Ligand Field Theory was postulated in the 1950s as a modification of crystal field theory and molecular orbital theory. It can explain the geometry of coordination compounds like octahedral, tetrahedral, and square planar using crystal field theory. However, ligand field theory also considers sigma and pi bonding, which are important for understanding the behavior of neutral ligands like carbon monoxide and the strong field ligands carbon monoxide and cyanide.

1. Ligand Field Theory
Centre for Nano and Material Sciences,
Jain University,
Jain Global Campus, Bangalore – 562112,
Karnataka, INDIA
Presented by: Supratim Chakraborty

2. Ligand Field Theory
Goldberg Chem. Ber.1906, 39, 1691
Crystal Field Theory (CFT):
• Crystal Field Theory was postulated by Hans Bethe and Van Vleck in early
1930s
• It explains the bonding between coordination compounds as electrostatic
interaction between positively charged metal ions and negatively charged
ligands.
• In case of neutral ligands dipole interaction between metal ion and ligand is
taken into account.
• CFT works well with small electronegative ligands such as F-, Cl-, and OH2 but
not with neutral ligands such as carbon monoxide (CO).
• However, to explain complex properties such as variable oxidation state,
catalytic properties, magnetic properties and electronic spectra more
sophisticated treatment was required. That came in terms of ligand field
theory (LFT).

3. Ligand Field Theory
Splitting of d – orb in presence of ligand:
• dz2 and dx2-y2 orbitals are pointed directly towards the axis; Z axis and X, Y axis
respectively.
• Whereas, dxy, dyz, and dzx are pointed between the axis; (X & Y), (Y & Z), and (Z & X)
respectively.
Essentials of Coordination Chemistry
http://dx.doi.org/10.1016/B978-0-12-803895-6.00001-X

4. Ligand Field Theory
Splitting of d – orb in octahedral complexes:
Approach of ligand in octahedral field:
Pointed directly towards
the approach of 6 ligands
Not in the same
directions as ligands
5 degenerate
d – orbitals of
free ions
Splitting of d
– orbitals in
octahedral
field
• dz2 and dx2-y2 orbitals (eg) are
higher in energy; Energy gap =
3/5 ΔO
• Whereas, dxy dyz and dzx orbitals
(t2g) are lowered in energy;
Energy gap = 2/5 ΔO
• Example: [Cr(III)Cl6]3-
Repulsion between ligand and metal removes
the degeneracy between the 5 d – orbitals.

5. Ligand Field Theory
Splitting of d – orb in tetrahedral complexes:
Far from the approach
of the ligands
More towards
the direction
of the ligands
Approach of ligand in tetrahedral field:
5 degenerate
d – orbitals of
free ions Splitting of d –
orbitals in
tetrahedral field
• dxy dyz and dzx orbitals (t2g) are higher in
energy; Energy gap = 2/5 Δt
• Whereas, dz2 and dx2-y2 orbitals (eg) are
lowered in energy; Energy gap = 3/5 Δt
• Example: [Fe(VI)O4]2-
Unlike octahedral as only 4 ligands are
approaching in tetrahedral so the electrostatic
repulsion is comparatively less and Δt = 4/9 Δo
X
Y
Z
Mn+

6. Ligand Field Theory
Splitting of d – orb in presence of ligands:
Compression of trans ligand
d(in) and d(out) distortions of
octahedral field:
• Square planner complexes have
similar type of splitting as d(out)
geometry.
• Jahn Teller distortion: “The shape of
transition metal complexes is
determined by the tendency of
electron pairs to occupy position as
far away as possible.”
d(in)
Removal of trans ligand
d(out)

7. Ligand Field Theory
Splitting of d – orb in low symmetry environments:
https://en.wikipedia.org/wiki/Crystal_field_theory

8. Splitting of d – orb in low symmetry environments:
Ligand Field Theory
https://en.wikipedia.org/wiki/Crystal_field_theory

9. Ligand Field Theory
In Ligand Field Theory specific electronic interactions between ligands and molecular
orbitals are taken into account.
Due to the directional nature of the approaching ligands in the octahedral field only the
following ligands of the metals will going to interact with the ligands: s, px, py, pz, dz2 and dx2 – y2.
Bonding Bonding
Ligand Orb Ligand Orb
S orb
px orb
py orb
pz orb
dz2 orb
dx2-y2 orb

10. Ligand Field Theory
x2 – y2 z2
xy yz zx
x2 – y2 z2
xy yz zx
L1 L2
L1 L2
• Among the six d orbitals only dz2 and dx2-y2
orbitals are pointed directly towards the axis; Z
axis and X, Y axis respectively.
• Those two orbitals will going to interact directly
with the 2 ligands (L1 and L2).
• From the interaction between the two ligand
orbitals and dz2 and dx2-y2 orbitals there will be
the formation of two b.o. and two a.o.
• As the a.o. are close to the energy of the d
orbitals so they will look like the d orbitals.
• Whereas b.o. being close to energy of the ligand
orbitals will resemble the shape of ligand orbitals.
• The xy, yz, and zx will going to remain as non
bonding orbitals.
Interaction of d – orbitals with ligands:
dz2 Ligand dx2-y2
Ligand
Non bonding
(t2g)
Anti bonding
(eg*)
Bonding (eg)

11. Ligand Field Theory
Interaction of s, p, and d – orbitals with ligands:
• Overall interactions of ligand
orbitals with the metal orbitals
is very complicated.
• Eg orbitals will going to interact
directly dz2 and dx2-y2 orbitals.
• A1g orbitals from the ligand will
going to interact with s orbitals
• T1U orbitals of the ligands will
interact with the px, py, and pz
orbitals.
S orb A1g
px py pz
T1u orbitals

12. Ligand Field Theory
The importance of Ligand Field Theory:
5 degenerate
d – orbitals of
free ions
Splitting of
d –
orbitals in
octahedral
field
In terms of the ability of the ligands to split the
d orbitals they are classified either as weak field
or strong field.
The series which lists the ligands in terms of
their splitting ability is called the
spectrochemical series.
I- < Br- < SCN- ~Cl- < F- < OH- ~ ONO- < C2O4
2- < H2O < NCS- < EDTA4- < NH3 ~ pyr ~ en <
bipy < phen < CN- ~ CO
Spectrochemical series:
What the CFT fails to explain is why CO > H2O > C2O4
2- > EDTA4- > I - ?
From the point of view of electrostatic repulsion the order should be reverse
i.e.,
EDTA4- > C2O4
2- > I- > H2O > CO. This can be explained by Ligand Field Theory.
http://wwwchem.uwimona.edu.jm/courses/LFT.html

13. Ligand Field Theory
Δ
Δ Δ
t2g
eg* eg*
eg*
π
π
π*
π*
π orbital
of I -
π* orbital
of CN-
π bonding of ligands with the metal orbitals:
Sigma bonding of ligands
with the metal orbitals
[M(II)(H2O)6]2+ [M(II)(CN)6]4-
[M(II)(I)6]4-
M C O
Metal  Ligand back bonding
π orbitals from I- are lower in
energy than metal t2g orbitals. So
the effective and experimental Δ
value becomes smaller. Δ(I-)
π* orbitals from CN- are higher in
energy than metal t2g orbitals. So the
effective and experimental Δ value
becomes bigger. Δ(CO /CN-)
π acceptor ligands
Ligand  Metal back bonding
π donor ligands
Absence of any π orbitals and
metal interaction has kept the
value of Δ in standard region.
<
<
Δ(H2O)

14. Summary:
Ligand Field Theory
• Ligand Field Theory was postulated by Orgel and Griffith in 1950s.
• It is a modified version of crystal field theory and molecular orbital theory.
• By the use of CFT it is possible to explain coordination compounds of
different geometries such as octahedral, tetrahedral, square planner,
square pyramidal, pentagonal bipyramidal etc.
• Two major aspects of Ligand Field Theory is sigma bonding and pi
bonding.
• CFT works well with small electronegative ligands such as F-, Cl-, and OH2
but not with neutral ligands such as carbon monoxide (CO).
• The characteristic behavior of strong field ligands such as carbon
monoxide (CO) or cyanide (CN-) pi bonding aspect of LFT becomes
important. (some unusual changes in this sentence structure that I can not
remember doing but noticed during presenting)