Renner–Teller effect

The Renner–Teller effect is observed in the spectra of molecules having electronic states that allow vibration through a linear configuration. For such molecules electronic states that are doubly degenerate at linearity (Π, Δ, ..., etc.) will split into two close-lying nondegenerate states for non-linear configurations. As part of the Renner-Teller effect, the rovibronic levels of such a pair of states will be strongly Coriolis coupled by the rotational kinetic energy operator causing a breakdown of the Born-Oppenheimer approximation. This is to be contrasted with the Jahn-Teller effect which occurs for polyatomic molecules in electronic states that allow vibration through a symmetric nonlinear configuration, where the electronic state is degenerate, and which further involves a breakdown of the Born-Oppenheimer approximation but here caused by the vibrational kinetic energy operator.

In its original formulation, the Renner–Teller effect was discussed for a triatomic molecule in a degenerate electronic state that has a linear equilibrium configuration. The 1934 article by Rudolf Renner[1] was one of 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 significantly. 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 rovibrational states served as the zeroth-order (no rovibronic coupling) wave functions in Renner's study. The rovibronic coupling acts as a perturbation.

Because Renner is the only author of the 1934 paper that first described the effect, it can be called simply the Renner effect. Renner did this work as a PhD student under the supervision of Teller and presumably Teller was perfectly happy not to be a coauthor. 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.

While Renner's theoretical study concerned carbon dioxide, a linear triatomic molecule, the first actual observation of the Renner–Teller effect was in an electronic excited state of the NH₂ molecule which is bent at equilibrium.[4]

Much has been published about the Renner–Teller effect since its first experimental observation in 1959; see the bibliography on pages 412-413 of the textbook by Bunker and Jensen.[5] Section 13.4 of this textbook discusses both the Renner-Teller effect (called the Renner effect) and the Jahn-Teller effect.