Ligand field theory considers the effect of different ligandenvironments (ligand fields) on the energies of the d-orbitals.

The energies of the d orbitals in different environmentsdetermines the magnetic and electronic spectral propertiesof transition metal complexes.

Ligand field theory combines an electrostatic model ofmetal-ligand interactions (crystal field theory) and a covalent model (molecular orbital theory).

Relative energies of metal-ion 3d electrons.

• Because the 4s2 electrons are lost before the 3d, the highest occupied molecular orbitals (HOMOs) in transition metal complexes will contain the 3d electrons.

M2+ 3d1 3d2 3d3 3d4 3d5 3d6 3d7 3d8 3d9 3d10

Sc Ti V Cr Mn Fe Co Ni Cu Zn

• The distribution of the 3d electrons between the d-orbitals in any given complex will determine the magnetic properties of the complex (the number of unpaired electrons, the total spin (S) and the magnetic moment of the complex).

• Electronic transitions between the highest occupied d-orbitals will be responsible for the energies (λmax) and intensities () of the d-d bands in the electronic spectra of metalcomplexes.

• Electronic transitions to and from the highest occupied d-orbitals will be responsible for the energies and intensities of the ligand-to-metal (LMCT) and metal-to-ligand (MLCT) charge transfer bands appearing in the electronic spectra of metal complexes.

Oh Td

d-orbitalsf ree ion

e

t2

Td ligand f ield

d-orbitalsf ree ion

eg

t2g

Oh ligand f ield

Td

Oh

Octahedral 3d Complexes

Δo ≈ P(pairing energy) Both low-spin (Δo ≤ P) and high-spin (P ≥ Δo ) complexes are found.

Tetrahedral Complexes

ΔTd = 4/9 Δo hence P >> ΔTd and tetrahedral complexes are always high spin

High-Spin and Low-Spin Complexes for 3d4 – 3d7 ions

Electronic structure of high-spin and low-spin Oh complexes

t2g5 (n = 1)

t2g3 eg

1 (n= 4) t2g4eg

2 (n = 4) t2g5 eg

2 (n =3)

t2g4 (n = 2)

t2g3 eg

2 (n = 5)

t2g6 eg

1 (n = 1)t2g6 (n = 0)

High Spin P >

Low Spin, > P

Other factors influencing the magnitude of Δ-splitting

• Oxidation State

Δo (M3+) > Δo(M2+) e.g. Δo for Fe(III) > Fe(II).

The higher oxidation state is likely to be low-spin

• 5d > 4d >3d

e.g. Os(II) > Ru(II) > Fe(II)

All 5d and 4d complexes are low-spin.

•The nature of the ligand. Spectrochemical Ligand Series

The ordering of the ligands in their ability to cause d-orbital splitting.

I- < Br- < Cl- < SCN- < NO3- < OH- < C2O4

2- < H2O ~ RS- < NCS- < NH3

~ imidazole < en < bipy < phen < NO2- < PPh3 < CN- < CO

Variations are due to σ-donating and Π-accepting properties of the ligand.

Small Δ-splitting ligands are called weak field ligands. Large Δ-splitting ligands are called strong field ligands.

Halide ions < O-donors < N-donors < Π-unsaturated

Weak field ligands _______________Strong field ligands

Small Δ-splitting Large Δ-splitting

dxy dxz dyz

dx2-y2

dz2

dz2dx2-y2

dxy dxz dyz

Energy

High spin 3d5 Low spin 3d5

n = 5, S = 5/2 n = 1, S = 1/2

Weak field ligand Strong field ligand

[Fe(H2O)6]3+ [Fe(CN)6]3-

Magnetic properties of transition metal complexes.

Paramagnetism arises from the spin and orbital motions of unpaired electrons

Diamagnetism arises from filled-shell electrons.

Origin of ParamagnetismSpin angular momentum of unpaired electrons obs =

Orbital angular momentum of unpaired electronsSpin-orbit coupling

Magnetic Moments of Transition Metal IonsThe magnetic moment is related theoretically to the total spin quantum number (S) and total orbital angular momentum quantum number (L) of the ion.

S+L =

For many transition metal complexes, the measured magnetic moment, obs, is very close to the spin-only magnetic moment (orbital motion quenched).

obs ≈ = where n = number of unpaired electrons

)1()1(4 LLSS

T(K) χ corrM x

)1(4 SS )2( nn

d5 d6 d7d4

HighSpin

LowSpin

n = 4 s = 4.90

n = 5 s = 5.92

n = 4 s = 4.90

n = 3 s = 3.87

n = 2 s = 2.83

n = 1 s = 1.73

n = 0 s =0

n = 1 s = 1.73

* *

* *

P >

> P

Magnetic moments of high-spin and low-spin states d4-d7

* Some additional orbital contribution to magnetic moment expected

n S S+L

1 1.73 3.00

2 2.83 4.47

3 3.87 5.20

4 4.90 5.48

5 5.92 5.92

)1()1(4 LLSS)1(4 SS )2( nn=

Orbital contributions to magnetic moments.Quenching of orbital motion

The ligand field restricts “orbital motions” of metal ion electrons.

“An electron will have orbital motion about an axis only when the orbital it occupies can be transformed into an equivalent (and equal energy) orbital by a simple rotation about that axis”

Only electrons in t2g orbitals contribute to the orbital magnetic moment, but not when the t2g orbitals are filled or half-filled.

dXZ dYZ

dX2 -y2 d xy

dxy and dx2-y2 equivalent after 45o rotation but have different energy in ligand field

dxz and dyz equivalent after 90o rotation

Account for the magnetic moments of the following complexes

[V(H2O)6]Cl3 = 3.10

[Co(NH3)6]Br2 = 4.55

K4[Fe(CN)6] = 0

Antiferromagnetic Coupling of Electron Spin

L

M

M

Ligand -mediated coupling

ML

Ligand -mediated coupling

M

Relative energies of d-orbitals in tetragonal and square planar geometries

x2-y2, z2

z2

xy

xy, xz, yz

x2-y2

z2

x2-y2

xy

xz, yz

d

free ion

octahedral tetragonal square planar

xz, yz