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1. V.SANTHANAM
DEPARTMENT OF CHEMISTRY
SCSVMV

2. Tetragonal Complexes
 Six coordinate complexes, notably those of
Cu2+
, distort from octahedral geometry.
 One such distortion is called tetragonal
distortion, in which the bonds along one axis
elongate, with compression of the bond
distances along the other two axes.

3. Tetragonal Complexes
 The elongation along
the z axis causes the d
orbitals with density
along the axis to drop in
energy.
 As a result, the dxz and
dyz orbitals lower in
energy.

4. Tetragonal Complexes
The compression
along the x and y axis
causes orbitals with
density along these
axes to increase in
energy.
.

5. Tetragonal Complexes
For complexes with 1-3 electrons in the eg set of orbitals, this
type of tetragonal distortion may lower the energy of the
complex.

6. Square Planar Complexes
For complexes with 2
electrons in the eg set of
orbitals, a d8
configuration,
a severe distortion may
occur, resulting in a 4-
coordinate square planar
shape, with the ligands
along the z axis no longer
bonded to the metal.

7. Square Planar Complexes
Square planar
complexes are quite
common for the d8
metals
in the 4th
and 5th
periods:
Rh(I), IR(I), Pt(II), Pd(II) and
Au(III). The lower transition
metals have large ligand
field stabalization energies,
favoring four-coordinate
complexes.

8. Square Planar Complexes
Square planar
complexes are rare for the
3rd
period metals. Ni(II)
generally forms tetrahedral
complexes. Only with very
strong ligands such as CN-
,
is square planar geometry
seen with Ni(II).

9. Square Planar Complexes
The value of ∆sp for a
given metal, ligands and
bond length is
approximately 1.3(∆o).

10. 4 – Coordinate Complexes
 Square planar and tetrahedral complexes are
quite common for certain transition metals.
 The splitting patterns of the d orbitals on the
metal will differ depending on the geometry
of the complex.

11. Tetrahedral Complexes
 The dz2 and dx2-y2 orbitals point
directly between the ligands in
a tetrahedral arrangement.
 As a result, these two orbitals,
designated as e in the point
group Td, are lower in energy.

12. Tetrahedral Complexes
 The t2 set of orbitals,
consisting of the dxy, dyz, and dxz
orbitals, are directed more in
the direction of the ligands.
 These orbitals will be higher
in energy in a tetrahedral field
due to repulsion with the
electrons on the ligands.

13. Tetrahedral Complexes
 The size of the splitting, ∆T, is
considerable smaller than
with comparable octahedral
complexes.
 This is because only 4 bonds
are formed, and the metal
orbitals used in bonding don’t
point right at the ligands as
they do in octahedral
complexes.

14. Tetrahedral Complexes
In general, ∆T ≈ 4/9
∆o. Since the splitting is
smaller, all tetrahedral
complexes are weak-
field, high-spin cases.

15. Octahedral, Tetrahedral & Square
Planar
CF Splitting pattern for
CF Splitting pattern for
various molecular geometry
various molecular geometry
M
dz2
dx2-y2
dxz
dxy
dyz
M
dx2-y2
dz2
dxz
dxy dyz
M
dxz
dz2
dx2-y2
dxy
dyz
Octahedral
Tetrahedral
Tetrahedral Square planar
Square planar
Pairing energy Vs. ∆
Weak field ∆ < Pe
Strong field ∆ > Pe
Pairing energy Vs. ∆
Weak field ∆ < Pe
Strong field ∆ > Pe
Small ∆  High Spin
Small ∆  High Spin Mostly d8
(Majority Low spin)
Strong field ligands
i.e., Pd2+
, Pt2+
, Ir+
, Au3+
Mostly d8
(Majority Low spin)
Strong field ligands
i.e., Pd2+
, Pt2+
, Ir+
, Au3+

16. The Jahn-Teller Effect
If the ground electronic configuration of a
non-linear complex is orbitally degenerate,
the complex will distort so as to remove the
degeneracy and achieve a lower energy.

17. The Jahn-Teller Effect
 The Jahn-Teller effect predicts which
structures will distort.
 It does not predict the nature or extent of the
distortion.
 The effect is most often seen when the orbital
degneracy is in the orbitals that point directly
towards the ligands.

18. The Jahn-Teller Effect
In octahedral complexes, the effect is
most pronounced in high spin d4
, low spin d7
and d9
configurations, as the degeneracy
occurs in the eg set of orbitals.
d4
d7
d9
eg
t2g

19. The Jahn-Teller Effect
The strength of the Jahn-Teller effect is
tabulated below: (w=weak, s=strong)
# e
# e-
-
1
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
10
High
High
spin
spin
*
* *
* *
* s
s -
- w
w w
w *
* *
* *
*
Low
Low
spin
spin
w
w w
w -
- w
w w
w -
- s
s -
- s
s -
-
*There is only 1 possible ground state configuration.
- No Jahn-Teller distortion is expected.

20. Summary
Crystal Field Theory provides a basis for explaining
many features of transition-metal complexes.
Examples include why transition metal complexes
are highly colored, and why some are paramagnetic
while others are diamagnetic.
The spectrochemical series for ligands explains nicely
the origin of color and magnetism for these
compounds.
 There is evidence to suggest that the metal-ligand
bond has covalent character which explains why these
complexes are very stable.
Molecular Orbital Theory can also be used to
describe the bonding scheme in these complexes.

21. Ligand Field Theory
Crystal Field Theory completely ignores
the nature of the ligand. As a result, it cannot
explain the spectrochemical series.
Ligand Field Theory uses a molecular
orbital approach. Initially, the ligands can be
viewed as having a hybrid orbital or a p orbital
pointing toward the metal to make σ bonds.

23. Ligand Field Theory
The A1ggroup
orbitals have the
same symmetry as an
s orbital on the
central metal.

24. Ligand Field Theory
TheT1ugroup
orbitals have the
same symmetry as
the p orbitals on the
central metal.
(T representations
are triply
degenerate.)

25. Ligand Field Theory
The Eggroup
orbitals have the
same symmetry as
the dz2 and dx2-y2
orbitals on the central
metal.
(E representations
are doubly
degenerate.)

26. Ligand Field Theory
Since the ligands
don’t have a
combination with t2g
symmetry, the dxy, dyz
and dxy orbitals on the
metal will be non-
bonding when
considering σ bonding.

27. Ligand Field Theory
The molecular
orbital diagram is
consistent with
the crystal field
approach.
Note that the
t2g set of orbitals is
non-bonding, and
the eg set of
orbitals is
antibonding.

28. Ligand Field Theory
The electrons
from the ligands
(12 electrons
from 6 ligands in
octahedral
complexes) will
fill the lower
bonding orbitals.
{

29. Ligand Field Theory
The electrons
from the 4s and
3d orbitals of the
metal (in the first
transition row)
will occupy the
middle portion of
the diagram.
{

30. Experimental Evidence for
Splitting
Several tools are used to confirm the
splitting of the t2g and eg molecular orbitals.
The broad range in colors of transition
metal complexes arises from electronic
transitions as seen in the UV/visible spectra of
complexes.
Additional information is gained from
measuring the magnetic moments of the
complexes.

31. Experimental Evidence for
Splitting Magnetic
susceptibility
measurements can be
used to calculate the
number of unpaired
electrons in a compound.
Paramagnetic
substances are attracted
to a magnetic field.

32. Magnetic Moments
A magnetic balance can be used to
determine the magnetic moment of a
substance. If a substance has unpaired
electrons, it is paramagnetic, and attracted to
a magnetic field.
For the upper transition metals, the spin-
only magnetic moment, μs, can be used to
determine the number of unpaired electrons.
μs = [n(n+2)]1/2

33. Magnetic Moments
The magnetic moment of a substance, in
Bohr magnetons, can be related to the
number of unpaired electrons in the
compound.
μs = [n(n+2)]1/2
Where n is the number of unpaired electrons

34. Magnetic Moments
Complexes with 4-7 electrons in the d
orbitals have two possibilities for the
distribution of electrons. The complexes can
be low spin, in which the electrons occupy the
lower t2g set and pair up, or they can be high
spin. In these complexes, the electrons will fill
the upper eg set before pairing.

35. Considering π Bonding
To obtain Γred for π bonding, a set of
cartesian coordinates is established for each
of the ligands. The direction of the σ bonds is
arbitrarily set as the y axis (or the py orbitals).
The px and pz orbitals are used in π bonding.

36. Considering π
Bonding
O
Oh
h E
E 8C
8C3
3 6C
6C2
2 6C
6C4
4
3C
3C2
2
(=C
(=C4
4
2
2
)
)
i
i 6S
6S4
4 8S
8S6
6 3
3σ
σh
h 6
6σ
σd
d
Γ
Γπ
π 12
12 0
0 0
0 0
0 -4
-4 0
0 0
0 0
0 0
0 0
0
y y
y
y y
y
x
x
x
x
x
x
z
z
z
z
z
z
Consider only the px and
pz orbitals on each of the
ligands to obtain Γπ.

37. Considering π Bonding
O
Oh
h E
E 8C
8C3
3 6C
6C2
2 6C
6C4
4
3C
3C2
2
(=C
(=C4
4
2
2
)
)
i
i 6S
6S4
4 8S
8S6
6 3
3σ
σh
h 6
6σ
σd
d
Γ
Γπ
π 12
12 0
0 0
0 0
0 -4
-4 0
0 0
0 0
0 0
0 0
0
This reduces toT1g +T2g +T1u +T2u. TheT2g set has the
same symmetry as the dxy, dyz and dxz orbitals on the
metal. TheT1u set has the same symmetry as the px, py
and pz orbitals on the metal.

38. Considering π Bonding
Τπ reduces to: T1g +T2g +T1u +T2u.
 TheT1g andT2u group orbitals for the ligands don’t
match the symmetry of any of the metal orbitals.
 TheT1u set has the same symmetry as the px, py and pz
orbitals on the metal. These orbitals are used primarily
to make the σ bonds to the ligands.
 TheT2g set has the same symmetry as the dxy, dyz and dxz
orbitals on the metal.

39. π Bonding
The main source of π bonding is between the
dxy, dyz and dxz orbitals on the metal and the d, p or
π* orbitals on the ligand.

40. π Bonding
The ligand may have empty d or π* orbitals
and serve as a π acceptor ligand, or full p or d
orbitals and serve as a π donor ligand.

41. π Bonding
The empty π antibonding orbital on CO can
accept electron density from a filled d orbital on
the metal. CO is a pi acceptor ligand.
empty π*
orbital
filled d
orbital

42. π Donor Ligands (LM)
All ligands are σ donors. Ligands with
filled p or d orbitals may also serve as pi donor
ligands. Examples of π donor ligands are I-
,
Cl-
, and S2-
. The filled p or d orbitals on these
ions interact with the t2g set of orbitals (dxy, dyz
and dxz) on the metal to form bonding and
antibonding molecular orbitals.

43. π Donor Ligands (LM)
The bonding orbitals,
which are lower in energy,
are primarily filled with
electrons from the ligand,
the and antibonding
molecular orbitals are
primarily occupied by
electrons from the metal.

44. π Donor Ligands (LM)
The size of ∆o
decreases, since it is now
between an antibonding t2g
orbital and the eg* orbital.
This is confirmed by the
spectrochemical series.
Weak field ligands are also
pi donor ligands.

45. π Acceptor Ligands (ML)
Ligands such as CN,
N2 and CO have empty
π antibonding orbitals
of the proper symmetry
and energy to interact
with filled d orbitals on
the metal.

46. π Acceptor Ligands (ML)
The metal uses the
t2g set of orbitals (dxy, dyz
and dxz) to engage in pi
bonding with the
ligand. The π* orbitals
on the ligand are
usually higher in energy
than the d orbitals on
the metal.

47. π Acceptor Ligands (ML)
The metal uses the
t2g set of orbitals (dxy, dyz
and dxz) to engage in pi
bonding with the
ligand. The π* orbitals
on the ligand are
usually higher in energy
than the d orbitals on
the metal.

48. π Acceptor Ligands (ML)
The interaction
causes the energy of
the t2g bonding orbitals
to drop slightly, thus
increasing the size of
∆o.

50. Summary
1. All ligands are σ donors. In general, ligand
that engage solely in σ bonding are in the
middle of the spectrochemical series. Some
very strong σ donors, such as CH3
-
and H-
are
found high in the series.
2. Ligands with filled p or d orbitals can also
serve as π donors. This results in a smaller
value of ∆o.

51. Summary
3. Ligands with empty p, d or π* orbitals can
also serve as π acceptors. This results in a
larger value of ∆o.
I-
<Br-
<Cl-
<F-
<H2O<NH3<PPh3<CO
π donor< weak π donor<σ only< π acceptor