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The Jahn-Teller effect is a geometric distortion of a non-linear molecular system that reduces its symmetry and energy. This distortion is typically observed among octahedral complexes where the two axial bonds can be shorter or longer than those of the equatorial bonds. This effect can also be observed in tetrahedral compounds. This effect is dependent on the electronic state of the system.
In 1937, Hermann Jahn and Edward Teller postulated a theorem stating that "stability and degeneracy are not possible simultaneously unless the molecule is a linear one," in regards to its electronic state. This leads to a break in degeneracy which stabilizes the molecule and by consequance, reduces its symmerty. Since 1937, the theorem has been revised which Housecroft and Sharpe have eloquently phrased as "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." This is most commonly observed with transition metal octahedral complexes, however, it can be observed in tetrahedral compounds as well.
For a given octahedral complex, the five d atomic orbitals are split into two degenerate sets when constructing a molecular orbital diagram. These are represented by the sets' symmetry labels: t2g (dxz, dyz, dxy) and eg (dz2 and dx2−y2). When a molecule possesses a degenerate electronic ground state, it will distort (Jahn-Teller effect) to remove the degeneracy and form a lower energy (and by consequence, lower symmetry) system. The octahedral complex will either elongate or compress the z ligand bonds as shown in Figure 1 below:
Fig. 1. Jahn-Teller distortions for an octahedral complex.
When an octahedral complex exhibits elongation, the axial bonds are longer than the equatorial bonds. For a compression, it is the reverse; the equatorial bonds are longer than the axial bonds. Elongation and compression effects are dictated by the amount of overlap between the metal and ligand orbitals. Thus, this distortion varies greatly depending on the type of metal and ligands. In general, the stronger the metal-ligand orbital interactions are, the greater the chance for a Jahn-Teller effect to be observed.
Elongation Jahn-Teller distortions occur when the degeneracy is broken by the stabilization (lowering in energy) of the d orbitals with a z component, while the orbitals without a z component are destabilized (higher in energy) as shown in Figure 2 below:
Fig. 2. Illustration of tetragonal distortion (elongation) for an octahedral complex.
This is due to the dxy and dx2−y2 orbitals having greater overlap with the ligand orbitals, resulting in the orbitals being higher in energy. Since the dx2−y2 orbital is antibonding, it is expected to increase in energy due to elongation. The dxy orbital is still nonbonding, but is destabilized due to the interactions.
Jahn-Teller elongations are well-documented for copper(II) octahedral compounds. A classic example is that of copper(II) fluoride as shown in Figure 3 below:
Fig. 3. Structure of octahedral copper(II) fluoride.
Notice that the two axial bonds are both elongated and the four shorter equatorial bonds are the same length as each other. According the theorem, the orbital degeneracy is eliminated by distortion, making the molecule more stable based on the model presented in Figure 2.
Compression Jahn-Teller distortions occur when the degeneracy is broken by the stabilization (lowering in energy) of the d orbitals without a z component, while the orbitals with a z component are destabilized (higher in energy) as shown in Figure 4 below:
Fig. 4. Illustration of tetragonal distortion (compression) for an octahedral complex.
This is due to the z-component d orbitals having greater overlap with the ligand orbitals, resulting in the orbitals being higher in energy. Since the dz2 orbital is antibonding, it is expected to increase in energy due to compression. The dxz and dyz orbitals are still nonbonding, but are destabilized due to the interactions.
For Jahn-Teller effects to occur in transition metals there must be degeneracy in either the t2g or eg orbitals. The electronic states of octahedral complexes are classified as either low spin or high spin. The spin of the system is dictated by the chemical environment. This includes the characteristics of the metal center and the types of ligands.
Figure 5 (below) shows the various electronic configurations for low spin octahedral complexes:
Fig. 5. Low spin octahedral coordination diagram (red indicates no degeneracies possible, thus no Jahn-Teller effects).
The figure illustrates that low spin complexes with d3, d5, d8, and d10 electrons cannot have Jahn-Teller distortions. These electronic configurations correspond to a variety of transition metals. Many common examples include Cr3+, Co3+, Ni2+, and Cu2+.
Figure 6 (below) shows the various electronic configurations for high spin octahedral complexes:
Fig. 6. High spin octahedral coordination diagram (red indicates no degeneracies possible, thus no Jahn-Teller effects).
The figure illustrates that low spin complexes with d3, d5, d8, and d10 electrons cannot have Jahn-Teller distortions. In general, degenerate electronic states occupying the eg orbital set tend to show stronger Jahn-Teller effects. This is primarily caused by the occupation of these high energy orbitals. Since the system is more stable with a lower energy configuration, the degeneracy of the eg set is broken, the symmetry is reduced, and occupations at lower energy orbitals occur.
Jahn-Teller distortions can be observed using a variety of spectroscopic techniques. In UV-VIS absorption spectroscopy, distortion causes splitting of bands in the spectrum due to a reduction in symmetry (Oh to D4h). Consider a hypothetical molecule with octahedral symmetry showing a single absorption band. If the molecule were to undergo Jahn-Teller distortion, the number of bands would increase as shown in Figure 7 below:
Fig. 7. Hypothetical absorption spectra of an octahedral molecule (left) and the same molecule with Jahn-Teller elongation (right). The red arrows indicate electronic transitions.
A similar phenomenon can be seen with IR and Raman vibrational spectroscopy. The number of vibrational modes for a molecule can be calculated using the 3n - 6 rule (or 3n - 5 for linear geometry) rule. If a molecule exhibits an Oh symmetry point group, it will have fewer bands than that of a Jahn-Teller distorted molecule with D4h symmetry. Thus, one could observe Jahn-Teller effects through either IR or Raman techniques. This effect can also be observed in EPR experiments as long as there is at least one unpaired electron.
|CuBr 2||4 Br at 240pm 2 Br at 318pm|
|CuCl 2||4 Cl at 230pm 2 Cl at 295pm|
|CuCl 2.2H 2O||2 O at 193pm 2 Cl at 228pm 2 Cl at 295pm|
|CsCuCl 3||4 Cl at 230pm 2 Cl at 265pm|
|CuF 2||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|
|KCuAlF 6||2 F at 188pm 4 F at 220pm|
|CrF 2||4 F at 200pm 2 F at 243pm|
|KCrF 3||4 F at 214pm 2 F at 200pm|
|MnF 3||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 t2g level, however distortions in bond lengths are much more distinctive when the degenerate electrons are in the e glevel.
This material is based upon work supported by the National Science Foundation under Grant Number 1246120