Programme Code- MSCCH-17/18/19

Course Code-CHE-501

Unit- 6 Crystal Field Theory (CFT)

Presented by-
Dr. Charu C. Pant
Department of Chemistry
Uttarakhand Open University, Haldwani
 CRYSTAL FIELD THEORY (CFT)

In view of the weaknesses of Valence Bond Theory (VBT), an

alternative bonding model was applied to transition metal
complexes. This is known as crystal field theory (CFT).
Brethe and Van Vlick have been proposed a theory to explain
the bonding in the ionic crystals, which is called as Crystal
Field Theory (CFT). Initially this theory was propound for the
ionic crystals but in 1952 Vage has been proposed this theory
for the metal-ligand bonding in the complex compounds,
which is known as CFT of the Coordination Chemistry.
 POSTULATES OF CFT
1. According to the CFT, central metal ion (CMI) of the

complexes being surrounded by the number of ligands.

2. According to this theory, ligands can be of the two types
which are givn below:
a. Negative ligands also known as point dipole.
b. Neutral ligands also known as point dipole.
3.According to CFT there does not occur any type of the
overlapping between the orbitals of the ligand and CMI i.e.
metal ligand bonding having zero % covalenay.
4. According to CFT always there occur an electro static
interaction between the +ve charge nucleus of the CMI and –
ve charge of the ligand i.e. metal- ligand bonding having
100% ionic character. Complexes are thus presumed to form
when CMI electrically attract ligand which may be either
anions or dipolar molecules.
If the complex containing neutral ligand then the –ve pole of
neutral ligand (point dipole) will be oriented toward the CMI.
 1. CFT FOR THE OCTAHEDRAL COMPLEXES
CFT of octahedral complexes can be defined in the following
steps:-
Step I- Shape of 5- d orbital’s of CMI:
Five d- orbitals of the CMI can be divided into two
different set of orbital’s which are
given below:-
a. t2g set (Non-axial set of d-orbital):
dxy dyz & dzx orbital’s are known as t2g set of orbital’s. All
these orbital being present between the axis due to which they
are also known as Non-axial set of d- orbitals.
 X Y Z
+ + +
+ + +
Y Z X

- - - - - -

dxy dyz dzx

t2g -orbitals (Non-axil)

X Z

eg- set of orbital's

Step II- Orientation of 6 ligands around the CMI in the octahedral
complexes
In the octahedral complexes all the six ligands being oriented toward the
CMI from the six opposite corners of the three cartition axis, which can
be represented:-
L
L
L

M+n

L
L
L
Step III- Crystal field splitting of the 5-d orbital’s of CMI:
When the CMI being present in the isolated form then all the five-d
orbital’s of the CMI having same energy and they are combindly known
as degenerates of 5- d orbital’s but if the ligand comes in the
environment of CMI the hypothetically energy of all the 5-d orbitals is
slightly increased due to the repulsion between the –ve charge of the
ligand and 5- d orbital’s finally when the 6 ligands comes in the
octahedral environment around the CMI to constrict the octahedral
complex then 5- d orbital’s of the CMI into lower energy t2g set and
higher energy eg- set of orbital’s, which is called as crystal field splitting
in the octahedral complexes. The energy difference b/w the spillited set
of orbitals is known as crystal field splitting energy difference (∆o).
 eg

0.6 ∆o

∆o
Hypothetical Degenerate set
of 5- d orbitals of CMI
Degenerate set -0.4∆o
of 5- d orbitals of CMI

t2g
Crystal filed spilliting
Step IV-Distribution of dn configuration of the CMI in the splitted
set of d-orbitals:
To define the distribution of dn configuration of CMI in the splitted set
of d-orbitals at first we have to define the strength of ligand i.e. spectro
chemical series.
Spectrochemical Series: According to the concept of CFT those ligands
which having the more splitting power are known as stronger ligands
while on the other hand those ligands which having the less spitting
power are known as weak ligands. After arranging the various ligands in
order of their uncrossing or decreasing splitting power the arrangement
which is obtained is known as spectro chemical series.
Arrangement of certain ligands in order of their increasing splitting
power according to spectro chemical series can be given as:
I− < Br− < S−2 < SCN− < Cl− < NO2− < F− < OH− < H2O < NCS− < py <
bipy < CN− < CO
The ligands interact weakly: - weak field ligands e.g. I−, Br−, S−2, SCN−,
Cl−
The ligands interact strongly: - strong field ligands e.g. NO2−,CN− ,CO
Similarly, if metal ions are different with same ligand, ∆o are different.
Metals with more positive charge and from 2nd and 3rd transition series
interact more (higher splitting).
Now distribution of dn configuration of the CMI can be given under the
two conditions:-
• If 0> P i.e. under the strong field octahedral condition:
If the octahedral complex containing stronger ligand than value of 0

being greater than the mean pairily energy (p), under such condition
destitution of the dn configuration of CMI in the splitted set of d-orbitals
can be given as:
 eg eg

(t2g1,eg0 )
d1 (t2g6,eg1 )
d7

t2g t2g

eg eg

(t2g2,eg0 ) (t2g6,eg2 )
d2 d8

t2g t2g

eg eg

(t2g3,eg0 ) (t2g6,eg3 )
d3 d9

t2g t2g

eg eg

(t2g4,eg0 ) (t2g6,eg4 )
d4 d10

t2g t2g
eg

(t2g5,eg0 )
d5

t2g

eg

(t2g6,eg0 )
d6

t2g
•If 0 <P i.e. under the weak field octahedral condition:

If : the octahedral complex containing weak ligand then value of 0

being less then mean paring energy (P), under such conditions
distribution of the dn configuration of the CMI in the splitted set of d
orbital’s can be given as:
 eg eg

(t2g1,eg0 )
d1 (t2g5,eg2 )
d7

t2g t2g

eg eg

(t2g2,eg0 ) (t2g6,eg2 )
d2 d8

t2g t2g

eg eg

(t2g3,eg0 ) (t2g6,eg3 )
d3 d9

t2g t2g

eg eg

(t2g3,eg1 ) (t2g6,eg4 )
d4 d10

t2g t2g
eg

(t2g3,eg2 )
d5

t2g

eg

(t2g4,eg2 )
d6

t2g
 Step V: Crystal field stabilization energy in the octahedral
0) p
complexes:
Crystal field splitting of the dn configuration in the octahedral complexes
can be given as: eg

0.6 ∆o
dn ∆o
-0.4 ∆o
t2g

Total no of e– in eg set = q (1 4)
Suppose total number of e– in t2g set = P (1 6)
Than decrease in energy of dn configuration by entrance of 1 e- in t2g set
= -0.4 ∆o
So decrease in energy of dn configuration by entrance of p e- in t2g set =
(-4.
Increase in energy of d dn configuration by entrance of 1e- in eg set = 0.6
∆o
 So increase in energy of dn configuration by enter of q e- in eg set =
(0.6∆o) q
Thus total energy change of dn configuration = (-0.4∆0) P + (0.6∆0) q
= (-0.4p + 6q) ∆0
This total amount of the energy change for the dn configuration is known
as crystal field stabilization energy (CFSE) for the dn configuration of
CMI in the octahedral complexes.
Thus
CFSE= (-0.4p +0. 6q) ∆0
CFSE= (-0.4 p +0.6q) 0 + nP
If the value of mean pairing energy being P and no of pairs in the t2g or eg
orbitals being n then nP amount of energy will also increases the energy
of dn configuration. Thus the net energy
 CFSE= (-0.4 p +0.6q) 0 + nP
2. CFT FOR THE TETRAHEDRAL COMPLEXES:
CFT tetrahedral complexes can be explained under the five different
steps, which are given below:
Step I Shape of 5- d orbitals: All the 5-d orbitals of the CMI can be
levied into 2 different set of orbitals, which are given below.
•‘e’- set: dx2 – y2 and dz2 orbital are combindly known as ‘e’ set of
axed set orbital’s.
•t2 set: dxy , dyz & dzx orbitals are cmbindly known as ‘t2’ – set or non
axial set of orbitals.
 X Z

2 2 dz2
d x -y

e -set
Z
X Y

Z X
Y

dzx
dxy dyz

t2 -set
Step II- Orientation of 4- ligands around the CMI in the tetrahedral
complexes:
In the tetrahedral complexes all the 4- ligands being oriented toward the
CMI from the non axial position, that can be represented as:-
L

M+n

L
Step III- Crystal filed splitting of the 5-d orbitals of CMI in
tetrahedral complexes:
When the CMI being present in the isolated form them, all the 5- d
orbitals of the CMI having same energy and they are combindly known
as degenerate set of 5- d orbitals of the CMI having same energy and
they are combindly known as degenerate set of 5- d orbitals, but when
the 4- ligands comes in the environment of CMI then there occur the
partial hypothetic repulsion between the –ve charge of the ligands and all
the 5- d orbitals due to which energy of all the 5-d orbitals of CMI is
slightly increased then after that finally tetrahedral environment from the
non axial position then there occur the splitting of all the 5 – d orbitals of
CMI into lower energy e- set and higher energy t2 set of orbitals which is
known as crystal field splitting in the tetrahedral complexes.
The energy difference between the splitted set of d- orbital is known as
crystal field splitting energy difference (∆t).

t2-set

0.4∆ t

∆t
Hypothetical degenrate
set of 5-d orbitals of CMI
Degenrate set of -0.6 ∆t
5-d orbitals of CMI
e- set
Step IV- Distribution of dn configuration of CMI in the tetrahedral complexes:
t2-set t2-set

d1 e 1, t 20

d6 e 3, t 23
e- set

e- set
t2-set

t2-set
2 e 1, t 20
d

d7 e4,t23
e- set

e- set
t2-set

t2-set
d 3 e 2, t 21

e 4, t 24
d8
e- set

e- set
t2-set
t2-set

d4
e 2, t 22
e4, t25
d9

e- set
e- set

t2-set t2-set

d5 e 2, t 23 e4, t26
d10

e- set
e- set
Step V- Crystal field stabilization energy in the tetrahedral
complexes:
Crystal field splitting diagram for the dn configuration of CMI in the
tetrahedral complexes can be represented as:-

t2-set

0.4 ∆ t
d6

-0.6 ∆ t
e- set

Suppose no. of e- in e set = q (1 4)

No. of e- in t2 set = p (1 6)
Than decrease in energy of dn configuration due to the entrance of (e-- in
e set = -0.6 ∆t
So decrease in energy of dn configuration due to the entrance of qe- in e
set = -.6 ∆t x q
Increase in energy of dn configuration due to entrance of e- in t2 set =
0.4∆t
So increase in energy of dn configuration due to entrance of p e-- in t2 set
=0.4 ∆t x p
Since net energy change of dn configuration = (-0.6 ∆t x q + 0.4 ∆t x p)
= (-0.6 x q + 0.4 x p) ∆t
This net amount of the energy change for the dn configuration is known
as CFSE of the tetrahedral complexes.
CFSE= (-0.6q + 0.4P) ∆t
Suppose the value of mean pairing energy is denoted by the symbol P
and total no. of the pair in the splitted set of d- orbitals denoted by the
symbol n then the nP amount of energy will also be involved is the CFSE
formula. Thus
CFSE= (-.6q + .4P) + nP
 3. CFT FOR THE SQUARE PLANNER COMPLEXES
CFT of the square planner complexes is arises from the CFT of
octahedral complexes. The crystal field splitting diagram for the square
planer complexes originated from the splitting diagram of octahedral
complexes in the two steps which can be represented as:-
If two trans ligands in an octahedral ML6 complex (consider those along
the z-axis) are moved either towards or away from the metal ion, the
resulting is said to be tetragonally distorted. Ordinarily such distortions
are not favored since they result in a net loss of bonding energy. In
certain situations, however, such a distortion is favored because of a
Jahn-Teller effect. A complex of general formula trans-Ma2b4 also will
have tetragonal symmetry.
For now, we will consider the limiting case of tetragonal elongation, a
square planar ML4 complex, for the purpose of deriving its d-orbital
splitting pattern. The crystal field diagram for the tetragonally distorted
complex and the square-planar complexes is shown below. Removal of
ligands from z-direction completely leads to the square-planar geometry.
This geometry is favoured by metal ions having a d8 configuration in the
presence of a strong field. This combination gives low-spin complexes
where the first four orbitals are occupied and the high-energy dx2-y2
orbital is unoccupied.
 Lb Lb
Lb Lb
Lb La Lb
Slight removal of the La ligand +n
Slight removal of the La ligand M+n M
M
+n

Lb Lb Lb Lb
Lb Lb La
La Squar planner complex
M-La # M-Lb
M-La = M-Lb
Pure octahedral complex
(Distorted octahedral)
Crystal Field splitting for square planner complex:
Square planar complexes are similar to octahedral complexes. The
difference is that square planar complexes have two ligands missing in
the z axis. There is a very large energy gap between the x2-y2 orbital and
the lower four orbitals. Square planar complexes are favored by metal
ions with d8 electron configurations. Since this configuration favours
low-spin complexes in which the four lower-energy orbitals are filled
and the high energy x2-y2 orbital is empty. The crystal field splitting
diagrame of square planner complex is given as:
 dx2-y2

∆Sp3
2 2
dx -y

eg
dxy
dx2-y2 dz2

dz2
dn ∆ Sp2
∆ Sp

dxy
t2g
dz2
dxy dyz dzx

dyz dzx ∆ Sp1

dyz dzx
 FACTOR AFFECTING THE CRYSTAL FIELD PARAMETER
Some factors which can affect the value of ∆ (Crystal field splitting
energy difference) are given below:
•Nature of ligands: With the increase in the strength of the ligands
present in the complexes the ∆ value for the complexes is increases.
Explanation: With the increase in the strength of the ligand ability of the
ligands to cause the closer approach with the CMA is increases by which
the repulsion between the ligand and d orbitals as well as ∆value is
increases.
Examples:
a. [Fe(CN)6]-4 ion containing the stronger CN- ligand while (Fe (Cl)6]-4
ion containing the weak Cl- ligand due to which the value for (Fe
(CN) ]-4 ion is found to be more then (Fe (CN) ]-4 ion.
b. [Co(F)6]-3 ion containing the stronger F- ligand while [Co(Cl)6]-3 ion
containing the weak Cl- ligand due to which the ∆ value for [Co(Cl)6]-3
ion is found to be less then [Co (F)6]-3 ion.
2. Nature of CMA:
a. Same CMA with different charge: If the complexes containing same
CMA with the different charge then the complex with the higher +ve
charge of the CMA will exhibit higher ∆value.
Explanation: In the complexes containing different charge of the CMA
then the complex with the higher +ve charge of the CMA exhibit higher
value because the CMA with higher +ve charge can attract the ligand
more closer toward itself by which the repulsion between the ligand and
d- orbital of CMA as well as value is increases.
a.
b. Different CMA with the different charge:
If the complexes containing the different charge then the complex which
containing higher +ve charge at the CMA exhibit higher ∆ value.
Explanation: If the complexes containing different CMA with the
different charge then the complex which containing higher +ve charge of
CMA exhibit the higher value because the CMA with the higher +ve
charge can attract the ligand more closer toward itself due to which the
repulsion between the ligand and d- orbital of CMA as well as ∆ value
are increases.
a. [V(H2O)6]+2 ion containing lower +ve charge (+2) at the CMA while
[Cr (H2O)6]+3 ion containing higher + ve charge (+3) at the CMA due
to which [Cr(H2O)6] +3 ion will exhibit higher ∆ value.
b. [Fe(NH3)6]+3 ion containing higher + ve charge of the CMA (+3)
while [Fe (NH3)6]+2 ion containing lower + ve charge of the CMA
(+2) due to which [Fe(NH3)6]+3 ion will exhibit higher ∆ value.

(C) Different CMA with same charge:

If the complexes containing different CMA with the same charge then
that complex which containing lower dn configuration of CMA will
exhibit higher ∆ value.
Explanation: This can be due to shielding effect.
Example: [Fe(H2O)6]+2 ion having 3d6 configuration of CMA while
[Co(H2O)6]+2 ion containing the 3d7 configuration of CMA and both
these complexes having same charge value, thus the former complex ion
with lower dn configuration will exhibit high ∆ value.
(d) Principal quantum no of dn configuration:
With the increase in the Principal quantum number of dn configuration of
CMA, the value of ∆ is increases.
In other word the ∆ value for the complexes of II-transition series
elements being 30% greater than the ∆ value for the complexes of I-
transition series elements and the ∆ value for the complexes of III-
transition series element being greater than the II-transition series
elements.
Example: [Fe(N)6]-4 ion exhibit lower value then the [Ru(N)]-4 ion
because Ru having the higher Principal quantum number of dn
configuration in compare to Fe.
 APPLICATIONS OF THE CFT

The following properties of transition metal complexes ca will be

explained on the basis of CFT.
1. According the CFT if the splitted set d-orbitals of the CMI present in
the complexes containing the unpaired e- than the complex well be called
as paramagnetic in rapture while if the splitted set of d-orbitales of the
CMI does not containing the unpaid e- then the complex will be called as
diamagnetic in nature.
Example:
(II) (Co (F)6]-3 ion
Configuration of Co = 3d7, 4S2
Oxidation state of CO = +3
Configure of CO+3 = 3d6
According to CFT
 eg

3d6

t2g

Since the splitted set of d- orbital containing 4 unpaired e- due to which

the complex ion [Co (F) 6]-3 ion will be paramagnetic in nature and
according to CFT.
µ= B.M.
(II) [Co (NH3)6]+3 ion
Configuration of Co = 3d7 4S2
Oxidation State of Co = +3
Configuration of CO+3 = 3d6
According to CFT
eg

3d6

t2g

2. Stability of the oxidation states: With the help of CFT we can

compare the stability of the different oxidation state exhibited by any
particular transition metal element under the strong field and weak field
condition by using the CFSE concept.
Example: CO (III) is more stabilized then the CO (II) under strong filed
condition Co (II) is more stabilized then the Co (III) under the weak filed
condition which can be explained by the CFSE concept of CFT.
3. Colour of the complexes: To define the colour of the complexes
formed by the d- block element at first white light is passed from the soln
of complex compound then,
(i.) If whole of the white light is transmitted by the sample then the
complex will be called as white in colour.
(ii.) If whole of the white light is absorb by the sample then the complex
is called as black in colour.
(iii.) If some of the radiations of the white light are absorbed and some
other radiation are transmitted, in such condition the complex can be
coloured only if the absorbed radiations belong to the visible range
(4000A0 – 7000 A0)
When the complex absorbed the radiation of visible range then the actual
colour of the complex will depend on the wavelength of that particular
radiation which is absorbed by the complex compound:-

4000A0 4350A0 4800A0 4900A0 5000A0 5600A0 5800A0 5900A0 6050A0 7000A0
Yellow
Colour of absorption Voilet Blue Green Blue Green Yellow Orange
green Red
blue Green

Yellow Yellow Blow

Orange Red Purple Voilet Blue
Complementry colour Green Green Green
 LIMITATIONS OF CFT
1. CFT considers the splitting of d- orbital but it does not consider the
splitting of other orbitals in the ligand field environment.
2. CFT can’t explain that how certain ligands having more splitting
power/ability while certain other ligands having very low splitting
ability.
3. According to the CFT metal ligand bond having 100% ionic character
but from the various experiment it was froved that metal ligand bonds
having certain extent of covalence with the ionic character.