Renner–Teller effect

The Renner–Teller effect or Renner effect is an effect due to rovibronic coupling on the electronic spectra of three- (or more) atomic linear molecules in degenerate electronic (Π, Δ, ..., etc.) states.

In its original formulation, the Renner–Teller effect was a vibronic coupling between the motions of the electrons and the nuclear vibrations in triatomic linear molecules. The article by Rudolf Renner (1934)[1] was the first that considered dynamic effects that go beyond the Born–Oppenheimer approximation, in which the nuclear and electronic motions in a molecule are uncoupled. This is a good approximation when the electronic energies are well separated. However, in linear molecules many of the electronic states are two-fold degenerate due to C_∞v or D_∞h symmetry, and the Born–Oppenheimer approximation breaks down. Since the best-known linear triatomic molecule (CO₂) is electronically non-degenerate in its ground state, Renner chose the electronically excited two-fold degenerate Π-state of this well-known molecule as a model for his studies. The products of purely electronic and purely nuclear vibrational states served as the zeroth-order (no vibronic coupling) wave functions in Renner's study. The vibronic coupling acts as a perturbation.

Because Renner is the only author of the 1934 paper that first described the effect, it was long called the Renner effect. However, in 1933 Gerhard Herzberg and Edward Teller had recognized that the potential of a triatomic linear molecule in a degenerate electronic state splits into two when the molecule is bent.[2] A year later this effect was worked out in detail by Renner.[1] Herzberg refers to this as the “Renner-Teller” effect in one of his influential books,[3] and this name is most commonly used, although it might be more appropriate to speak of the “Renner-Herzberg” or “Renner-Herzberg-Teller” effect as Herzberg was the first author on the 1933 paper.

While Renner's theoretical study concerned the linear triatomic molecule CO₂, the first actual observation of the Renner–Teller effect was in the electronic absorption spectrum of NH₂ and its isotopologue ND₂.[4] In 1959 Dressler and Ramsay found that the first electronically excited states of these triatomic molecules have a linear geometry and they observed in these excited states an unusual type of vibronic structure: the Renner–Teller effect.

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