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

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 (α_e=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.