Renner-Teller effect
Encyclopedia
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 electron
s and the nuclear vibrations
in triatomic linear molecules
. The article by Renner (1934) 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, as Herzberg's
prestigious books refer to it as the Renner–Teller effect (after Edward Teller
), it is now more common to use both names.
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 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 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).
Rovibronic coupling
Rovibronic coupling denotes the simultaneous interactions between rotational, vibrational, and electronic degrees of freedom in a molecule. When a rovibronic transition occurs, the rotational, vibrational, and electronic states change simultaneously, unlike in rovibrational coupling...
on the electronic spectra
Molecular electronic transition
Molecular electronic transitions take place when electrons in a molecule are excited from one energy level to a higher energy level. The energy change associated with this transition provides information on the structure of a molecule and determines many molecular properties such as color...
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
Vibronic coupling
In theoretical chemistry, the vibronic coupling terms, , are proportional to the interaction between electronic and nuclear motions of molecules. The term "vibronic" originates from the concatenation of the terms "vibrational" and "electronic"...
between the motions of the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s and the nuclear vibrations
Molecular vibration
A molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion...
in triatomic linear molecules
Molecular geometry
Molecular geometry or molecular structure is the three-dimensional arrangement of the atoms that constitute a molecule. It determines several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism, and biological activity.- Molecular geometry determination...
. The article by Renner (1934) 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
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...
) 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, as Herzberg's
Gerhard Herzberg
Gerhard Heinrich Friedrich Otto Julius Herzberg, was a pioneering physicist and physical chemist, who won the Nobel Prize for Chemistry in 1971, "for his contributions to the knowledge of electronic structure and geometry of molecules, particularly free radicals". Herzberg's main work concerned...
prestigious books refer to it as the Renner–Teller effect (after Edward Teller
Edward Teller
Edward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he did not care for the title. Teller made numerous contributions to nuclear and molecular physics, spectroscopy , and surface physics...
), it is now more common to use both names.
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
Isotopologue
Isotopologues are molecules that differ only in their isotopic composition. Simply, the isotopologue of a chemical species has at least one atom with a different number of neutrons than the parent....
ND2. 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.
Much has been published about the Renner–Teller effect after its first experimental observation in 1959. At present, authors referring to it 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).
External links
- http://www.worldscibooks.com/chemistry/3201.html English translation of Renner's paper (1934).
- H. Hettema's English translation of Renner's paper (1934) in Google books