Coordination chemistry - CFT

1. V.SANTHANAM
DEPARTMENT OF CHEMISTRY
SCSVMV

2. LIMITATIONS OF VBT
The valence bond approach could not explain
the following
Electronic spectra
Magnetic moments of most complexes.
So a more radical approach was put forward
which had only room for electrostatic forces

3. CRYSTAL-FIELD THEORY
 Model explaining bonding for transition metal
complexes
 Originally developed to explain properties for
crystalline material
 Electrostatic interaction between lone-pair
electrons result in coordination.

4. CFT assumptions
Separate metal and ligand high energy
Coordinated Metal - ligand stabilized
Destabilization due to ligand -d electron
repulsion
 Splitting due to octahedral field.

5. Crystal Field Theory
The electron pairs on the ligands are viewed
as point negative charges
 They interact with the d orbitals on the
central metal.
The nature of the ligand and the tendency
toward covalent bonding is ignored.

6. d Orbitals

7. Approach of ligands – O
h
field

8. Crystal Field Theory
The repulsion
between ligand lone
pairs and the d
orbitals on the metal
results in a splitting of
the energy of the d
orbitals.

9. Crystal field theory
d-orbitals align along the octahedral axis d-orbitals align along the octahedral axis
will be affected the most.will be affected the most.
More directly the ligand attacks the metal More directly the ligand attacks the metal
orbital, the higher the energy of the d-orbital, the higher the energy of the d-
orbital.orbital.
In an octahedral field the degeneracy of the In an octahedral field the degeneracy of the
five d-orbitals is liftedfive d-orbitals is lifted

10. i

11. Ligand approach octahedral field – e
g
set

12. Ligand approach octahedral field – t
2g

set

13. Splitting of the d-Orbitals
The dThe d
z2z2 and d and d
x2-y2 x2-y2 orbitals lie on the same orbitals lie on the same
axes as negative charges.axes as negative charges.
Therefore, there is a large, unfavorable Therefore, there is a large, unfavorable
interaction between ligand (-) orbitals.interaction between ligand (-) orbitals.
These orbitals form the degenerate These orbitals form the degenerate
high energy pair of energy levels.high energy pair of energy levels.

14. d Orbital Splitting
In some texts and articles, the gap in the d
orbitals is assigned a value of 10Dq.
The upper (e
g
) set goes up by 6Dq, and the
lower set (t
2g
) goes down by 4Dq.
The actual size of the gap varies with the
metal and the ligands.

15. The dThe d
xyxy , d , d
yxyx and d and d
xzxz orbitals bisect the orbitals bisect the
negative charges.negative charges.
Therefore, there is a smaller repulsion Therefore, there is a smaller repulsion
between ligand & metal for these orbitals.between ligand & metal for these orbitals.
These orbitals form the degenerate low These orbitals form the degenerate low
energy set of energy levels.energy set of energy levels.

16. d-orbitals not pointing directly at axis are least
affected (stabilized) by electrostatic interaction
d-orbitals pointing directly at axis are
affected most by electrostatic interaction

17. d Orbital Splitting
________
Spherical
field
__ __
d
z
2 d
x
2-
y
2
__ __ __
d
xy
d
xz
d
yz
∆
o
+ 0.6∆
o
- 0.4∆
o
Octahedral field
e
g
t
2g
Free ion

18. Splitting pattern – O
h

field
The energy gap is The energy gap is
referred to as referred to as
Do (10 Dq)
Also known as Also known as
crystal field splitting crystal field splitting
energyenergy

19. Factors affecting the magnitude of splitting
Many experiments have shown that the magnitude
of splitting is depending upon both metal and
ligands.
JORGENSON’S RELATION
Do = Do = f . gf . g
f – metal parameter
g – ligand parameter

20. Metal factors
Charge on the metal ion
Number of d- electrons
Principle quantum number of the metal d
electron

21. Number of d electrons - I
Different charges same metal (No. of d electrons)
[Fe(H
2
O)
6
]
2+
- 3 d
6
-10,400 cm
-1
[Fe(H
2
O)
6
]
3+
- 3d
5
- 13,700 cm
-1
[Co(H
2
O)
6
]
2+
- 3 d
7
- 9,300 cm
-1
[Co(H
2
O)
6
]
3+
- 3d
6
- 18,200 cm
-1

22. Number of d electrons - II
Same charge different metal ions
[Co(H
2
O)
6
]
2+
- 3 d
7
- 9,300 cm
-1
[Ni(H
2
O)
6
]
2+
- 3 d
8
- 8,500 cm
-1

23. Charge on the metal ion
Same charge different metal
[V(H
2
O)
6
]
2+
- 3d
3
- 12,400 cm
-1
[Cr(H
2
O)
6
]
2+
- 3d
3
-17,400 cm
-1

24. summary
For complexes having same geometry and
same ligands the crystal field splitting
Increases with the increase in charge on the
ion (Same number of d - electrons)
Decreases with increasing number of d -
electrons (Same charge on the ion)

25. Principle quantum number
With increasing n value the splitting increases
[Co(NH
3
)
6
]
3+
- 3d
6
- 23,000 cm
-1
[Rh(NH
3
)
6
]
3+
- 4d
6
- 34,000 cm
-1
[Ir(NH
3
)
6
]
3+
- 5d
6
- 41,000 cm
-1

26. Effect of ligand field
strength
Weak field Free ion strong field

27. Crystal field stabilisation
energy
Already it is seen that t2g levels are lowered
while e
g
levels are raised in energy.
The d – electron and ligand repulsion only
increases the energy.
But the energy content of the system must
be a constant.
So to maintain the centre of gravity the t
2g

levels are getting lowered to an equivalent
amount.

28. + 0.6 ∆o
- 0.4 ∆o
e
g
t
2g
Total energy change = 2 x (+ 0.6∆o) + 3 (- 0.4 ∆o) = 0

29. Crystal field stabilisation
energy
Depending upon the field created by the
ligands the electrons are occupying the
various orbitals available.
When t
2g
levels are getting filled the system is
getting lowered in energy
Energy content increases if e
g
levels are filled
If both of them are filled then the difference
between increases and decrease in energy is
calculated which is called crystal field
stabilisation energy

30. CFSE
Gain in energy = + 0.6 ∆o x p
Loss in energy = - 0.4 ∆o x q
 Net change in energy = [+ 0.6 x p + - 0.4 x q] ∆o
∆o = 10Dq
CFSE = [ -4Dq x q + 6Dq x p]

31. Splitting and Pairing
energy
Pairing energy is the energy required for
accommodating second electron as a spin
pair to the first one in an orbital, against the
electrostatic repulsion.
When the ligands are stronger, the splitting
of d orbitals is high.
If splitting energy is more than the pairing
energy then according to Hund’s rule the
incoming electrons start to pair in the t2g
level itself

32. .
Fourth e- has choice:
 Higher orbital if D is small; High spin
 Lower orbital if D is large: Low spin.
Weak field ligands - Small D - High spin complex
Strong field Ligands -Large D - Low spin complex

33. d
1
–d
3
systems
Weak field Free ion strong field
Do
Do
CFSE
d
1
- - 4Dq
d
2
- - 8Dq
d
3
- - 12Dq

34. Weak field d
4
Free ion strong field
CFSE - -6Dq CFSE - - 16Dq + P

35. Weak field d
5
-Free ion strong field
CFSE - - 20Dq + 2PCFSE - 0 Dq

36. Weak field d
6
-Free ion strong field
CFSE - - 24Dq + 3PCFSE - -4Dq +P

37. Weak field d
7
Free ion strong field
CFSE - - 18Dq + 3PCFSE - -8Dq +2P

38. Weak field d
8
Free ion strong field
CFSE - - 12Dq + 3PCFSE - -12Dq +3P

39. Weak field d
9
Free ion strong field
CFSE - -6Dq +4P

40. Weak field d
10
Free ion strong field
CFSE - 0Dq +5P

41. Crystal Field Stabilization Energy
The first row transition metals in water are all
weak field, high spin cases.
d
n
CFSE d
n
CFSE
1 -4Dq 6 -4Dq + P
2 -8Dq 7 -8Dq + 2P
3 -12Dq 8 -12Dq + 3P
4 -6Dq 9 -6Dq + 4P
5 0 10 0 + 5P

42. High Spin vs. Low Spin
3d metals are generally high spin complexes
except with very strong ligands. CN
-
forms
low spin complexes, especially with M
3+
ions.
4d & 5d metals generally have a larger value of
∆
o
than for 3d metals. As a result, complexes
are typically low spin.

43. Colour of the complex
The colors exhibited by most transition
metal complexes arises from the splitting of
the d orbitals.
As electrons transition from the lower t
2g
set
to the e
g
set, light in the visible range is
absorbed.

44. Colour of the complexes
The splitting due to the
nature of the ligand
can be observed and
measured using a
spectrophotometer
Smaller values of ∆
o

result in colors in the
green range. Larger
gaps shift the color to
yellow.

45. Spectrochemical / Fajan –Tsuchida
series
Depending on the ligands present in a
complex the splitting value varies.
By taking a particular metal, in a fixed
geometric field, the ligands are arranged in
the increasing order of the splitting caused
by them

46. Spectrochemical / Fajan –Tsuchida
series
I
-
< Br
-
<S
2-
<Cl
-
< NO
3
-
< N
3
-
< F
-
< OH
-
<
C
2
O
4
2-
< H
2
O < NCS
-
< CH
3
CN < pyridine <
NH
3
< en < bipy < phen < NO
2
-
< PPh
3
< CN
-
< CO
Field Strength increases
Field Strength increases
Field Strength increases

47. Color Absorption of Co
3+
Complexes
The Colors of Some Complexes of the CoThe Colors of Some Complexes of the Co
3+ 3+
IonIon
The complex with fluoride ion, [CoFThe complex with fluoride ion, [CoF
66]]
3+3+
, is high spin and has one absorption band. , is high spin and has one absorption band.
The other complexes are low spin and have two absorption bands. In all but one The other complexes are low spin and have two absorption bands. In all but one
case, one of these absorptionsis in the visible region of the spectrum. The case, one of these absorptionsis in the visible region of the spectrum. The
wavelengths refer to the center of that absorption band.wavelengths refer to the center of that absorption band.
Complex IonComplex IonWavelength of Wavelength of Color of Light Color of Light Color of ComplexColor of Complex
light absorbed light absorbed Absorbed Absorbed
[CoF[CoF
66] ]
3+3+
700 (nm)700 (nm) RedRed GreenGreen
[Co(C[Co(C
22OO
44))
33] ]
3+3+
600, 420600, 420 Yellow, violetYellow, violetDark greenDark green
[Co(H[Co(H
22O)O)
66] ]
3+3+
600, 400600, 400 Yellow, violetYellow, violetBlue-greenBlue-green
[Co(NH[Co(NH
33))
66] ]
3+3+
475, 340475, 340 Blue, violetBlue, violetYellow-orangeYellow-orange
[Co(en)[Co(en)
33] ]
3+3+
470, 340470, 340 Blue, ultraviolet Blue, ultravioletYellow-orangeYellow-orange
[Co(CN)[Co(CN)
66] ]
3+3+
310310 Ultraviolet UltravioletPale YellowPale Yellow

48. The Spectrochemical Series
The complexes of cobalt (III) show the shift in color due to the ligand.

(a) CN
–
(b) NO
2
–
(c) phen (d) en (e) NH
3
(f) gly (g) H
2
O (h) ox
2–
(i) CO
3
2–

49. Experimental Evidence for CFSE
The hydration energies of the first row
transition metals should increase across the
period as the size of the metal ion gets smaller.
M
2+
+ 6 H
2
O(l)  M(H
2
O)
6
2+
The heats of hydration show two “humps”
consistent with the expected LFSE for the metal
ions. The values for d
5
and d
10
are the same as
expected with a LFSE equal to 0.

50. Experimental Evidence for CFSE

51. Experimental Evidence of CFSE
dd
oo
dd
11
dd
22
dd
33
dd
44
dd
55
dd
66
dd
77
dd
88
dd
99
dd
1010
LFSELFSE
In terms In terms
of of ΔΔ
oo
00.4.4.8.81.21.2.6.600.4.4.8.81.21.2.6.6 00

52. Structure of spinels
Spinels are mixed oxides having general
formula AB
2
O
4
A is a divalent metal ion i.e. - A
2+
 B is a trivalent metal ion i.e. - B
3+
The metals A and B may be same or different
In spinels the oxide ions are arranged in cubic
close packed lattice

53. Structure of spinels
In such situation each oxide ion will have 12
neighboring oxide ion at equidistant
The lattice contains two types of coordination
sites
Octahedral holes- surrounded by six oxide
ions – one hole per one oxide ion
Tetrahedral holes –surrounded by four oxide
ions – two holes per one oxide ion

56. Structure of spinels
Number of tetrahedral holes is twice the
number of octahedral holes.
There are three types of spinels
Normal
 Inverse
Partially inverse

57. Normal spinel
 All the divalent cations occupy one of the eight
available tetrahedral holes
Trivalent cations occupy the octahedral holes
Represented as A
2+
[B
3+
2
]O
4
Examples: FeCr
2
O
4
, Mn
3
O
4
, FeCr
2
S
4
, ZnAl
2
S
4
and
ZnCr
2
Se
4

58. Structure of spinels

60. Structure of spinel - MgAl
2
O
4

61. Inverse spinels
All divalent ions and half of the trivalent ions
occupy octahedral holes and other half of the
trivalent cations in the tetrahedral holes.
Represented as B
3+
[A
2+
B
2+
]O
4
Examples: CuFe
2
O
4
, MgFe
2
O
4
, Fe
3
O
4,
TiMn
2
O
4
,
TiFe
2
O
4
, TiZn
2
O
4
and SnZn
2
O
4

64. Partial inverse spinels

Examples of partially inverse spinel structures
include MgFe
2
O
4
, MnFe
2
O
4
and NiAl
2
O
4

65. Reason for inversion
Let us consider the mixed oxides Mn3O4
(Normal spinel) and Fe3O4 (inverse spinel)
Oxide ions are creating a weak field
The table shows values of CFSE for the ions in
different sites
Site Mn
3+
(d
4
)Mn
2+
(d
5
)Fe
3+
(d
5
)Fe
2+
(d
6
)
Octahedral 6Dq 0 0 4Dq
Tetrahedral1.78Dq 0 0 2.67Dq

66. The values clearly shows that both trivalent
ions are having higher CFSE values at
octahedral holes.
So preferably they tend to occupy the
octahedral sites
This makes all the Mn
3+
ions to occupy the
octahedral sites and Mn
2+
ions in tetrahedral
sites
Thus Mn
3
O
4
is a normal spinel

67. In the case of Fe
3
O
4
, Fe
3+
ions are expected to
be in the tetrahedral holes .
 Fe
3+
ion in an octahedral hole is having higher
CFSE.
So half of them are occupying octahedral
sites making the structure inverse

68. Stabilisation of oxidation state
By using the CFSE values the stability of certain
oxidation state of a metal can be explained.
In aqueous solutions Co
2+
is stable and Co
3+
is not
formed easily
This is a direct consequence of higher CFSE for
[Co(H
2
O)
6
]
2+
(d
7
) [-8Dq]than [Co(H
2
O)
6
]
3+
(d
8
) [-4Dq]
Similarly [Co(NH
3
)
6
]
3+
(d
6
) [-24Dq] has higher CFSE
than [Co(NH
3
)
6
]
2+
(d
7
) [-18Dq] so it is more stable.

69. Stereochemistry of
complexes
Based on CFSE values we can say that why
Cu
2+
is forming only square planar complexes
rather than octahedral
SP symmetry complex has higher CFSE
Cu
2+
in SP CFSE = 1.22 ∆o
Cu
2+
in Oh CFSE = 0.18 ∆o