Jahn Teller Theorem

 

What is Jahn Teller Theorem?

How various spin states exhibit Jahn Teller distortions?

Spectroscopy and Jahn Teller distortions.

 

Jahn teller theorem:

In 1937, Herman Jahn and Edward Teller postulated a theorem stating that” stability and degeneracy are not possible simultaneously unless the molecule is a linear one.” This leads to a break in degeneracy which stabilizes the molecule and as a result its symmetry is reduced.

Housecroft and Sharpe have eloquently phrased it 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"

Jahn Teller theorem is also known as Jahn Teller Distortions.

Jahn Teller Distortions in Octahedral complexes:

Although this is commonly observed with octahedral complexes, tetrahedral complexes also can undergo these Jahn Teller distortions. In an octahedral complex five d atomic orbitals are split into two degenerate sets t2g(dxy,dxz,dyz) and eg(dx²-y²and dz²).

When a molecule is degenerate it will distort to remove the degeneracy and octahedral complex will either elongate or compress z ligand bonds.

Elongation:

Elongation in Jahn Teller distortions occur when the degeneracy is broken by stabilization of the orbitals with z component while the orbitals without z component are destabilized. Reason is the greater overlap between dx²-y² and dxy orbitals with the ligand orbitals as a result these orbitals become high in energy.

Compression:

Compression in Jahn Teller distortion occurs when the degeneracy is broken by stabilization of d orbitals without z component while the orbitals with a z component are destabilized. This is due to greater overlap of orbitals with z component with the ligands, resulting in orbitals having high energy.

Spin States:

The electronic states of octahedral complexes are classified as either low spin or high spin.

Low Spin

Low spin complexes with d3, d6, d8 and d10 electrons cannot have Jahn Teller distortions examples include Cr³⁺,Ni²⁺ etc.

High spin

High spin complexes with d3, d5, d8 and d10 electrons cannot have Jahn Teller distortions.

Spectroscopy and Jahn Teller distortions:

Jahn Teller distortions can be observed using a variety of spectroscopy techniques.

(i)              In UV-VIS spectroscopy distortion causes splitting of bands in the spectrum due to a reduction in symmetry i.e. the number of bands increases.

(ii)            Similarly in IR and Raman vibrational spectroscopy in which the number of vibrational modes for a molecule can be calculated by 3n-6 rule or 3n-5 rule for linear geometry, the number of bands in octahedral molecule will be fewer than in distorted on.

 Important questions related to this topic:

 Strong Jahn-teller distortion is not observed for octahedral complexes of:

1) Cu²⁺

2) Low spin Cr²⁺

3) High spin Mn³⁺

4) High spin Cr²⁺

^Answer:2

Jahn teller effect is not observed in high spin complexes of:

A) Mn²⁺

B) Cr²⁺

C) Cu²⁺

D) Fe³⁺

^{Answer: A}

 Why does the absorption spectrum of aqueous [Ti(OH₂)₆]³⁺ exhibit a broad band with a shoulder?

1) Due to Jahn-Teller distortion in the ground state

2) Due to Compton effect

3) Due to jahn-Teller distortion in the excited state

4) Due to square planar geometry

Answer:3