Jahn-Teller effect
Overview
 
The Jahn–Teller effect, sometimes also known as Jahn–Teller distortion, or the Jahn–Teller theorem, describes the geometrical distortion of non-linear molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s under certain situations. This electronic effect
Electronic effect
An electronic effect influences the structure, reactivity, or properties of molecule but is neither a traditional bond nor a steric effect. In organic chemistry, the term stereoelectronic effect is also used to emphasize the relation between the electronic structure and the geometry of a...

 is named after Hermann Arthur Jahn and 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...

, who proved, using group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...

, that orbital non-linear spatially degenerate molecules cannot be stable.
Discussions
Encyclopedia
The Jahn–Teller effect, sometimes also known as Jahn–Teller distortion, or the Jahn–Teller theorem, describes the geometrical distortion of non-linear molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s under certain situations. This electronic effect
Electronic effect
An electronic effect influences the structure, reactivity, or properties of molecule but is neither a traditional bond nor a steric effect. In organic chemistry, the term stereoelectronic effect is also used to emphasize the relation between the electronic structure and the geometry of a...

 is named after Hermann Arthur Jahn and 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...

, who proved, using group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...

, that orbital non-linear spatially degenerate molecules cannot be stable. The theorem essentially states that any non-linear molecule with a spatially degenerate
Degenerate energy level
In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, and in Quantum Mechanics it is represented mathematically by the Hamiltonian for the system having more...

 electronic ground state will undergo a geometrical distortion that removes that degeneracy, because the distortion lowers the overall energy of the complex.

Transition metal chemistry

The Jahn–Teller effect is most often encountered in octahedral complexes of the transition metals, and is very common in six-coordinate copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

(II) complexes. The d9 electronic configuration of this ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

 gives three electrons in the two degenerate eg
Crystal field theory
Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes,...

 orbitals, leading to a doubly degenerate electronic ground state. Such complexes distort along one of the molecular fourfold axes (always labelled the z axis), which has the effect of removing the orbital and electronic degeneracies and lowering the overall energy. The distortion normally takes the form of elongating the bonds to the ligands lying along the z axis, but occasionally occurs as a shortening of these bonds instead (the Jahn–Teller theorem does not predict the direction of the distortion, only the presence of an unstable geometry). When such an elongation occurs, the effect is to lower the electrostatic repulsion between the electron-pair on the Lewis basic ligand and any electrons in orbitals with a z component, thus lowering the energy of the complex. If the undistorted complex would be expected to have an inversion centre, this is preserved after the distortion.

In octahedral complexes, the Jahn–Teller effect is most pronounced when an odd number of electrons occupy the eg orbitals; i.e., in d9, low-spin
Crystal field theory
Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes,...

 d7 or high-spin
Crystal field theory
Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes,...

 d4 complexes, all of which have doubly degenerate ground states. This is because the eg orbitals involved in the degeneracy point directly at the ligands, so distortion can result in a large energetic stabilisation. Strictly speaking, the effect should also occur when there is a degeneracy due to the electrons in the t2g orbitals (i.e. configurations such as d1 or d2, both of which are triply degenerate). However, the effect is much less noticeable, because there is a much smaller lowering of repulsion on taking ligands further away from the t2g orbitals, which don't point directly at the ligands involved (see the table below). The same is true in tetrahedral complexes; distortion is less because there is less stabilisation to be gained because the ligands are not pointing directly at the orbitals.

The expected effects for octahedral coordination are given in the following table:
w: weak Jahn–Teller effect (t2g orbitals unevenly occupied), s: strong Jahn–Teller effect expected (eg orbitals unevenly occupied), blank: no Jahn–Teller effect expected.

The Jahn–Teller effect can be demonstrated experimentally by investigation of the UV-VIS absorbance spectra of inorganic compounds, where it often causes splitting of bands. It is also readily apparent in the crystal structures of many copper(II) complexes. Additional, detailed information
about the anisotropy of such complexes and the nature of the ligand binding can be however obtained from the fine structure of their unpaired electron spins in the low-temperature Electron spin resonance spectra.

Organic chemistry

The Jahn–Teller effect is also sometimes encountered in organic chemistry, as in the case of cyclooctatetraene
Cyclooctatetraene
1,3,5,7-Cyclooctatetraene is an unsaturated derivative of cyclooctane, with the formula C8H8. It is also known as [8]annulene. This polyunsaturated hydrocarbon is a colorless to light yellow flammable liquid at room temperature...

. The cited reference however is in disagreement with another paper in which the pseudo Jahn–Teller effect (also sometimes called the "second order Jahn–Teller effect") is apparently not present in the D4h transition structure. A clear case however is the case of the COT radical anion, wherein the traditional frost circle π MO diagram (image at right) shows clearly a non-equally filled set of degenerate orbitals. This configuration therefore distorts according to the Jahn–Teller effect (see reference for computational detail of distortion specifics).

See also

  • Crystal field theory
    Crystal field theory
    Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes,...

  • Potential energy surface
    Potential energy surface
    A potential energy surface is generally used within the adiabatic or Born–Oppenheimer approximation in quantum mechanics and statistical mechanics to model chemical reactions and interactions in simple chemical and physical systems...

  • Diabatic
    Diabatic
    A diabatic process is one in which heat transfer takes place, which is the opposite of an adiabatic process. In quantum chemistry, the potential energy surfaces are obtained within the adiabatic or Born-Oppenheimer approximation...

  • Conical intersection
    Conical intersection
    In quantum chemistry, a conical intersection of two potential energy surfaces of the same spatial and spin symmetries is the set of molecular geometry points where the two potential energy surfaces are degenerate . Conical intersections are ubiquitous in both trivial and non-trivial chemical...

  • Avoided crossing
    Avoided crossing
    [Image:Avoided_crossing.png|thumb|right|300px|An avoided energy level crossing in a two level system subjected to an external magnetic field. Note the energies of the diabatic states, \scriptstyle...

  • 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"...

  • Renner-Teller effect
    Renner-Teller effect
    The Renner–Teller effect or Renner effect is an effect due to rovibronic coupling on the electronic spectra of three- atomic linear molecules in degenerate electronic states....

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