Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

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Abstract
The effects of vibrational anharmonic terms and of the gK -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x 1, x 2, … depend on the anharmonic force constants. The functions Fi can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the Fi s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v 2+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v 2 including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v 2=1 is now found to be 4gK . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.