JAHN TELLER THEOREM

 

The six coordinated complex will be called as a regular octahedral complex if all the six distances between metal and ligand is same (ML₁ = ML₂ = ML₃ = ML₄ = ML₅ = ML₆). In other words, a regular octahedral complex is formed if the arrangement of electrons in t_2g and e_g are symmetrical.

Instead if the arrangement of electrons in t_2g and e_g are unsymmetrically filled then, the regular octahedral geometry will be unstable and they transform into a distorted octahedral geometry which is called TETRAGONAL DISTORTION.

1.   Tetragonally elongated distorted octahedral complex: Here the axial bonds are longer than the equatorial bonds (ML₁ = ML₆ > ML₂ = ML₃ = ML₄ = ML₅). Example: CuF₂

2.   Tetragonally compressed distorted octahedral complex: Here the equatorial bonds are longer than the axial bonds (ML₁ = ML₆ < ML₂ = ML₃ = ML₄ = ML₅). Example: K₂CuF₄

These distortion depends upon the type of metal and ligands. The stronger the metal-ligand interactions, the greater is the chance for Jahn-Teller effect.

 

STATEMENT OF JAHN TELLER DISTORTION:

“For any non-linear molecule in degenerate electronic state which is unstable will undergo Jahn-Teller distortion (JTD) to form a system of lower symmetry and lower energy, thereby removing the degeneracy.”

 

CASES INVOLVED IN JTD OF OCTAHEDRAL COMPLEXES:

	CONDITIONS			OUTCOME		REASON
	If the arrangement of electrons in t2g and eg are symmetrical			No Jahn-Teller distortion (JTD)		All the six ligand experiences repulsive force of same amount.
	If the arrangement of electrons in t2g is unsymmetrical and eg is symmetrical			Slight JahnTeller distortion (JTD)		The lobes of t2g set d-orbitals lies in between the approaching ligands (between the axis).
	If the arrangement of electrons in t2g is symmetrical and eg is unsymmetrical			Strong Jahn- Teller distortion (JTD)		The lobes of eg set d-orbitals lies directly in the path of approaching ligands (along the axis).
		STRONG FIELD/LOW SPIN/LARGE ∆ VALUE	JAHN TELLER DISTORTION		WEAK FIELD/HIGH SPIN/ SMALL ∆ VALUE		JAHN TELLER  DISTORTION
d1		t2g1 eg0	Weak JTD		t2g1 eg0		Weak JTD
d2		t2g2 eg0	Weak JTD		t2g2 eg0		Weak JTD
d3		t2g3 eg0	No JTD		t2g3 eg0		No JTD
d4		t2g4 eg0	Weak JTD		t2g3 eg1		Strong JTD
d5		t2g5 eg0	Weak JTD		t2g3 eg2		No JTD
d6		t2g6 eg0	No JTD		t2g4 eg2		Weak JTD
d7		t2g6 eg1	Strong JTD		t2g5 eg2		Weak JTD
d8		t2g6 eg2	No JTD		t2g6 eg2		No JTD
d9		t2g6 eg3	Strong JTD		t2g6 eg3		Strong JTD
d10		t2g6 eg4	No JTD		t2g6 eg4		No JTD