1. Coordination Chemistry II
Bonding, including crystal field theory and ligand field theory

2. Basis for Bonding Theories
Models for the bonding in transition metal complexes must be consistent with observed behavior. Specific data used include stability (or formation) constants, magnetic susceptibility, and the electronic (UV/Vis) spectra of the complexes.

3. Bonding Approaches
Valence Bond theory provides the hybridization for octahedral complexes. For the first row transition metals, the hybridization can be: d2sp3 (using the 3d, 4s and 4p orbitals), or sp3d2 (using the 4s, 4p and 4d orbitals).
The valence bond approach isn’t used because it fails to explain the electronic spectra and magnetic moments of most complexes.

5. Crystal Field Theory
In crystal field theory, the electron pairs on the ligands are viewed as point negative charges that 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. Crystal Field Theory
Ligands, viewed as point charges, at the corners of an octahedron affect the various d orbitals differently.

8. Crystal Field Theory

9. 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.

10. d Orbital Splitting __ __ dz2 dx2-y2 ∆o __ __ __ __ __ __ __ __
__ __
dz2 dx2-y2 eg
0.6∆o ∆o
__ __ __ __ __
Spherical field
0.4∆o
__ __ __
dxy dxz dyz
t2g
Octahedral field

11. d Orbital Splitting
In some texts and articles, the gap in the d orbitals is assigned a value of 10Dq. The upper (eg) set goes up by 6Dq, and the lower set (t2g) goes down by 4Dq.
The actual size of the gap varies with the metal and the ligands.

12. d Orbital Splitting
The colors exhibited by most transition metal complexes arises from the splitting of the d orbitals. As electrons transition from the lower t2g set to the eg set, light in the visible range is absorbed.

13. d Orbital Splitting
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.

14. The Spectrochemical Series
Based on measurements for a given metal ion, the following series has been developed:
I-<Br-<S2-<Cl-<NO3-<N3-<F-<OH-<C2O42-<H2O
<NCS-<CH3CN<pyridine<NH3<en<bipy<phen
<NO2-<PPh3<CN-<CO

15. The Spectrochemical Series
The complexes of cobalt (III) show the shift in color due to the ligand.
(a) CN–, (b) NO2–, (c) phen, (d) en, (e) NH3, (f) gly, (g) H2O, (h) ox2–, (i) CO3 2–.

16. Ligand Field Strength Observations
1. ∆o increases with increasing oxidation number on the metal.
Mn+2<Ni+2<Co+2<Fe+2<V+2<Fe+3<Co+3
<Mn+4<Mo+3<Rh+3<Ru+3<Pd+4<Ir+3<Pt+4
2. ∆o increases with increases going down a group of metals.

17. 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.

19. Octahedral Symmetry

20. Octahedral Symmetry

21. Ligand Field Theory
Consider the group orbitals of all six ligands in octahedral geometry. Oh E
8C3
6C2
6C4
3C2 (=C42) i
6S4
8S6
3σh
6σd Γσ 6 2 4
This reduces to A1g + Eg + T1u

22. Ligand Field Theory
The A1g group orbitals have the same symmetry as an s orbital on the central metal.

23. Ligand Field Theory (T representations are triply degenerate.)
The T1u group orbitals have the same symmetry as the p orbitals on the central metal.
(T representations are triply degenerate.)

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

25. 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.

26. 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.

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

28. 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. {

29. 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.

30. 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.

31. 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

32. Where n is the number of unpaired electrons
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

33. 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.

34. High and Low Spin Complexes
If the gap between the d orbitals is large, electrons will pair up and fill the lower (t2g) set of orbitals before occupying the eg set of orbitals. The complexes are called low spin.

35. High and Low Spin Complexes
In low spin complexes, the size of ∆o is greater than the pairing energy of the electrons.

36. High and Low Spin Complexes
If the gap between the d orbitals is small, electrons will occupy the eg set of orbitals before they pair up and fill the lower (t2g) set of orbitals before. The complexes are called high spin.

37. High and Low Spin Complexes
In high spin complexes, the size of ∆o is less than the pairing energy of the electrons.

38. Ligand Field Stabilization Energy
The first row transition metals in water are all weak field, high spin cases. do d1 d2 d3 d4 d5 d6 d7 d8 d9
d10
LFSE
.4Δo .8
1.2 .6 .4

39. Experimental Evidence for LFSE
The hydration energies of the first row
transition metals should increase across the period as the size of the metal ion gets smaller.
M H2O(l)  M(H2O)62+

40. Experimental Evidence for LFSE
The heats of hydration show two “humps” consistent with the expected LFSE for the metal ions. The values for d5 and d10 are the same as expected with a LFSE equal to 0.

41. Experimental Evidence of LFSEdo d1 d2 d3 d4 d5 d6 d7 d8 d9
d10
LFSE
.4Δo .8
1.2 .6 .4

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 M3+ ions.
4d & 4d metals generally have a larger value of ∆o than for 3d metals. As a result, complexes are typically low spin.

43. Effect of Metal Charge on Splitting

44. Nature of the Ligands
Crystal field theory and ligand field theory differ in that LFT considers the nature of the ligands. Thus far, we have only viewed the ligands as electron pairs used for making σ bonds with the metal. Many ligands can also form π bonds with the metal. Group theory greatly simplifies the construction of molecular orbital diagrams.

45. 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.

46. Considering π Bonding z x z y x y x y y x
Consider only the px and pz orbitals on each of the ligands to obtain Γπ. z z y z x y z x Oh E
8C3
6C2
6C4
3C2 (=C42) i
6S4
8S6
3σh
6σd Γπ 12 -4

47. Considering π Bonding Oh E 8C3 6C2 6C4 3C2 (=C42) i 6S4 8S6 3σh 6σd Γπ12 -4
This reduces to T1g + T2g + T1u + T2u. The T2g set has the same symmetry as the dxy, dyz and dxz orbitals on the metal. The T1u set has the same symmetry as the px, py and pz orbitals on the metal.

48. Considering π Bonding
π reduces to: T1g + T2g + T1u + T2u.
The T1g and T2u group orbitals for the ligands don’t match the symmetry of any of the metal orbitals.
The T1u 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.
The T2g set has the same symmetry as the dxy, dyz and dxz orbitals on the metal.

49. 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.

50. 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.

51. π Bonding empty π* orbital filled d orbital
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

52. 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.

53. 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.

54. σ Bonding vs.  Bonding

55. 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.

56. 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.

57. 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.

58. 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.

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

60. Effect of Ligand on Splitting

62. Summary
1. All ligands are σ donors. In general, ligands 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.

63. 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

64. 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.

65. 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.

66. 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.

67. Tetrahedral Complexes
The size of the splitting, ∆T, is considerably 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.

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

69. 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.

70. 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.

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

72. 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.

73. 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.

74. 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 stabilization energies, favoring four-coordinate complexes.

75. 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).

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

77. 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.

78. 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.

79. 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.
d d7 d9 eg
t2g

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