H₂O are essentially equivalent in accuracy to results from previous semiclassical applications. H₃⁺ and CO₂, on the other hand, have not been studied previously by semiclassical methods, in part because of the 1:1 and 2:1 resonances respectively present in these molecules. The results of the present calculations are in reasonable agreement with quantum eigenvalues which have been calculated for H₃⁺ and CO₂, with errors which are consistent with those obtained for H₂O and SO₂.