1. Transition-Metal Complexes are extremely colorful!
What is the origin of this
color?
K3[Fe(CN)6]
[Co(NH3)5Cl]Cl2

2. What’s responsible for these colors?…………….
green
green/blue
blue
purple
What’s responsible for these colors?…………….

3. Metal complex history
Alfred Werner postulated the existence of a symmetric “shell” of water ligands around nickel ions in 1893 – the coordination theory of metal complexes

4. How to explain the structure of metal complexes
Crystal field (CF) theory – Hans Bethe (1928 – University of Tubingen) “Termaufspaltung in Kristallen (Splitting of Terms in Crystals)”
Ligand field (LF) theory – John Van Vleck (1932 – Harvard University) “The Theory of the Variations in Paramagnetic Anisotropy among Different Salts of the Iron Group”

5. How to explain the structure of metal complexes
In the 1950s, new formulations of molecular orbital theory, such as those we’ve been studying, revitalized CF and LF theory.
Leslie Orgel ( Cambridge University), “The effects of crystal fields on the properties of transition-metal ions”

6. Crystal Field Theory
400
500
600
800
The relationship between colors and complex metal ions

7. Crystal Field Model
A purely ionic model for transition metal complexes.
Ligands are considered as point charge.
Predicts the pattern of splitting of d-orbitals.
Used to rationalize spectroscopic and magnetic properties.

8. d-orbitals: look attentively along the axis
Linear combination of
dz2-dx2 and dz2-dy2
d2z2-x2-y2

9. Octahedral Field

10. We assume an octahedral array of negative charges placed around the metal ion (which is positive).
The ligand and orbitals lie on the same axes as negative charges.
Therefore, there is a large, unfavorable interaction between ligand (-) and these orbitals.
These orbitals form the degenerate high energy pair of energy levels.
The dxy, dyz, and dxz orbitals bisect the negative charges.
Therefore, there is a smaller repulsion between ligand and metal for these orbitals.
These orbitals form the degenerate low energy set of energy levels.

12. In Octahedral Field
dx2-y2
dz2
dxy
dxz
dyz

15. In Tetrahedral Field

18. Magnitude of 
Oxidation state of the metal ion
[Ru(H2O)6] cm-1
[Ru(H2O)6] cm-1
Number of ligands and geometry
t< o
t= 4/9o
Nature of the ligand
I-<S2-<SCN-<Cl-<NO3-<N3-<F-<OH-<C2O42-<H2O<…..CN-<CO

19. Crystal Field Splitting Energy (CFSE)
In Octahedral field, configuration is: t2gx egy
Net energy of the configuration relative to the average energy of the orbitals is:
= (-0.4x + 0.6y)O
O = 10 Dq
BEYOND d3
In weak field: O  P, => t2g3eg1
In strong field O  P, => t2g4
P - paring energy

20. Ground-state Electronic Configuration, Magnetic Properties and Colour

21. When the 4th electron is assigned it will either go into the higher energy eg orbital at an energy cost of Do or be paired at an energy cost of P, the pairing energy. d4
Strong field =
Low spin
(2 unpaired)
Weak field =
High spin
(4 unpaired)
P < Do
P > Do
Coulombic repulsion energy and exchange energy

22. Ground-state Electronic Configuration, Magnetic Properties and Colour
[Mn(H2O)6]3+
Weak Field Complex
the total spin is 4  ½ = 2 High Spin Complex
[Mn(CN)6]3-
Strong field Complex
total spin is 2  ½ = 1
Low Spin Complex

23. Placing electrons in d orbitals
1 u.e.
5 u.e. d5
0 u.e.
4 u.e. d6
1 u.e.
3 u.e. d7
2 u.e. d8
1 u.e. d9
0 u.e.
d10

24. What is the CFSE of [Fe(CN)6]3-?
CN- = s.f.l.
C.N. = 6  Oh
Fe(III)  d5
l.s.
h.s. 3- eg
t2g
+ 0.6 Doct
- 0.4 Doct
CFSE = 5 x Doct + 2P =
- 2.0 Doct + 2P
If the CFSE of [Co(H2O)6]2+ is -0.8 Doct, what spin state is it in?
C.N. = 6  Oh
Co(II)  d7
l.s.
h.s. eg
t2g 2+
+ 0.6 Doct
- 0.4 Doct
CFSE = (5 x Doct)
+ (2 x 0.6 Doct) +2P = Doct+2P
CFSE = (6 x Doct)
+ (0.6 Doct) + 3P= Doct + P

25. The origin of the color of the transition metal compounds
Ligands influence O, therefore the colour

26. The colour can change depending on a number of factors e.g.
1. Metal charge
2. Ligand strength

27. Assigned transition: eg t2g This corresponds to the energy gap
The optical absorption spectrum of [Ti(H2O)6]3+
Assigned transition: eg t2g
This corresponds to the energy gap
O = 243 kJ mol-1

28. absorbed color
observed color

29. Spectrochemical Series: An order of ligand field strength based on experiment:
Weak Field
I-  Br- S2- SCN- Cl- NO3- F-  C2O42- H2O NCS- CH3CN NH3 en  bipy phen NO2- PPh3 CN- CO
Strong Field

30. causes an electron to be promoted into a higher energy orbital
d-orbitals
absorption of a photon
causes an electron to be
promoted into a higher
energy orbital
the photon energy
corresponds to
visible light

31. [CrF6]3-
[Cr(H2O)6]3+
[Cr(NH3)6]3+
[Cr(CN)6]3-
As Cr3+ goes from being attached to a weak field ligand to a strong field ligand,  increases and the color of the complex changes from green to yellow.

32. Limitations of CFT
Considers Ligand as Point charge/dipole only
Does not take into account of the overlap of ligand and metal orbitals
Consequence
e.g. Fails to explain why CO is stronger ligand than CN- in complexes having metal in low oxidation state

33. Metals in Low Oxidation States
In low oxidation states, the electron density on the metal ion is very high.
To stabilize low oxidation states, we require ligands, which can simultaneously bind the metal center and also withdraw electron density from it.

34. Stabilizing Low Oxidation State: CO Can Do the Job

35. Stabilizing Low Oxidation State: CO Can Do the Job
Ni(CO)4], [Fe(CO)5], [Cr(CO)6], [Mn2(CO)10], [Co2(CO)8], Na2[Fe(CO)4], Na[Mn(CO)5]

36. O C M
 orbital serves as a very weak donor to a metal atom

37. absorption of a photon
causes an electron to be
promoted into a higher
energy orbital
dz2
dz2
dxz

38. The d–orbitals point along the axes σ–type orbitals π–type orbitals
point between the axes

39. Notice: the d–orbitals
are not all
degenerate
dz2, dx2-y2
dxz, dxy, dyz
Thus, symmetry arguments alone tell us that the the d–orbitals split into two inequivalent sets

40. t1u a1g eg t2g M+n empty partially filled 4pz px py 4s 3dxz dyz dxy
dz2
dx2–y2
t2g eg
M+n

41. a1g* t1u a1g eg * HOMO-LUMO region t2g t2g eg eg M+n t1u eg a1g L t1u
Like SF6, except the d–orbitals
fall below the s and the p
a1g*
(σ∗)
The ligand LGO’s are all filled,
because each ligand contributes
a lone pair as part of its Lewis
base properties
4pz px py
the metal’s electrons
go into the HOMO/LUMO
region of the MO
t1u
splitting
corresponds
to a wavelength
of visible light 4s
a1g
eg *
dz2
dx2–y2
(σ∗)
HOMO-LUMO
region
dxy
t2g
dyz
dxz
3dxz
dyz
dxy
dz2
dx2–y2
(nonbonding)
t2g eg
LGO(1)
LGO(2)–LGO(4)
LGO(5)
LGO(6) eg
M+n
t1u eg
(σ)
a1g
the ligand electrons
fill the entire bonding
region of the MO
LGO pics L
t1u
(σ)

42. Oh Symmetry Adapted Orbitals
LGO(1)
LGO(5)
LGO(6)
LGO(2)
LGO(3)
LGO(4) 42

43. eg * ΔO t2g (σ∗) HOMO-LUMO region the octahedral ligand field
dz2
dx2–y2
(σ∗)
eg *
the octahedral
ligand field
splitting parameter
HOMO-LUMO
region ΔO
dyz
dxy
dxz
(nonbonding)
t2g

44. σ–bonding only a1g* t1u a1g eg * HOMO-LUMO region t2g t2g eg eg M+n
(σ∗)
σ–bonding only
4pz px py
t1u 4s
a1g
eg *
dz2
dx2–y2
(σ∗)
HOMO-LUMO
region
dxy
t2g
dyz
dxz
3dxz
dyz
dxy
dz2
dx2–y2
(nonbonding)
t2g eg
LGO(1)
LGO(2)–LGO(4)
LGO(5)
LGO(6) eg
M+n
t1u eg
(σ)
a1g L
t1u
(σ)

45. π–interaction with some
π–bonding influences the magnitude
of the d–orbital splitting ΔO
dz2
dx2–y2
(σ∗)
dz2
dx2–y2
(σ∗)
eg *
eg * ΔO
π–acceptors ΔO
(NO, CO, CN–)
dyz
dxy
dxz
(nonbonding)
t2g
dxy
dxz
dyz
t2g
(π)
σ–bonding only
π–interaction with some
ligands causes this splitting
to increase

46. σ–bonding only a1g* t1u a1g eg * HOMO-LUMO region t2g t2g eg eg M+n
(σ∗)
σ–bonding only
4pz px py
t1u 4s
a1g
eg *
dz2
dx2–y2
(σ∗)
HOMO-LUMO
region
dxy
t2g
dyz
dxz
3dxz
dyz
dxy
dz2
dx2–y2
(nonbonding)
t2g eg
LGO(1)
LGO(2)–LGO(4)
LGO(5)
LGO(6) eg
M+n
t1u eg
(σ)
a1g L
t1u
(σ)

47. π–bonding with a π-acceptor ligand a1g* t1u a1g eg * HOMO-LUMO region
(σ∗)
4pz px py
t1u 4s
a1g
eg *
dz2
dx2–y2
(σ∗)
HOMO-LUMO
region
3dxz
dyz
dxy
dz2
dx2–y2
dxy
t2g
dyz
dxz
t2g eg
LGO(1)
LGO(2)–LGO(4)
LGO(5)
LGO(6) eg
M+n
t1u eg
(σ)
a1g L
t1u
(σ)

48. Oh Symmetry Adapted Orbitals
π–symmetry orbitals 48

49. π–bonding interactions occur with the metal’s t2g orbitals
another LGO with
t2g symmetry
dyz L L z y M x L L
the d–orbital shown above
only interacts with
ligands that lie along the
y– and z–axes

50. π–bonding interactions occur with the metal’s t2g orbitals
a third LGO with
t2g symmetry
dxy L z y L M L x L
the d–orbital shown above
only interacts with
ligands that lie along the
y– and x–axes

51. π–interaction with some
π–bonding influences the magnitude
of the d–orbital splitting ΔO
dz2
dx2–y2
(σ∗)
dz2
dx2–y2
(σ∗)
eg *
eg *
π–donors ΔO ΔO
dxy
dxz
dyz
t2g
(π*)
dyz
dxy
dxz
(nonbonding)
t2g
Cl–, SR–, I–, Br–
σ–bonding only
π–interaction with some
ligands causes this splitting
to decrease

52. σ–bonding only a1g* t1u a1g eg * HOMO-LUMO region t2g t2g eg eg M+n
(σ∗)
σ–bonding only
4pz px py
t1u 4s
a1g
eg *
dz2
dx2–y2
(σ∗)
HOMO-LUMO
region
dxy
t2g
dyz
dxz
3dxz
dyz
dxy
dz2
dx2–y2
(nonbonding)
t2g eg
LGO(1)
LGO(2)–LGO(4)
LGO(5)
LGO(6) eg
M+n
t1u eg
(σ)
a1g L
t1u
(σ)

53. π–bonding with a π-donor ligand a1g* t1u a1g eg * HOMO-LUMO region t2g
(σ∗)
4pz px py
t1u 4s
a1g
eg *
dz2
dx2–y2
(σ∗)
HOMO-LUMO
region
dxy
t2g
dyz
dxz
3dxz
dyz
dxy
dz2
dx2–y2
t2g eg
LGO(1)
LGO(2)–LGO(4)
LGO(5)
LGO(6) eg
M+n
t1u eg
(σ)
a1g L
t1u
(σ)

54. Properties of first row transition–metal complexes
generic ligand L
properties include:
• fairly covalent bonds
• highly colored
• paramagnetic
• highly reactive
(in many cases)
[Mn+L6](n-6q)
metal complex
the origin of these properties lie
in the metal ion’s electronic structure.
ie, the relative energies of the
d-orbitals, and their population
with electrons

55. π–interaction with some
π–bonding influences the magnitude
of the d–orbital splitting ΔO
dz2
dx2–y2
(σ∗)
dz2
dx2–y2
(σ∗)
eg *
eg *
π–donors ΔO ΔO
dxy
dxz
dyz
t2g
(π*)
dyz
dxy
dxz
(nonbonding)
t2g
Cl–, SR–, I–, Br–
σ–bonding only
π–interaction with some
ligands causes this splitting
to decrease

56. π–interaction with some
π–bonding influences the magnitude
of the d–orbital splitting ΔO
dz2
dx2–y2
(σ∗)
dz2
dx2–y2
(σ∗)
eg *
eg * ΔO
π–acceptors ΔO
(NO, CO, CN–)
dyz
dxy
dxz
(nonbonding)
t2g
dxy
dxz
dyz
t2g
(π)
σ–bonding only
π–interaction with some
ligands causes this splitting
to increase