Jahn-Teller effect

The Jahn-Teller effect, sometimes also known as Jahn-Teller distortion, describes the geometrical distortion of non-linear molecules under certain situations. The effect is named after Hermann Arthur Jahn and Edward Teller, who first proposed it in a theorem in 1937.[1] The theorem essentially states that any non-linear molecule with a degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy. This also has the effect of lowering the overall energy of the complex.

In transition metal chemistry

Enlarge picture
The Jahn-Teller effect is responsible for the tetragonal distortion of the hexaaquacopper(II) complex ion, [Cu(OH2)6]2+, which might otherwise possess octahedral geometry. The two axial Cu−O distances are 238 pm, whereas the four equatorial Cu−O distances are ~195 pm.
The Jahn-Teller effect is most often encountered in octahedral complexes of the transition metals, and is very common in six-coordinate copper(II) complexes. The d9 electronic configuration of this ion gives three electrons in the two degenerate eg 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 d7 or high-spin 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:
Jahn-Teller effect
Number of d electrons 1 2 3 4 5 6 7 8 9 10
High spinwwswws ! Low spin | w || w || || w || w || || s || || s ||


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.

In organic chemistry

The Jahn-Teller effect is also sometimes encountered in organic chemistry, as in the case of cyclooctatetraene [2]. 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 transistion structure [3]. 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) [4].

See also

References

1. ^ H. Jahn and E. Teller (1937). "Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934-1990) 161 (905): 220-235. DOI:10.1098/rspa.1937.0142. 
2. ^ Frank-Gerrit Klärner (2001). "About the Antiaromaticity of Planar Cyclooctatetraene". Angewandte Chemie, Int. Ed. Eng. 40 (21): 3977-3981. DOI:10.1002/1521-3773(20011105)40:21%3C3977::AID-ANIE3977%3E3.0.CO;2-N. 
3. ^ Michael J. Bearpark (2002). "The pseudo-Jahn-Teller effect: a CASSCF diagnostic". Molecular Physics 100 (11): 1735-1739. DOI:10.1080/00268970110105442. 
4. ^ Michael J. Bearpark (2000). "Observation of Both Jahn-Teller Distorted Forms (b1g and b2g) of the Cyclooctatetraene Anion Radical in a 1,2-Disubstituted System". J. Am. Chem. Soc. 122 (13): 3211-3215. DOI:10.1021/ja9943501. 
  • Miessler, G. L. & Tarr, D. A., Inorganic Chemistry (3rd ed), 2004, pp 370-373, Pearson Prentice Hall.
  • Shriver, D. F. & Atkins, P. W. (1999). Inorganic Chemistry (3rd ed) pp 235-236. Oxford University Press ISBN 0-19-850330-X.
nonlinear system is a system which is not linear i.e. a system which does not satisfy the superposition principle. Less technically, a nonlinear system is any problem where the variable(s) to be solved for cannot be written as a linear sum of independent components.
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molecule is defined as a sufficiently stable electrically neutral group of at least two atoms in a definite arrangement held together by strong chemical bonds.[1][2] In organic chemistry and biochemistry, the term molecule
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Hermann Arthur Jahn (b. 31 May 1907, Colchester, England; d. 24 October 1979 Southampton) was an English scientist of German extraction.[1] With Edward Teller, he was responsible for identifying the Jahn-Teller effect.[2]

Jahn received a B.Sc.
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Edward Teller

Edward Teller in 1958 as Director of the Lawrence Livermore National Laboratory.
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degenerate if they are all at the same energy level. Physical states differ if and only if they are linearly independent. An energy level is said to be degenerate if it contains two or more different states.
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octahedral molecular geometry describes a molecular geometry in which 6 ligands are symmetrically arranged around a central atom in an octahedral geometry. All six ligands are chemically equivalent. The central atom is often a transition metal.
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2, 1
(mildly basic oxide)
Electronegativity 1.90 (Pauling scale)
Ionization energies
(more) 1st: 745.5 kJmol−1
2nd: 1957.9 kJmol−1
3rd: 3666 kJmol−1

Atomic radius 135 pm
Atomic radius (calc.
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ion is an atom or molecule which has lost or gained one or more electrons, making it positively or negatively charged. A negatively charged ion, which has more electrons in its electron shells than it has protons in its nuclei, is known as an anion
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Crystal field theory (CFT) 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
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    A Lewis base is any molecule or ion that can form a new coordinate covalent bond, by donating a pair of electrons, named after the American chemist Gilbert Lewis. The term base is ambiguous. This is one interpretation.
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    Crystal field theory (CFT) 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
    ..... Click the link for more information.
    Crystal field theory (CFT) 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
    ..... Click the link for more information.
    Ultraviolet-visible spectroscopy or ultraviolet-visible spectrophotometry (UV/ VIS) involves the spectroscopy of photons and spectrophotometry. It uses light in the visible and adjacent near ultraviolet (UV) and near infrared (NIR) ranges.
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    1,3,5,7-Cyclooctatetrene (COT) 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.
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    Crystal field theory (CFT) 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
    ..... Click the link for more information.
    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.
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    diabatic representation in which the nuclear kinetic energy operator is diagonal. In this representation, the coupling is due to the electronic energy and is a scalar quantity which is much more easy to estimate numerically.
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    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 (intersect).
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    The eigenvalues of a Hermitian matrix depending on N continuous real parameters cannot cross except at a manifold of N-2 dimensions. In the case of a diatomic molecule (one parameter, which describes the bond length), this means that the eigenvalues do not cross.
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    In theoretical chemistry, the vibronic coupling terms (which are neglected within the Born-Oppenheimer approximation) are proportional to the interaction between electronic and nuclear motions of molecules.
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    In its original formulation the Renner-Teller effect is a (so-called vibronic) coupling in triatomic linear molecules between the motions of the electrons and the nuclear vibrations.
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    Edward Teller

    Edward Teller in 1958 as Director of the Lawrence Livermore National Laboratory.
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    Hermann Arthur Jahn (b. 31 May 1907, Colchester, England; d. 24 October 1979 Southampton) was an English scientist of German extraction.[1] With Edward Teller, he was responsible for identifying the Jahn-Teller effect.[2]

    Jahn received a B.Sc.
    ..... Click the link for more information.
    Edward Teller

    Edward Teller in 1958 as Director of the Lawrence Livermore National Laboratory.
    ..... Click the link for more information.
    digital object identifier (or DOI) is a permanent identifier given to a document, which is not related to its current location. A typical use of a DOI is to give a scientific paper or article a unique identifying number that can be used by anyone to locate details of the paper, and
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    Angewandte Chemie is a weekly peer-reviewed chemistry journal with broad scope. Its impact factor is 10.232 (in 2006), which is the highest value for a chemistry-specific journal that publishes original research.
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    digital object identifier (or DOI) is a permanent identifier given to a document, which is not related to its current location. A typical use of a DOI is to give a scientific paper or article a unique identifying number that can be used by anyone to locate details of the paper, and
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    Molecular physics is the study of the physical properties of molecules and of the chemical bonds between atoms that bind them. Its most important experimental techniques are the various types of spectroscopy.
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    digital object identifier (or DOI) is a permanent identifier given to a document, which is not related to its current location. A typical use of a DOI is to give a scientific paper or article a unique identifying number that can be used by anyone to locate details of the paper, and
    ..... Click the link for more information.
    digital object identifier (or DOI) is a permanent identifier given to a document, which is not related to its current location. A typical use of a DOI is to give a scientific paper or article a unique identifying number that can be used by anyone to locate details of the paper, and
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