Crystal field theory was proposed in the 1950s to describe the bonding in ionic crystals and metal complexes. It uses an electrostatic model to explain how ligands interact with the d-orbitals of a central metal ion. This interaction splits the degeneracy of the d-orbitals into lower-energy orbitals (t2g) and higher-energy orbitals (eg). The crystal field splitting energy is determined by factors like the ligand type, metal oxidation state, and complex geometry. Crystal field theory can be used to determine properties of complexes such as color, magnetism, and spinel structures. It provides explanations for phenomena like Jahn-Teller distortions but has limitations and cannot fully describe covalent bonding.

2. INTRODUCTION
Crystal field theory –
•
Proposed by Bethe and van Vleck. Used in 195o
•
It defines the bonding in ionic crystals due to which this theory is
known as crystal field theory.
•
Orgel used the concept of crystal field theory to define nature of
bonding between ligands and metals.
•
This theory involves an electrostatic approach to the bonding in
complexes.

3. Werner’s theory
• Alfred Werner
• 1893
• Nobel prize in 1913
According to this theoryComplex metal shows two types of valency which are as follows:(a) Primary valencies
(b) Secondary valencies

4. Primary valency –
1.
2.
3.
4.
It is equal to the oxidation state of central metal atom.
It is non directional in nature .
It can not define the geometry.
Primary valency exhibiting species can or can not retain their individual identity.
Secondary valency1. It is equal to the co-ordination number of central metal atom.
2. Secondary valency exhibiting species are directional in nature.
3. Secondary valency of central metal atom is responsible for geometry of
complexes.
4. Those species which exhibit the secondary valency in the complex can not retain
their individual identity.

5. Example- Complex =[Co(NH₃)6 ]Cl3
1.Primary valency = +3
2.Secondary valency = 6 (C.N)
3.Primary valency is exhibited by 6NH₃ ligand.
4.Secondary valency is exhibited by 3Cl ligand.
5.Geometry = octahedral.

6. Limitation of Werner’s theory 1- This theory was failed to define the geometry in the case of four secondary
valency.
2- This theory was failed to define the nature of bonding between the ligand and
central metal atom.
To overcome this limitation a new theory was proposed which is VALENCE
BOND THEORY.

7. Valence bond theory
•Proposed by Pauling and Slater in 193o.
• Hybridization based theory.
• Define covalent nature of bonding between metal and ligand.
• Define properties of complexes.
Limitation of Valence bond theory –
1. VBT was failed to define the color of the various complexes.
2. VBT can not define the strength of the ligands.
3. According to VBT four co-ordinated complex of Cu in +2 oxidation state
being always square planar. Which is not explained by VBT.
4. VBT was failed to define the orbital contribution in the magnetic moment value
of the complexes.

8. Postulates of crystal field theory
1- Central metal atom is surrounded by ligands to form complex.
2- Type of ligand
 Point charge
 Point dipole
3-The bonding between metal cation and ligands arises due to electrostatic
interaction . Thus the bond between metal and ligand is purely ionic.
4-The interaction between electron of the metal cation and those of the ligand is
entirely repulsive. These repulsive forces are responsible for the splitting of the d
orbital of the metal cation.
5- The d orbital which are degenerate in free metal ion have their degeneracy
destroyed by the approach of ligand during the formation of complex.

9. CRYSTAL FIELD THEORY FOR OCTADERAL COMPLEXCrystal field theory for octahedral complex can be explained in following
five step which are as follows.
Step1- SHAPE OF d ORBITAL-

10. 1. STEP 2
Orientation of ligand around central metal atom

11. STEP 3-CRYSTAL FIELD SPLITTING OF THE OCTADERAL
COMPLEX
eg
t2g
Degenerate 5d
orbital
Metal ion and ligand
at infinite distance
away
Hypothetical
Degenerate
5d orbital
3d orbital are split into
Two sets

12. STEP 4Arrangement of dⁿ configuration of central metal ion in t2g and eg set
of orbitalTo define the arrangement of dⁿ of central metal atom in octahedral complex at first
we have to define spectrochemical series.
SPECTROCHEMICAL SERIES- Arrangement of the ligand in order of their increasing
splitting power to the dⁿ configuration is known as spectrochemical series. Which is
given below.

13. In case of strong
ligand
Either weak or strong ligand
In case of weak
ligand

14. Either strong or weak ligand

15. STEP 5-
Crystal Field Splitting Energy (CFSE)
• In Octahedral field, configuration is: t2gpegq
• Net energy of the configuration relative to the average
energy of the orbital's is:
= (-0.4p + 0.6q)O
• BEYOND d3
In strong field O  P, => t2g4 eg o
In weak field: O  P, => t2g3eg1
P - paring energy

17. CFT FOR TETRAHEDRAL COMPLEX
CFT for tetrahedral complex can also be explained in five steps which are as
follows.
STEP 1- Shape of 5d orbital1. Axial or eg set of the orbital- Out of 5d orbital two orbital mm and
being present over axis are known as axial set of orbital.
2. Non-axial or t2g set of the orbital- Out of 5d orbital remaining three orbital
being present between the axis are known as non-axial set of orbital.

18. STEP 2- ORIENTATION OF LIGAND AROUND CENTRAL METAL ION
IN TETRAHEDRAL COMPLEX
OR

19. STEP 3-CRYSTAL FIELD SPLITTING FOR TETRAHEDRAL
COMPLEX

20. STEP 4- Arrangement of electron in d orbital in tetrahedral complex
Either weak or strong ligand it will be of high spin.

21. SETP 5 – Crystal field energy difference in tetrahedral
complex
CFSE value for tetrahedral complex = (-.6q+.4p)∆t
where, q = the number of electron in eg set of orbital ,
p = number of electron in t2g set of orbital.

22. CFT FOR SQUARE PLANAR COMPLEX
1. In the octahedral complex all six metal ligand bond being identical .If the ligand
related with the z- axis are slightly removed outward then their occur the
formation of distorted octahedral complex.
2. In second step ligand related with z-axis are completely removed outward then
their occur the formation of square planer complex .

24. Factor affecting the value of ∆
1. Oxidation state of metal ion-
2. Nature of ligandStrong ligand = high ∆ value
Weak ligand = low ∆ value
3. Geometry- ∆ value is also affected by geometry of complex.

25. Applications of CFT
Determination of CFSE value– With the help of CFT we can determine the CFSE
value of the octahedral and tetrahedral complex by following formula.
CFSE value for tetrahedral complex = (-.6q+.4p)∆ț+ nP
CFSE value for octahedral complex = (-.4p+.6q)∆₀ + nP
n = no of paired electron
P = pairing energy
p and q are no. of electron in eg and t2g set of orbital respectively

26. 3. Geometry- ∆ value is also affected by geometry of complex.
Application of CFT
Determination of CFSE VALUE – with the help of CFT we can determine the CFSE
value of
the octahedral and tetrahedral complex by
following
CFSE value for formula.
tetrahedral complex = (.6q+.4p)∆ț+ nP
CFSE value for octahedral complex = (-.4p+.6q)∆₀
+ nP
n = no of paired electron
P = pairing energy
p and q are no. of electron in eg and t2g set of orbital respectively

27. Use of CFSE value
Spinel structure determination = All the mix oxide with the general formula
AB2O4 are known as spinel from the name of mineral spinel MgAl2O4 in
which both the A2+ and B3+ cation be similar or different.

28. Example 1- Mn3O4 ( O is a weak field ligand)
CFSE under weak field octahedral condition
0
-.6∆₀
CFSE under weak field tetrahedral condition
0
-.18∆₀
Will occupy octahedral void since its CFSE value is more negative.
and mnm will occupy tetrahedral void.
Therefore it is a normal spinel.
Example2-
CFSE under weak field octahedral condition
-.4∆₀
0
CFSE under weak field tetrahedral condition
-.27∆₀
0
It is a inverse spinel.

29. Color of the complexes
1.
2.
3.
Absorb all EMR – black
Transmitted all EMR - White
Absorb radiation of visible range – colored
Complexes shows color because of the phenomena of d-d transition.
d-d transition phenomena-

31. Color can change depending on the following factor:
1.Metal charge( size of metal)
2. Ligand strength

33. Magnetic behavior
If d orbital contain no unpaired electron = Diamagnetic
If d orbital contains unpaired electron = paramagnetic
 = {n(n+2)}1/2 B
Magnetic moment = •
Where n is no. of unpaired electron
Where
•
B = eh/4me = 9.274 10-24 J T-1

34. Ionic radii of transition metal ion= for given oxidation state ionic radii are
regularly decreases in transition metal complex.

35. JAHN – TELLER EFECT
If both the eg orbital are symmetrically filled- all ligand repel equally.
Result = regular octahedron
If asymmetrically filled - some ligand are repel more than other.
Result = Distorted octahedron

36. Consider eg configuration

37. Consider eg configuration =
Z- OUT DISTORTION-

38. Published in 1937 .
 This theorem state that there can not be unequal occupation of orbital with
identical energy. To avoid such unequal occupation, the molecule distort so that
these orbital are no longer degenerate.
The effect of John Teller is best documented for Cu(ІІ)

39. Limitation of CFT
1. This theory does not consider the splitting of the orbital other than d
orbital.
2. The order of ligand in the spectrochemical series can not be explained
solely on electrostatic ground.
3.
CFT was failed to explain co-valency in certain metal ligand bond.
4. CFT can not define the orbital contribution in magnetic moment of
complex.
CFT = Crystal field theory

40. REFRENCES
Gary L. Miessler and Donald A. Tarr
V Ramalingam
Alen G Sharpe
www.wikipedia/ crystal field theory

41. THANK YOU