Chemistry 401

Measurement of 10Dq

Usually done spectroscopically, move electron from t_2g to e_g orbital with no spin change

hν = 10Dq in this case

Because of electron–electron repulsion, the lowest energy transition is not always equal to 10Dq.

ConfigurationLowest Energy Spin–Allowed Transition

 

 

d¹10Dq

 

d²8Dq

 

d³10Dq

 

d⁴ (hs)10Dq

 

d⁴ (ls)~ 9Dq

 

d⁵ (hs)none

 

d⁵ (ls)~ 8.5Dq

 

d⁶ (hs)10Dq

 

d⁶ (ls)~ 9Dq

 

d⁷ (hs)10Dq

 

d⁷ (ls)~ 9Dq

 

d⁸8Dq

 

d⁹10Dq

 

d¹⁰none

 

Complication : charge transfer transitions

M–L →hν M⁺–L^– Metal to Ligand Charge Transfer (MLCT)

M–L →hν M^––L⁺ Ligand to Metal Charge Transfer (LMCT)

CT transitions are usually much more intense than d–d transitions so can be distinguished by molar absorptivity

ε (CT) ~ 10³ – 10⁴ L/mol–cm

ε (d–d spin allowed) ~ 10¹ – 10² L/mol–cm

ε (d–d spin forbidden) ~ 10^–1 – 10⁰ L/mol–cm

How does Crystal Field theory change if the complexes are not octahedral?

Consider a tetragonal case:

Need to introduce additional parameters, δ₁ and δ₂

The situation is such that E(x²–y²) – E(xy) = 10Dq (moving the ligand along the z axis should have no effect on the relative energies of the orbitals in the xy plane).

For compression case :

[E(x²–y²) + δ₂] – [E(xy) + 2δ₁] = 10Dq

[E(x²–y²) – E(xy)] + δ₂ - 2δ₁ = 10Dq

10Dq + δ₂ -2δ₁ = 10 Dq

δ₂ = 2δ₁

Can we predict when this will happen? Yes, using the Jahn-Teller theorem

Jahn-Teller Theorem: In a nonlinear molecule a degenerate electronic state will distort to remove the degeneracy and to increase the stability

Consider d¹

In an O_h geometry, the electronic state is triply degenerate (the single electron can be in one of three orbitals of identical energy).

Axial elongation gives a state that is still degenerate (doubly) so would need to further distort.

Axial compression leads to a singly degenerate state and increased stability.

LFSE = –4Dq – 2δ₁

This should occur even if all the ligands are the same!

Which configurations should be J-T active?

configurationJ-T active?distortion

 

d¹yescompression

 

d²yeselongation

 

d³no 

 

d⁴ (hs)yeseither

 

d⁴ (ls)yescompression

 

d⁵ (hs)no 

 

d⁵ (ls)yeselongation

 

d⁶ (hs)yescompression

 

d⁶ (ls)no 

 

d⁷ (hs)yeselongation

 

d⁷ (ls)yeseither

 

d⁸no 

 

d⁹yeseither

 

d¹⁰no 

 

Tetrahedral Complexes

Tetrahedral symmetry is fairly common but can not be treated as a distortion from O_h

Ligands between axes are destabilized, ligands along axes are stabilized.

The splitting in T_d complexes is always less than the splitting in O_h complexes with the same ligands (Δ_t < Δ_o). (Fewer ligands give a smaller electrostatic field; in the exact ionic limit Δ_t = 4    9Δ_o.)

This means that T_d complexes are always high spin and usually bluer.