Chemistry 401

Crystal Field Theory or Ligand Field Theory

An ionic approach to understanding bonding in transition metal complexes

Consider the O_h case : what is the effect of the negative electron density from the ligands on the energies of the valence (d) orbitals

Δ_o = 10Dq = Crystal Field Splitting parameter or Ligand Field parameter

Occupation of the t_2g orbitals gives a little extra stabilization of the complex

Ligand Field Stabilization Energy (LFSE)

d electron configurationLigand Field configurationLFSE unpaired electrons

 

 

d¹t_2g¹4Dq 1

 

d²t_2g²8Dq 2

 

d³t_2g³12Dq 3

 

d⁴t_2g⁴16Dq – P 2 (ls)

 

d⁴t_2g³e_g¹6Dq 4 (hs)

 

d⁵t_2g⁵20Dq – 2P 1 (ls)

 

d⁵t_2g³e_g²0Dq 5 (hs)

 

d⁶t_2g⁶24Dq – 2P 0 (ls)

 

d⁶t_2g⁴e_g²4Dq 4 (hs)

 

d⁷t_2g⁶e_g¹18Dq – P 1 (ls)

 

d⁷t_2g⁵e_g²8Dq 3 (hs)

 

d⁸t_2g⁶e_g²12Dq 2

 

d⁹t_2g⁶e_g³6Dq 1

 

d¹⁰t_2g⁶e_g⁴0Dq 0

 

P = spin pairing energy

hs = high spin

ls = low spin

Influences on Dq:

metal : charge, size (Z*)

ligands : charge, orbitals available for bonding (σ, π), ring formation

Spectrochemical series

ligands ordered by relative size of Dq for any metal ion ligands ordered by ligand field strength

I^– < Br^– < S^2– < SCN^– < Cl^– < NO₃^– < F ^– < ox^2– < H₂O < SCN^– < CH₃CN < NH₃ < en < bipy < phen < NO₂^– < PPh₃ < CN^– < CO

High spin vs low spin

Complexes are high spin if Dq is small : weak field case

Complexes are low spin if Dq is large : strong field case

Magnetic susceptibility measurements, which measure the size of the magnetic moment, are used to distinguish the spin state.

The magnetic moment reflects the total available angular momentum in transition metal complexes (especially first row), most of this comes from spin (the orbital contribution is said to be quenched):

μ = g[S(S+1)]^½μ_B

g ~ 2 (fundamental constant); μ_B = Bohr magneton

Since each unpaired electron has S = ½

μ = [n(n+2)] ^½ μ_B

n = number of unpaired spins