A variational method for the calculation of ro-vibronic levels of any orbitally degenerate (Renner-Teller) triatomic molecule

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Abstract
The variational method for the determination of ro-vibrational energy levels has been extended to the ro-vibronic energy levels of Renner-Teller triatomic molecules. A previously derived hamiltonian ℋ(R 1, R 2, θ, [bcirc]n) has been used, with [bcirc]n z replaced by [bcirc]n z +Ḽ z . Expansion functions having the correct symmetry in D ∞h (Σ g +, Σ g -, Σ u +, Σ u -) or C ∞v (Σ+, Σ-) are selected, for any J value, from a recipe which is general for any type of Renner-Teller system. The method is demonstrated for the lowest A' and A" surfaces of CH2 +, whose analytic representation has been obtained from ab initio data. The barrier to linearity is 931 cm-1 for the A' state. Ro-vibronic levels for J⩽2, up to 9000 cm-1 above the A' minimum (αe=137°) are determined. The bending levels show the same Renner-Teller characteristic interaction determined by other workers who have included the effect of the stretches in a less rigorous way. Fermi-resonance between specific energy levels does not appear to be important for the reported levels of CH2 +, although it is shown that there are marked differences in the calculated spectra when the stretching modes are omitted.