Jahn-Teller Distortion: The Stability Phenomenon

Hermann Jahn and Edward Teller in 1937 offered a theorem that stated;

“A non-linear molecular system in an electronic degenerate state will undergo distortion that will remove the degeneracy, lower the symmetry and hence lower the overall energy”.

This distortion is known as Jahn-Teller distortion (JTD) and the effect is called the Jahn-Teller effect (JTE).

The Jahn-Teller effect is one that lowers the symmetry in certain geometries, in order to bring the molecules into a more stable, lower energy state. This effect is associated with certain types of (d-orbital containing) electronic configurations only. The affected geometries include tetrahedral and most commonly, octahedral.

In octahedral geometry, the types of distortions that occur are tetragonal elongation and compression which involve the movement of ligands on the z-axis. However, the inversion center is still preserved after the distortion (both the ligands on the z-axis are still equidistant from the center).

t_2g orbitals = d_xy, d_yz, d_xz

e_g orbitals = d_x²-y², d_z²

A non-linear molecular system in an electronic degenerate state refers to the uneven distribution of electrons in the d orbitals, especially the e_g set of orbitals (d_x²-y² and d_z²). This is because the e_g set of orbitals is more affected (force of repulsion) by the ligands in the octahedral geometry, as the ligands approach the central metal atom on its axes (and not in between the axes, as in the t_2g set of orbitals).

The Jahn-Teller effect is most obvious in octahedrally coordinated metal ions with (high-spin) d⁴, (low-spin) d⁷, and d⁹ electronic configurations, all of which leave an unpaired electron in either of the e_g orbitals. The Jahn-Teller theorem, however, does not explain the direction of distortion (tetragonal compression or elongation); it only signifies that distortion will occur, to lift the degeneracy and lower the energy.

When tetragonal compression or elongation takes place in an octahedral geometry, usually one of the orbitals in the e_g set (d_x²-y² or d_z²) is half-filled. However, it is the tetragonal elongation that is the more common distortion of octahedral geometry.

Octahedral Complexes: Compression and Elongation

Among octahedral complexes, compression and elongation occur to get stability.

In tetragonal compression, the d_x²-y² orbital is lowered in energy whereas the d_z² orbital is increased in energy. As the ligands on the z-axis move towards the central atom/ion, repulsion is increasingly caused between the ligand electrons and those in the orbital lying on the z-axis (d_z² orbital). Hence the energy of the d_z² orbital is increased, with a corresponding decrease in energy of the d_x²-y² orbital. However, the net energy of the two orbitals is decreased by stabilization due to the overall distortion.

Alternatively in the tetragonal elongation, the d_x²-y² orbital is raised in energy, and the d_z² orbital is lowered in energy, as the ligands on the z-axis move away from the central atom/ion. Despite this change in energy of the orbitals individually, once again the net energy of the two orbitals is decreased because of the distortion. 

Examples of Jahn-Teller Distortion

Examples of such distortions include complexes of Mn³⁺, Cr²⁺ in high-spin configurations and Ni³⁺, Co²⁺ in low-spin configurations as well as Cu²⁺ and Ag⁺ ions. The most well-known and observed are those of the copper ion in the (+2) oxidation state.

The Jahn-Teller effect is also there for electrons in the t_2g set of orbitals (in between the axes) but since these orbitals do not coincide with the approach of ligands, the effect is much less pronounced (Weak J-T distortions). Hence, there will be weaker distortions for systems with d¹, d², low-spin d⁴ and d⁵, and high-spin d⁶ and d⁷ electronic configurations.

Other than coordination chemistry, the Jahn-Teller effect can also be noticed in antiaromatic organic compounds such as the cyclobutadiene and cyclooctatetraene (-1) anion, where the geometry of the molecule is distorted due to unequal distribution of electrons in one degenerate set of orbitals.

Related topics

• Difference between singlet and triplet state
• What does principal quantum number determine?
• Torsional strain

Applications of Jahn-Teller Distortion Effect

The Jahn-Teller effect is responsible for a number of phenomena in various fields such as stereochemistry, spectroscopy, crystal chemistry, molecular and solid-state physics, materials sciences, etc. 

Concepts Berg

Why is it that with the Jahn-Teller effect, complexes with d³ d⁶ d⁸ d¹⁰ cannot have distortions?

For distortions in the octahedral geometry, there needs to be an uneven distribution of electrons in the e_g or t_2g set of orbitals. However, distortions of the t_2g set are less noticeable since the ligands approach on the axes (e_g set of orbitals) in the octahedral symmetry and not in between the axes (t_2g set of orbitals). So, a lesser repulsion from the ligands and eventually, less distortion. 

In octahedral low spin d⁶, d³, d⁸, and d¹⁰ complexes, electrons are all evenly distributed in their respective set of orbitals. Hence, there are no distortions. In case of high spin d⁶ complexes, there is an uneven distribution of electrons in the t_2g set of orbitals but since the ligands do not approach the t_2g set of orbitals directly, the distortion is less pronounced. 

What is Jahn-Teller distortion? Explain Jahn-Teller distortion in Cu(H₂O)₆ ²⁺?

Jahn-Teller distortion is the lowering of symmetry by distorting the octahedral or the tetrahedral geometry in order to bring a complex into a more stable, lower energy state. 

Since there are six H₂O ligands, the complex has an octahedral geometry. The Cu²⁺ ion is a d⁹ system. There is an unequal distribution of electrons in the e_g set of orbitals. To stabilize this complex, Jahn-Teller distortion will take place. 

However, the Jahn-Teller theorem does not predict the direction of distortion, only that it will take place. So the distortion could be tetragonal elongation or compression, where the d-orbitals with a z-axis component will be lowered in energy in the former case whereas, the orbitals with a z-axis component will be raised in energy along with a corresponding decrease in energy of the other orbitals in case of the latter.

What is the direct cause of the Jahn-Teller effect?

The direct cause of the Jahn-Teller effect is the uneven distribution of electrons in either of the e_g or t_2g set of orbitals. This means that there is in fact, some room for stabilization of the complex by removing the degeneracy, which is achieved by Jahn-Teller distortion.

Jahn-teller distortion examples:

There are noticeable distortions in high-spin d⁴, low-spin d⁷, and d⁹ electronic configurations since all of these leave an unpaired electron in one of the orbitals of the e_g set. There are weaker distortions in systems with electronic configurations of d¹, d², low-spin d⁴, and d⁵, and high-spin d⁶ and d⁷, leaving unequal distribution of electrons in the t_2g set of orbitals.

All the central atoms/ions with any of these configurations will be affected by Jahn-Teller distortions. Some examples of Jahn-Teller distortions are complexes of Mn³⁺, Cr²⁺ in high-spin configurations and Ni³⁺, Co²⁺ in low-spin configurations, and Cu²⁺ along with Ag⁺ among without spin ionic complexes.

Jahn-teller distortion in octahedral complexes:

In the octahedral geometry, ligands approach the central atom/ion on the axes so the t_2g set of orbitals is raised in energy and there is a corresponding decrease in energy of the e_g set of orbitals. 

The distortions are most noticeable in complexes with high-spin d⁴, low-spin d⁷, and d⁹ electronic configurations because all of these configurations leave an unpaired electron in one of the orbitals of the eg set. There are weaker distortions for systems with d¹, d², low-spin d⁴, and d⁵, and high-spin d⁶ and d⁷ electronic configurations, as these leave an uneven distribution of electrons in the t_2g set.

Jahn-teller distortion is observed in:

The Jahn-Teller distortion has its effects in fields such as spectroscopy, stereochemistry, crystal chemistry, materials science, and molecular and solid-state physics.

Jahn-Teller distortions are observed in octahedral and tetrahedral geometries in coordination chemistry. In organic chemistry, the distortions are noticed in antiaromatic organic compounds such as cyclobutadiene and cyclooctatetraene (-1) anion. 

What are the criteria for a John Teller distortion in a molecule?

The Jahn-Teller effect is a process of spontaneous symmetry breaking that lowers the symmetry in certain geometries, in order to bring the molecules into a more stable, lower energy state. 

For the Jahn-Teller effect to take place, there must be “A non-linear molecular system in an electronic degenerate state”. This refers to an uneven distribution of electrons either in the e_g or the t_2g set of orbitals for octahedral and tetrahedral geometries.

What is the Jahn Teller theorem for coordination compounds?

In coordination chemistry, the Jahn-Teller theorem is an effect that lowers the symmetry in specific geometries, in order to bring the molecules into a lower energy state. For the effect to take place, there should be an uneven distribution of electrons in either of the sets of d orbitals. 

The affected geometries include tetrahedral and most commonly, octahedral. In octahedral geometry, the types of distortions that occur are tetragonal elongation and compression which involve the movement of ligands on the z-axis.

What is a half-filled t_2g orbital in a d orbital?

A half-filled t_2g orbital refers to the presence of a single, unpaired electron in one of the orbitals of the t_2g set (d_xy, d_xz, d_yz). The electronic configurations that give rise to this possibility are d¹, d², low-spin d⁴ and d⁵, and high-spin d⁶ and d⁷ in the octahedral geometry.

Is ethylene diamine a symmetric ligand?

Yes, ethylene diamine has a C-2 rotational axis, making it a symmetric ligand.

Reference books

• The Jahn-Teller Effect: Fundamentals and Implications for Physics and Chemistry edited by Horst Köppel (Heidelberg University), David R. Yarkony (Johns Hopkins University), Heinz Barentzen (Heidelberg University)

Reference links

• Jahn–Teller effect (Wikipedia)

• Jahn-Teller Distortions and Effects (Chem Libretexts)