1. High Spin Ground States: d2, d3, d6, and d7
We have taken care of the d0, d1, d4, d5, d6, d9, and d10 configurations. Now have to do d2, d3, d6, and d7 configurations. It turns out that all we have to do is solve d2.
d3 and d8 are both two d-holes in a spherical shell, yielding reversed splitting: 3, 2, 1
d2 and d7 both are electrons on top of a spherical shell yielding a splitting pattern: 1, 2, 3
But it is not so easy. Here is our approach:
We know the symmetry of the GS of the free d2 ion. How? We can get the terms for d2 using the methods applied earlier to p2, etc. They are 3F, 1D, 3P, 1G, 1S.
We identify the GS as 3F. How?
We saw earlier that F in octahedral environment splits to A2g + T1g + T2g; in tetrahedral we would get A2 + T1 + T2. Our problem is the energy ordering. Which is GS?
Thus the 3F GS for d2 splits into 3A2g + 3T1g + 3T2g. The 4F GS for d3 splits into 4A2g + 4T1g + 4T2g. Where did the spin multiplicities come from??
But how do we decide on what becomes the GS after the splitting due to the ligands?
We use a correlation diagram. It shows the affect of increasing the ligand field strength from zero (free ion) to very high where energy ordering is determined solely by the occupancy of the t2g and the eg orbitals.

2. d2
Free Ion terms
We have two electrons in the eg orbitals. It can be shown that these give rise to 1A1g, 1Eg, and 3A2g which have same energy in strong ligand field.
Connect the terms of the same symmetry without crossing.
Similarly, splitting occurs for these occupancies.
Real complexes
Configurations based on splitting of d electrons. Dominant in very strong fields.
We have included the 3T1g originating from the 3P. We will need it immediately. Same symmetry as lower energy 3T1g from the 3F.
Splitting of free ion terms.

3. Orgel diagram for d2, d3, d7, d8 ions
This curvature will complicate interpretation of spectra.
Energy
A2 or A2g
Same symmetry; crossing forbidden
And now
d2 and d7 in tetrahedral (reversed due to tetrahedral field)
and
d3 and d8 in octahedral (reversed due to d-holes).
Note the reversed ordering of the splitting coming from F (T1/T2/A2). The lower T1(g) now aims up and should cross the upper T1(g) but does not due to interaction with the upper T1(g). Now have strong curvature to avoid crossing.
First look at
d2 and d7 in octahedral (2 elecs on a spherical cloud)
and
d3 and d8 in tetrahedral (double reversal: d-holes and tetrahedral)
All states shown are of the same spin. Transitions occur between them but weakly.
Note the weak interaction of the two T1, the curvature.
T1 or T1g
T1 or T1g P
T1 or T1g
T2 or T2g
T1 or T1g
T1 or T1g F
T2 or T2g
T1 or T1g
A2 or A2g
d2, d7 tetrahedral d2, d7 octahedral
d3, d8 octahedral d3, d8 tetrahedral
Ligand field strength (Dq)

4. Move to Tanabe-Sugano diagrams.
d1 – d3 and d8 – d9 which have only high spin GS are easier. Here is d2.
Correlation diagram for d2.
Convert to Tanabe-Sugano.
Tanabe-Sugano

5. Electronic transitions and spectra
d2 Tanabe-Sugano diagram
V(H2O)63+, a d2 complex

6. Configurations having only high spin GSd2 d1 d9
Slight curving. d8 d3
Note the two lines curving away from each other.
Note the two lines curving away from each other.

7. Configurations having either high or low spin GS
The limit between
high spin and low spin

8. Determining Do from spectra
Exciting d-hole from eg to t2g
Exciting electron from t2g to eg
Exciting electron from t2g to eg
Exciting d-hole from eg to t2g
One transition allowed of energy Do

9. Determining Do from spectra
Here the mixing is not a problem since the “mixed” state is not involved in the excitation.
mixing d3 d8
Lowest energy transition = Do

10. E (T1gA2g) - E (T1gT2g) = Do
For d2 and d7 (=d5+d2) which involves mixing of the two T1g states, unavoidable problem.
Ground state and excited state
mixing which we saw earlier. d2
But note that the difference in energies of two excitations is Do. d7
E (T1gA2g) - E (T1gT2g) = Do
Make sure you can identify the transitions!!

11. Can use T-S to calculate Ligand Field Splitting. Ex: d2, V(H2O)63+
Observed spectrum
u1: 17,800 cm-1
u2: 25,700 cm-1
Technique: Fit the observed energies to the diagram.
We must find a value of the splitting parameter, Do/B, which provides two excitations with the ratio of 25,700/17,800 = 1.44
E/B
Now can use excitation energies
For u1: E/B = 17,800 cm-1 /B = 29 yielding B = 610 cm-1
By using 31 = Do/B = Do/610 obtain Do = 19,000 cm-1
The ratio of u2/u1 = 1.44 is obtained at Do / B= 31
First, clearly u1 should correspond to 3T1  3T2 But note that the u2 could correspond to either 3T1  3A2 or 3T1  3T1.
DO/B
Again, the root, basic problem is that the two T1 s have affected each other via mixing. The energy gap depends to some extent on the mixing!

12. The d5 case All possible transitions forbidden
Very weak signals, faint color

13. Jahn-Teller Effect found if there is an asymmetrically occupied e set.
Can produce two transitions.
This picture is in terms of the orbitals. Now for one derived from the terms.

14. Continue with d9
GS will have d-hole in either of the two eg orbitals. ES puts d-hole in either of the three t2g orbitals.
For example, the GS will have the d-hole in the x2-y2 orbital which is closer to the ligands.

15. Some examples of spectra

16. Charge transfer spectra
Metal character
LMCT
Ligand character
Ligand character
MLCT
Metal character
Much more intense bands

17. Coordination Chemistry Reactions of Metal Complexes

18. Substitution reactions
Labile complexes <==> Fast substitution reactions (< few min)
Inert complexes <==> Slow substitution reactions (>h)
a kinetic concept
Not to be confused with
stable and unstable (a thermodynamic concept; DGf <0)

19. Mechanisms of ligand exchange reactions in octahedral complexes
Ia if association
is more important
Id if dissociation
is more important

21. of dissociative reactions
Kinetics
of dissociative reactions
Using Steady State Approximation, concentration of ML5 is always very low;
rate of creation = rate of consumption

22. of interchange reactions
Fast equilibrium
K1 = k1/k-1
k-1 >> k2
Kinetics
of interchange reactions
Again, apply Steady State.
For [Y] >> [ML5X]
common experimental
condition!

23. Kinetics of associative reactions

24. Dissociative Associative
Principal mechanisms of ligand exchange in octahedral complexes
Dissociative
Associative

25. (5-coordinated intermediate)
MOST COMMON
Dissociative pathway
(5-coordinated intermediate)
Associative pathway
(7-coordinated intermediate)

26. Experimental evidence for dissociative mechanisms
Rate is independent of the nature of L

27. Experimental evidence for dissociative mechanisms
Rate is dependent on the nature of L

28. Inert and labile complexes
Some common thermodynamic and kinetic profiles
Exothermic
(favored, large K)
Large Ea, slow reaction
Exothermic
(favored, large K)
Large Ea, slow reaction
Stable intermediate
Endothermic
(disfavored, small K)
Small Ea, fast reaction

29. Labile or inert?
LFAE = LFSE(sq pyr) - LFSE(oct)

30. Why are some configurations inert and some are labile?

31. Substitution reactions in square-planar complexes
the trans effect
(the ability of T to labilize X)

32. Synthetic applications
of the trans effect
Cl- > NH3, py

33. Mechanisms of ligand exchange reactions in square planar complexes

34. Electron transfer (redox) reactions
-1e (oxidation)
M1(x+)Ln + M2(y+)L’n
M1(x +1)+Ln + M2(y-1)+L’n
+1e (reduction)
Very fast reactions (much faster than ligand exchange)
May involve ligand exchange or not
Very important in biological processes (metalloenzymes)

35. Reactions ca. 100 times faster than ligand exchange
Outer sphere mechanism
[Fe(CN)6] [IrCl6]2-
[Fe(CN)6] [IrCl6]3-
[Co(NH3)5Cl]+ + [Ru(NH3)6]3+
[Co(NH3)5Cl] [Ru(NH3)6]2+
Reactions ca times faster
than ligand exchange
(coordination spheres remain the same)
r = k [A][B]
Tunneling
mechanism

36. Inner sphere mechanism
[Co(NH3)5Cl)]2+:::[Cr(H2O)6]2+
[Co(NH3)5Cl)] [Cr(H2O)6]2+
[Co(NH3)5Cl)]2+:::[Cr(H2O)6]2+
[CoIII(NH3)5(m-Cl)CrII(H2O)6]4+
[CoII(NH3)5(m-Cl)CrIII(H2O)6]4+
[CoIII(NH3)5(m-Cl)CrII(H2O)6]4+
[CoII(NH3)5(m-Cl)CrIII(H2O)6]4+
[CoII(NH3)5(H2O)]2+ + [CrIII(H2O)5Cl]2+
[CoII(NH3)5(H2O)]2+
[Co(H2O)6] NH4+

37. than outer sphere electron transfer (bridging ligand often exchanged)
Inner sphere mechanism
Reactions much faster
than outer sphere electron transfer
(bridging ligand often exchanged)
r = k’ [Ox-X][Red] k’ = (k1k3/k2 + k3)
Tunneling
through bridge
mechanism