Renner-Teller effect: Difference between revisions
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In [[molecular spectroscopy]], the '''Renner–Teller effect''' or '''Renner effect''' is an effect of molecular rotations and vibrations on the [[molecular electronic transition|electronic spectra]] of | In [[molecular spectroscopy]], the '''Renner–Teller effect''' or '''Renner effect''' is an effect of molecular rotations and vibrations on the [[molecular electronic transition|electronic spectra]] of linear molecules in degenerate electronic (Π, Δ, ..., etc.) states. | ||
In his original paper Renner (1934)<ref>R. Renner, ''Zur Theorie der Wechselwirkung zwischen Elektronen- und Kernbewegung bei dreiatomigen, stabförmigen Molekülen'', [On the theory of the interaction between electronic and nuclear motion of three-atomic bar-shaped molecules] Z. Phys. vol. '''92''', 172-193 (1934). English translation in H. Hettema, ''Quantum Chemistry, Classic Scientific Papers'', World Scientific, Singapore (2000).</ref> | In his original paper Renner (1934)<ref>R. Renner, ''Zur Theorie der Wechselwirkung zwischen Elektronen- und Kernbewegung bei dreiatomigen, stabförmigen Molekülen'', [On the theory of the interaction between electronic and nuclear motion of three-atomic bar-shaped molecules] Z. Phys. vol. '''92''', 172-193 (1934). English translation in H. Hettema, ''Quantum Chemistry, Classic Scientific Papers'', World Scientific, Singapore (2000).</ref> did not consider rotations, but only the coupling between [[electron]]s and [[molecular vibration|nuclear vibrations]] in triatomic linear molecules. This article was the first that considered dynamic effects that go beyond the [[Born-Oppenheimer approximation|Born-Oppenheimer (BO) approximation]] (which neglects altogether the effect of the nuclear motions on the electrons in a molecule). The BO approximation is good when the electronic energies are well separated. However, in linear molecules many of the electronic states are two-fold degenerate due to ''C<sub>∞v</sub>'' or ''D<sub>∞h</sub>'' [[point group symmetry]], and the BO approximation breaks down. Since the best-known linear triatomic molecule ([[Carbon dioxide|CO<sub>2</sub>]]) is electronically non-degenerate in its ground state, Renner chose the electronically excited two-fold degenerate Π-state of this molecule as a prototype model for his studies. The products of purely electronic and purely nuclear vibrational states serve as the zeroth-order (no coupling) wave functions in Renner's study. A simple model for vibronic coupling (coupling between vibrations and electrons) acts as a perturbation. | ||
Because Renner is the only author of the 1934 paper that first described the Renner-Teller effect, it was long called the ''Renner effect''. However, as [[Gerhard Herzberg|Herzberg's]] prestigious book<ref>G. Herzberg, ''Molecular Spectra and Molecular Structure'' Vol. III, Reprint Edition, Krieger, Malabar (1991)</ref> refers to it as the ''Renner–Teller'' effect (after [[Edward Teller]]), it is now more common to use the names of both physicists. | Because Renner is the only author of the 1934 paper that first described the Renner-Teller effect, it was long called the ''Renner effect''. However, as [[Gerhard Herzberg|Herzberg's]] prestigious book<ref>G. Herzberg, ''Molecular Spectra and Molecular Structure'' Vol. III, Reprint Edition, Krieger, Malabar (1991)</ref> refers to it as the ''Renner–Teller'' effect (after [[Edward Teller]]), it is now more common to use the names of both physicists. | ||
Revision as of 05:55, 11 May 2009
In molecular spectroscopy, the Renner–Teller effect or Renner effect is an effect of molecular rotations and vibrations on the electronic spectra of linear molecules in degenerate electronic (Π, Δ, ..., etc.) states.
In his original paper Renner (1934)[1] did not consider rotations, but only the coupling between electrons and nuclear vibrations in triatomic linear molecules. This article was the first that considered dynamic effects that go beyond the Born-Oppenheimer (BO) approximation (which neglects altogether the effect of the nuclear motions on the electrons in a molecule). The BO approximation is good 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 point group symmetry, and the BO 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 molecule as a prototype model for his studies. The products of purely electronic and purely nuclear vibrational states serve as the zeroth-order (no coupling) wave functions in Renner's study. A simple model for vibronic coupling (coupling between vibrations and electrons) acts as a perturbation.
Because Renner is the only author of the 1934 paper that first described the Renner-Teller effect, it was long called the Renner effect. However, as Herzberg's prestigious book[2] refers to it as the Renner–Teller effect (after Edward Teller), it is now more common to use the names of both physicists.
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. In 1959 Dressler and Ramsay[3] 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.
Much has been published about the Renner–Teller effect after its first experimental observation in 1959. At present, authors referring to it[4] have usually broader physical phenomena and molecules larger than three-atoms in mind. Usually one considers now effects not only due to the coupling of electrons with vibrations, but also electronic couplings with rotations (rovibronic coupling).
References
- ↑ R. Renner, Zur Theorie der Wechselwirkung zwischen Elektronen- und Kernbewegung bei dreiatomigen, stabförmigen Molekülen, [On the theory of the interaction between electronic and nuclear motion of three-atomic bar-shaped molecules] Z. Phys. vol. 92, 172-193 (1934). English translation in H. Hettema, Quantum Chemistry, Classic Scientific Papers, World Scientific, Singapore (2000).
- ↑ G. Herzberg, Molecular Spectra and Molecular Structure Vol. III, Reprint Edition, Krieger, Malabar (1991)
- ↑ K. Dressler and D. A. Ramsay, Phil. Trans. Roy. Soc. London, vol. 251A, 553 (1959)
- ↑ P. R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, NRC Research Press, Ottawa (1998).
See also
External links
- [1] English translation of Renner's paper (1934).