The Jahn-Teller Theorem
The Jahn-Teller Theorem (named after Hermann Arthur Jahn and Edward Teller),
was published in 1937 and essentially means that:
"any non-linear molecular system in
a degenerate electronic state will be unstable and will undergo
distortion to form a system of lower symmetry and lower energy
thereby removing the degeneracy"
In an octahedral crystal field, the t2g orbitals occur
at lower energy than the eg orbitals. This is a
reflection of the orientation of the orbitals since the t2g
are directed between bond axes while the eg point along bond axes.
The shielding effect this has on the electrons is used to explain why the
Jahn-Teller effect is generally only important for odd number occupancy
of the eg level.
The effect of Jahn-Teller distortions is best documented for
Cu(II) complexes (with 3 electrons in the eg level)
where the result is that most complexes are found to have
elongation along the z-axis.
The Jahn-Teller Theorem does NOT say how large a
distortion should occur.
Take for example, the 3 copper complexes shown below:
hexakis(pyridine N-oxide)copper(II) dinitrate dihydrate (cupyno6)
tris(octamethylpyrophosphoramide)copper(II) perchlorate (cuompp)
The distance between atoms is
displayed in response to mouse clicks, click on the Cu(II) then drag to
a coordinating atom to see the distance.
Determine the 6 bond lengths around each Cu(II) ion, I've started
you off by showing 1 bond length for each. Having found the
others, determine whether the molecules correspond to elongation
or contraction of 2 bonds (the z-direction).
Apparent exceptions to the theorem are probably examples of what
has been called the "dynamic Jahn-Teller effect". In
these cases either the time frame of the measurement does not
allow the distortion to be seen because of the molecule randomly
undergoing movement or else the distortion is so small as to be
For one of the copper complexes above, the bond lengths are
apparently identical. If the X-ray structure of the sample is
redone at varying temperatures it is sometimes possible to
"freeze" a molecule into a static position showing the
A well documented example includes complexes of the type M
2PbCu(NO 2) 6.
For M=Cs, below 285K the molecule shows tetragonal symmetry, for
M=K this occurs at below 273K, for M=Rb at less than 276K and for
M=Tl at temperatures less than 245K.
Above these temperatures the molecules appear octahedral due to
the dynamic Jahn-Teller effect.
Some examples of Jahn-Teller distorted
||4 Br at 240pm 2 Br at 318pm
||4 Cl at 230pm 2 Cl at 295pm
|CuCl 2.2H 2O
||2 O at 193pm 2 Cl at 228pm 2 Cl at 295pm
||4 Cl at 230pm 2 Cl at 265pm
||4 F at 193pm 2 F at 227pm
|CuSO 4.4NH 3.H 2O
||4 N at 205pm 1 O at 259pm 1 O at 337pm
|K 2CuF 4
||4 F at 191pm 2 F at 237pm
||2 F at 188pm 4 F at 220pm
||4 F at 200pm 2 F at 243pm
||4 F at 214pm 2 F at 200pm
||2 F at 209pm 2 F at 191pm 2 F at 179pm
The Jahn-Teller Theorem predicts that distortions should occur
for any degenerate state, including degeneracy of the t
2g level, however distortions in bond lengths are much
more distinctive when the degenerate electrons are in the e
In the electronic spectrum of an aqueous solution of Ti(III), a d
1octahedral system, the absorption band is not
symmetric but rather shows a distinct broad shoulder. This has
been interpreted in terms of a lowering of the degeneracy of the
t 2g level and promotion to the excited state occurring
to either of the two orbitals, the d z2 and d
x2-y2, which will no longer be degenerate. Thus, two
transitions are possible but because the energy difference is
small, a shoulder appears rather than 2 distinct peaks.
H.A. Jahn and E. Teller, Proc. R. Soc. London A, 161, 220-235, 1937.
H.A. Jahn, Proc. R. Soc. Lond. A 164, 117-131, 1938.
Jahn Teller on Wikipedia
P.T.Miller, P.G.Lenhert and M.D.Joesten, Inorg. Chem.,
11, 2221, 1972.
J.S.Wood, C.P.Keijzers and R.O.Day, Acta Crystallogr., Sect.C
(Cr. Str. Comm.), 40, 404, 1984.
M.D.Joesten, M.S.Hussain and P.G.Lenhert, Inorg. Chem.,
9, 151, 1970.
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Lancashire, all rights reserved.
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The Department of Chemistry, University of the West Indies,
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Created November 2000. Links checked and/or last
modified 26th November 2013.