1. Placing electrons in d orbitals (strong vs weak field)
Strong field Weak field
Strong field Weak field d1 d2
Strong field Weak field
Strong field Weak field d3 d4
So, what is going on here!!

2. Strong field Weak field
When the 4th electron is assigned it will either go into the higher energy eg orbital at an energy cost of D0 or be paired at an energy cost of P, the pairing energy.
Strong field Weak field d4
Pairing Energy!!.
Strong field =
Low spin
(2 unpaired)
D0,
Weak field =
High spin
(4 unpaired)
P < Do
P > Do

3. = sum of all Pc and Pe interactions
Pairing Energy, P
The pairing energy, P, is made up of two parts.
Pc: Coulombic repulsion energy caused by having two electrons in same orbital. Destabilizing energy contribution of Pc for each doubly occupied orbital.
Pe: Exchange stabilizing energy for each pair of electrons having the same spin and same energy. Stabilizing contribution of Pe for each pair having same spin and same energy
= sum of all Pc and Pe interactions
How do we get these interactions?

4. Placing electrons in d orbitals
High Low
High Low
High Low
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

5. Detail working out…. d5 1 u.e. 5 u.e.
High Field Low Field (Low Spin) (High Spin)
What are the energy terms for both high spin and low spin?
1 u.e.
5 u.e. d5
Low Field
Coulombic Part = 0
High Field
Exchange part = for 3Pe + Pe
Coulombic Part = 2Pc
P = 4Pe
Exchange part = for 3Pe
LFSE = 3*(-2/5D0) + 2 (3/5D0) = 0
For Pe
P = 2Pc + 4Pe
High Field – Low Field = -2D0 +2Pe
LFSE = 5 * (-2/5D0) = -2D0
When D0 is larger than Pe the high field arrangement (low spin) is favored.

6. Positive favors high spin. Neg favors low spin.

7. Interpretation of Enthalpy of Hydration of hexahydrate using LFSE
d0 d d2 d3 d4 d5 d6 d7 d8 d9 d10
LFSE (in D0)

8. Splitting of d orbitals in a tetrahedral fieldDt e
Dt = 4/9Do
Always weak field (high spin)

10. Extreme elongation: from octahedral to square planar
Less repulsions along the axes
where ligands are missing

11. A correction to preserve
A crystal-field aproach: from octahedral to square planar
A correction to preserve
center of gravity

12. Magnetic properties of metal complexes
Diamagnetic complexes
very small repulsive interaction with external magnetic field
no unpaired electrons
Paramagnetic complexes
attractive interaction with external magnetic field
some unpaired electrons

13. Values of magnetic moment

14. Measured magnetic moments include contributions from both spin and orbital spin. In the first transition series complexes the orbital contribution is small and usually ignored.

15. Coordination Chemistry: Molecular orbitals for metal complexes

16. The symmetry of metal orbitals in an octahedral environment
A1g
T1u

17. The symmetry of metal orbitals in an octahedral environment
T2g Eg

18. The symmetry of metal orbitals in an octahedral environment

19. Metal-ligand s interactions in an octahedral environment
Six ligand orbitals of s symmetry approaching the metal ion along the x,y,z axes
We can build 6 group orbitals of s symmetry as before
and work out the reducible representation

20. s
If you are given G, you know by now how to get the irreducible representations
G = A1g + T1u + Eg

21. Now we just match the orbital symmetries

22. non bonding
anti bonding
“metal character”
“d0-d10 electrons”
6 s ligands x 2e each
12 s bonding e
“ligand character”

23. Introducing π-bonding
2 orbitals of π-symmetry
on each ligand
We can build 12 group orbitals
of π-symmetry

24. We now look at things more closely.
Gπ = T1g + T2g + T1u + T2u
The T2g will interact with the metal d t2g orbitals. The ligand pi orbitals do not interact with the metal eg orbitals.
We now look at things more closely.

25. Anti-bonding LUMO(π)
First, the CN- ligand

26. Some schematic diagrams showing how p bonding occurs with a ligand having a d orbital (such as in P), or a p* orbital, or a vacant p orbital.

27. The bonding orbitals, essentially the ligand lone pairs,
ML6 s-only bonding
non bonding
anti bonding
“metal character”
“d0-d10 electrons”
The bonding orbitals, essentially the ligand lone pairs,
will not be worked with further.
6 s ligands x 2e each
12 s bonding e
“ligand character”

28. t2g eg eg t2g Stabilization π-bonding may be introduced
as a perturbation of the t2g/eg set:
Case 1 (CN-, CO, C2H4)
empty π-orbitals on the ligands
ML π-bonding (π-back bonding)
These are the SALC formed from the p orbitals of the ligands that can interac with the d on the metal.
t2g (π*)
t2g eg eg Do
D’o
Do has increased
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s + π
(empty π-orbitals on ligands)

29. eg eg t2g t2g t2g (π*) t2g (π) π-bonding may be introduced
as a perturbation of the t2g/eg set.
Case 2 (Cl-, F-)
filled π-orbitals on the ligands
LM π-bonding eg eg
D’o Do
Do has decreased
t2g (π*)
Destabilization
t2g
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s + π
(filled π-orbitals)

30. Putting it all on one diagram.
Strong field / low spin
Weak field / high spin

31. Spectrochemical Series
Purely s ligands:
D: en > NH3 (order of proton basicity)
donating which decreases splitting and causes high spin:
D: H2O > F > RCO2 > OH > Cl > Br > I (also proton basicity)
p accepting ligands increase splitting and may be low spin
D: CO, CN-, > phenanthroline > NO2- > NCS-

32. Merging to get spectrochemical series
CO, CN- > phen > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I-
Weak field, p donors small D high spin
Strong field, p acceptors large D low spin
s only

33. Turning to Square Planar Complexes
Most convenient to use a local coordinate system on each ligand with
y pointing in towards the metal. py to be used for s bonding.
z being perpendicular to the molecular plane. pz to be used for p bonding perpendicular to the plane, p^.
x lying in the molecular plane. px to be used for p bonding in the molecular plane, p|.

34. ML4 square planar complexes
ligand group orbitals and matching metal orbitals
s bonding
p bonding (in)
p bonding (perp)

35. ML4 square planar complexes
MO diagram
Sample π- bonding eg
s-only bonding

36. A crystal-field aproach: from octahedral to tetrahedral
Less repulsions along the axes
where ligands are missing

37. A correction to preserve
A crystal-field aproach: from octahedral to tetrahedral
A correction to preserve
center of gravity

38. “there cannot be unequal occupation of orbitals with identical energy”
The Jahn-Teller effect
Jahn-Teller theorem:
“there cannot be unequal occupation of orbitals with identical energy”
Molecules will distort to eliminate the degeneracy

40. Angular Overlap Method
An attempt to systematize the interactions for all geometries.
The various complexes may be fashioned out of the ligands above
Linear: 1,6
Trigonal: 2,11,12
T-shape: 1,3,5
Tetrahedral: 7,8,9,10
Square planar: 2,3,4,5
Trigonal bipyramid: 1,2,6,11,12
Square pyramid: 1,2,3,4,5
Octahedral: 1,2,3,4,5,6

41. Cont’d
All s interactions with the ligands are stabilizing to the ligands and destabilizing to the d orbitals. The interaction of a ligand with a d orbital depends on their orientation with respect to each other, estimated by their overlap which can be calculated.
The total destabilization of a d orbital comes from all the interactions with the set of ligands.
For any particular complex geometry we can obtain the overlaps of a particular d orbital with all the various ligands and thus the destabilization.

42. ligand
dz2
dx2-y2
dxy
dxz
dyz 1
1 es 2 3 4 5 6 7
1/3 8 9 10 11
3/16
9/16 12
1/4
Thus, for example a dx2-y2 orbital is destabilized by (3/4 +6/16) es = 18/16 es in a trigonal bipyramid complex due to s interaction. The dxy, equivalent by symmetry, is destabilized by the same amount. The dz2 is destabililzed by 11/4 es.