1. Electronic spectra of transition metal complexes
Chapter 7
Electronic spectra of transition metal complexes

2. 3d Multi-electron Complexes
The interaction is called Russel-Saunders or L-S coupling. The interactions produce atomic states called microstates that are described by a new set of quantum numbers. ML = total orbital angular momentum =Σml MS = total spin angular momentum = Σms

3. Determining the Energy States of an Atom
A microstate table that contains all possible combinations of ml and ms is constructed. Each microstate represents a possible electron configuration. Both ground state and excited states are considered.

4. Energy States
Microstates would have the same energy only if repulsion between electrons is negligible. In an octahedral or tetrahedral complex, microstates that correspond to different relative spatial distributions of the electrons will have different energies. As a result, distinguishable energy levels, called terms are seen.

5. Energy States
To obtain all of the terms for a given electron configuration, a microstate table is constructed. The table is a grid of all possible electronic arrangements. It lists all of the possible values of spin and orbital orientation. It includes both ground and excited states, and must obey the Pauli Exclusion Principle.

6. Constructing a Microstate Table
Consider an atom of carbon. Its highest occupied orbital has a p2 electron configuration. Microstates correspond to the various possible occupation of the px, py and pz orbitals.

7. Constructing a Microstate Table
ml = microstate: Configurations: ___ ___ ___ (1+,0+) ___ ___ ___ (0+,-1+) ___ ___ ___ (1+,-1+) These are examples of some of the ground state microstates. Others would have the electrons (arrows) pointing down.

8. Constructing a Microstate Table
ml = microstate: Configurations: ___ ___ ___ (1+,1-) ___ ___ ___ (0+,0-) ___ ___ ___ (-1+,-1-) These are examples of some of the excited state microstates.

9. Microstate Table for p2
For the carbon atom, ML will range from +2 down to -2, and MS can have values of +1 (both electrons “pointing up”), 0 (one electron “up”, one electron “down”), or -1 (both electrons “pointing down”).

10. Microstate Table for p2 The table includes all possible microstates.
    MS
The table includes all possible microstates. ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

11. Constructing a Microstate Table
Once the microstate table is complete, the microstates are collected or grouped into atomic (coupled) energy states.

12. Constructing a Microstate Table
For two electrons, L = l1+ l2, l1+ l2-1, l1+ l2-2,…│l1- l2│ For a p2 configuration, L = 1+1, 1+1-1, 1-1. The values of L are: 2, 1 and 0. L is always positive, and ranges from the maximum value of Σl.

13. Constructing a Microstate Table
For two electrons, S = s1+ s2, s1+ s2-1, s1+ s2-2,…│s1- s2│ For a p2 configuration, S = ½ + ½ , ½ + ½ -1. The values of S are: 1 and 0.

14. Atomic Quantum Numbers
Quantum numbers L and S describe collections of microstates, whereas ML and MS describe the individual microstates themselves.

15. Constructing a Microstate Table
The microstate table is a grid that includes all possible combinations of L, the total angular momentum quantum number, and S, the total spin angular momentum quantum number. For two electrons, L = l1+ l2, l1+ l2-1, l1+ l2-2,…│l1- l2│ S = s1+ s2, s1+ s2-1, s1+ s2-2,…│s1- s2│

16. Constructing a Microstate Table
Once the microstate table is complete, all microstates associated with an energy state with specific value of L and S are grouped. It doesn’t matter which specific microstates are placed in the group. Microstates are grouped and eliminated until all microstates are associated with a specific energy state or term.

17. Term Symbols
Each energy state or term is represented by a term symbol. The term symbol is a capitol letter that is related to the value of L.
L = 1 2 3 4
Term Symbol S P D F G

18. Term Symbols
The upper left corner of the term symbol contains a number called the multiplicity. The multiplicity is the number of unpaired electrons +1, or 2S+1.

19. Microstate Table for p2
    MS
Eliminate microstates with ML=+2-2, with Ms=0. ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

20. Microstate Table for p2
    MS
These microstates are associated with the term 1D. ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

21. Microstate Table for p2
    MS
Eliminate microstates with ML=+1-1, with Ms=+1-1 ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

22. Microstate Table for p2
    MS
Eliminate microstates with ML=+1-1, with Ms=+1-1 ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

23. Microstate Table for p2
    MS
These microstates are associated with the term 3P. ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

24. Microstate Table for p2
    MS
One microstate remains. It is associated with the term 1S. ML +1 -1
+2:
1+1-
+1:
1+0+
1-0- 0:
-1+1+
-1-1-
-1:
-1+0+
-1-0-
-2:
-1+-1-

25. Term States for p2
The term states for a p2 electron configuration are 1S, 3P, and 1D. The term symbol with the greatest multiplicity and highest value of ML will be the ground state. 3P is the ground state term for carbon.

26. Determining the Relative Energy of Term States
1. For a given electron configuration, the term with the greatest multiplicity lies lowest in energy. (This is consistent with Hund’s rule.) 2. For a term of a given multiplicity, the greater the value of L, the lower the energy.

27. Determining the Relative Energy of Term States
For a p2 configuration, the term states are 3P, 1D and 1S. The terms for the free atom should have the following relative energies: 3P< 1D <1S

28. Determining the Relative Energy of Term States
The rules for predicting the ground state always work, but they may fail in predicting the order of energies for excited states.

29. Energy States for a d2 Configuration
A microstate table for a d2 electron configuration will contain 45 microstates (ML = 4-4, and MS=1, 0 or -1) associated with the following terms: 1S, 1D, 1G, 3P, and 3F

30. Energy States for a d2 Configuration
Problem: Determine the ground state of a free atom with a d2 electron configuration, and place the terms in order of increasing energy.
1S, 1D, 1G, 3P, and 3F

31. Determining the Ground State Term
We only need to know the ground state term to interpret the spectra of transition metal complexes. This can be obtained without constructing a microstate table. The ground state will a) have the maximum multiplicity b) have the maximum value of ML for the configuration obtained in part (a).

32. Characteristics of electronic spectra
Wavelength Energy of electronic transition
Shape. Gaussian Band Shape - coupling of electronic and vibrational states
Intensity. Molar absorptivity,  (M1cm1) due to probability of electronic transitions.
d) Number of bands Transitions between States of given dn configuration.

33. Band intensity in electronic spectra (e)
Electronic transitions are controlled by quantum mechanical selection rules which determine the probability (intensity) of the transition.
Transition εmax (M1cm1)
Spin and Symmetry forbidden "d-d" bands
Spin allowed and Symmetry forbidden "d-d" bands (Oh)
(Td) 10 – 103
Spin and Symmetry allowed LMCT and MLCT bands x 104

34. Spin Selection Rule: There must be no change in the spin multiplicity (2S + 1) during the transition.
i.e. the spin of the electron must not change during the transition.
Symmetry (Laporte) Selection Rule: There must be a change in parity (g ↔ u) during the transition
Since s and d orbitals are g (gerade) and p orbitals are u(ungerade), only
s ↔ p and p ↔ d transitions are allowed and d → d transition are formally forbidden. [i.e. only transitions for which Δl = ± 1 are allowed].
d → d bands are allowed to the extent that the starting or terminal level of the transition is not a pure d-orbital. (i.e. it is a molecular orbital of the complex with both metal and ligand character).

35. States for dn configurations
Russel-Saunders Coupling
Angular momentum of individual electrons couple to give total angular
momentum for dn configuration ML = ∑ml
Spin momentum of individual electron spins couple together to give total
spin, S = ∑s
Inter-electronic repulsions between the electrons in the d orbitals give rise to
ground state and excited states for dn configurations.
States are labeled with Tern Symbols
Electonic transitions between ground and excited states are summarized in
Orgel and Tanabe-Sugano diagrams .
Term Symbols (labels for states) contain information about L and S for state Hund’s Rules. i) Ground state has maximum spin, S ii) For states of same spin, ground state has maximum L.

36. Number of d-d bands in electronic spectrum
Excitation from ground state to excited stated of dn configuration
Triple degeneracy of a d2 ion’s 3T2g ground state due to three possible sites for hole in t2g level
Singly degenerate 3T2g ground state. Only one possible arrangement for
three electrons in t2g level
Triple degenerate ground state for d7 Three possible sites for hole in t2g level
Singly degenerate 3T2g ground state. Only one possible arrangement for
six t2g electrons.

37. Labeling of d-d bands in electronic spectrum.
Consider states of dn configuration
Determine free ion ground state Term Symbol (labels for states)
Assign splitting of states in ligand field
Spectroscopic labeling of bands.
Orgel diagrams (high-spin)
Tanabe-Sugano diagrams (high-spin and low-spin)

38. Individual electron l = 2, ml = 2, 1, 0, -1, -2
Maximum ml = l
l = , 1, 2, 3,
Orbital: s, p, d , f
_______________________________
dn configuration, L = 0, 1, 2, 3, 4
Term Symbol S, P, D, F, G
ML = Σ ml, maximum ML = L
Spin Multiplicity = 2 S +1

39. Free ion ground state Term Symbols for dn configurations Term Symbols (labels for states) contain information about L and S for ground state Hund’s Rules. i) Ground state has maximum spin, S ii) For states of same spin, ground state has maximum L

42. Splitting of the weak field dn ground state terms in an octahedral ligand field
Ground state determined by inspection of degeneracy of terms for given dn

44. Orgel Diagrams
Mn3+
Ti3+
Cr3+
V2+

46. (a) [Ni(H20)6]2+ (b) [Ni(NH3)6]2+

48. The Tanabe-Sugano diagram for the d2 ion

49. Evidence for covalent bonding in metal-ligand interactions The Nephelauxetic Effect (“cloud expansion”)
Reduction in electron-electron repulsion upon complex formation
Racah Parameter, B: electron-elctronic repulsion parameter
Bo is the inter- electronic repulsion in the gaseous Mn+ ion.
B is the inter- electronic repulsion in the complexed MLxn+ ion.
The smaller values for B in the complex compared to free gaseous ion is taken as evidence of smaller inter-electronic repulsion in the complex due to a larger “molecular orbital” on account of overlap
of ligand and metal orbital, i.e. evidence of covalency (cloud expansion”).
Nephelauxetic Ratio, β = B Bo

50. Nephelauxetic Effect Nephelauxetic Ligand Series
I < Br < CN < Cl < NCS < C2O42- < en < NH3 < H2O < F
Small β Large β
Covalent Ionic
Nephelauxetic Metal Series
Pt4+ < Co3+ < Rh3+~Ir3+ < Fe3+ < Cr3+ < Ni2+ < V4+< Pt2+~ Mn2+
Small β Large β
Large overlap Small overlap
Covalent Ionic

51. Empirical Racah parameters, h, k β = 1– [h(ligand) x k(metal)]
Cr(NH3) β = 1 –hk
β = 1 –(1.4)(0.21) =
Cr(CN)63- β = 1 –hk
β = 1 –(2.0)(0.21) =
Bo - B = hligands x kmetal ion Bo

53. __________________________________________________________________
Typical Δo and λmax values for octahedral (ML6) d-block metal complexes
__________________________________________________________________
Complex Δo cm-1 ~ λmax (nm) Complex Δo cm-1 λmax (nm)
___________________________________________________________________________________
[Ti(H2O)6] , [Fe(H2O)6] ,
[V(H2O)6] , [Fe(H2O)6] ,
[V(H2O)6] , [Fe(CN)6] ,
[CrF6] , [Fe(CN)6] ,
[Co(H2O)6]3+, l.s. 20, [Fe(C2O4)3] ,
[Cr(H2O)6] , [Co(CN)6]3- l.s ,
[Cr(H2O)6] , [Co(NH3)6]3+ l.s ,
[Cr(NH3)6] , [Ni(H2O)6] ,
[Cr(en)3] , [Ni(NH3)6] ,
[Cr(CN)6] , [Ni(en)3] ,

54. 1. Assign the metal oxidation state in the following compounds.
a. K2[PtCl6]
b. Na2[Fe(CO)4]
c. [Mn(CH3)(CO)5]
2. Account for the following:
The manganous ion, [Mn(H2O)6]2+, reacts with CN- to form [Mn(CN)6]4- which has
m = 1.95 B.M., but with I- to give [MnI4]2- which has m = 5.93 B. M.
[Co(NH3)6]Cl3 is diamagnetic, whereas Na3[CoF6] is paramagnetic ( = B.M).
[PtBr2Cl2]2 is diamagnetic and exists in two isomeric forms, whereas [NiBr2Cl2]2
has a magnetic moment,  = 3.95 B.M., and does not exhibit isomerism.
Copper(II) complexes are typically blue with one visible absorption band in their
electronic spectra whereas copper(I) complexes are generally colorless.
Assign a spectroscopic label to the Cu2+ transition.