Ligand field theory considers the effect of different ligand
environments (ligand fields) on the energies of the dorbitals.
The energies of the d orbitals in different environments
determines the magnetic and electronic spectral properties
of transition metal complexes.
Ligand field theory combines an electrostatic model of
metal-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
Sc
3d2
Ti
3d3
V
3d4
Cr
3d5
Mn
3d6
Fe
3d7
Co
3d8
Ni
3d9
Cu
3d10
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 (e) of the d-d bands in the electronic spectra of metal
complexes.
•
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
High-Spin and Low-Spin Complexes for 3d4 – 3d7 ions
 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
Electronic structure of high-spin and low-spin Oh complexes
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- < C2O42- < 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
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 Paramagnetism
Spin angular momentum of unpaired electrons
Orbital angular momentum of unpaired electrons
Spin-orbit coupling
obs =
χM
corr
x T(K)
Magnetic Moments of Transition Metal Ions
The 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 = 4S (S  1)  L(L  1)
For many transition metal complexes, the measured magnetic moment, obs, is very
close to the spin-only magnetic moment (orbital motion quenched).
obs ≈
4S (S  1)
=
n(n  2)
where n = number of unpaired electrons
Magnetic moments of high-spin and low-spin states d4-d7
d4
d5
d6
d7
High
Spin
P > 
n=4
s = 4.90
 > P
n=5
s = 5.92
n=4
s = 4.90 *
n=3
s = 3.87 *
Low
Spin
n=2
s = 2.83 *
n=1
s = 1.73 *
n=0
s =0
n=1
s = 1.73
* Some additional orbital contribution to magnetic moment expected
S
n
4S (S  1)
=
n(n  2)
S+L
4S (S  1)  L( L  1)
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
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”
d
XZ
dxz and dyz equivalent after 90o
rotation
Only electrons in t2g orbitals
contribute to the orbital magnetic
moment, but not when the t2g
orbitals are filled or half-filled.
dxy and dx2-y2 equivalent after 45o
rotation but have different energy in
ligand field
d
YZ
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
Ligand -mediated coupling
M
M
L
Ligand -mediated coupling
M
L
M
Relative energies of d-orbitals in tetragonal and square planar geometries