CHE-501 Lecture 4 Crystal Field Theory by Dr. Charu C. Pant
CHE-501 Lecture 4 Crystal Field Theory by Dr. Charu C. Pant
CHE-501 Lecture 4 Crystal Field Theory by Dr. Charu C. Pant
Course Code-CHE-501
Presented by-
Dr. Charu C. Pant
Department of Chemistry
Uttarakhand Open University, Haldwani
CRYSTAL FIELD THEORY (CFT)
- - - - - -
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:
(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
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
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.
3d6
t2g
3d6
t2g
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