1. Chemistry 481(01) Spring 2016 Instructor: Dr. Upali Siriwardane
Office: CTH 311 Phone
Office Hours:
M,W 8:00-9:00 & 11:00-12:00 am;
Tu,Th, F 9: :30 a.m.
April 5 , 2016: Test 1 (Chapters 1, 2, 3, 4)
April 28, 2016: Test 2 (Chapters  (6 & 7)
May 17, 2016: Test 3 (Chapters. 19 & 20)
May 18, Make Up: Comprehensive covering all Chapters

2. Chapter 20. d-Metal complexes: electronic structure and properties
20.1 Crystal Field theory
20.2 Ligand Field theory
Electronic spectra
20.3 Electronic spectra of atoms
20.4 Electronic spectra of complexes
20.5 Charge-transfer bands
20.6 Selection rules and intensities
20.7 Luminescence
Magnetism
20.8 Cooperative magnetism
20.9 Spin crossover complexes

3. Crystal Field theory (CFT)
The ligands are viewed simply as mere point charges.  One focuses on the valence d orbitals of the central transition metal atom and examines how the relative energies of the d orbitals change upon introduction of external negative point charges (the ligands). 

4. Ligand Field theory (LFT)
Direct application of Molecular Orbital (MO) theory using SALC of Ligand Molecular and Metal d orbital directly leads to following diagrams

6. MO energy levels for an octahedral complex with six ligands [Cr(CO)6]

7. Electronic Transition in Transition metal Complexes
Transition between metal-centered orbitals with d-character (d-d transition).
Transition between metal- and ligand-centered MOs which transfer charge from metal to
ligand or ligand to metal.

8. Charge Transfers (CT) Note: When Charge transfer (CT) give rise to
intense absorptions (), CT absorption bands in electronic spectra are usually broad
whereas d-d bands are much weaker. In some spectra, CT mask bands
due to d-d transitions often occurs at higher
energies than d-d absorptions.
MLCT = metal-to-ligand charge transfer
LMCT = ligand-to-metal charge transfer

9. Spectrum of d2 complex [Cr(NH3)6]3+

10. Electronic Spectra of Transition Metals
Why are so many coordination compounds colored, in contrast to most organic compounds?
Low energy transitions between different electron configurations.
[Co(OH2)6]2+ [CoCl4]2-
Pink Blue
[Ni(OH2)6]2+ [Ni(NH3)6]2-
Green Blue

11. UV-vis Spectra of Transition Metal Complexes

12. What causes the change in color of Solution?
Electronic Transitions
“One-Electron Model” for hydrogen Doesn’t work for electronic spectra
Must consider how electrons interact with one another.
Quantum Numbers of Multi-electron Atoms Electron configurations are more complicated than we’ve considered so far

13. Quantum Numbers for single Electrons

14. Electron-Electron Repulsions
Hunds Rule
Electron Repulsions result in:
Electrons occupying separate orbitals when possible
Electrons in separate orbitals have parallel spins
Easy to describe individual electrons, more complicated to describe “sets” of electrons.
p2, p3, d2, d3, d4, f2, f3, f5 etc

15. Vector Addition of ml and ms
These are obtained by the vectorial addition of the individual electron Orbital Angular Momentum i.e. the ml values and the Spin Angular Momentum i.e. the ms values
Must first ask which order is the vectorial addition to be carried out ? If we consider just 2 electrons in an
incomplete shell:
Which is the stronger coupling : ms1.ms2 and ml1.ml2
Or ms1.ml1 and ms2.ml2 ?
This choice gives rise to 2 coupling schemes :
a) Russell-Saunders coupling (RS) b) jj-coupling

16. Example Consider a Carbon Atom Electron Configuration: 1s2 2s2 2p2
Do the 2-p electrons have the same energy?
Three major energy levels for the p2 electron configuration
Lowest energy major level is further split into three levels
The two electrons in p2 configuration are not independent
Orbital angular momenta interact
Spin angular momenta interact
Russell-Saunders or
LS Coupling

17. Russell-Saunders or LS Coupling
Interactions produce atomic states called microstates described by new quantum numbers:
ML = Sml Total orbital angular momentum
Ms = Sms Total spin angular momentum

18. Labelling Term Symbols
Maximum Values of
L = 0, 1, 2, 3, 4 etc…
S P D F G etc… cf 1 -electron case (orbitals)
S = 0, 1/2, 1, 11/2, 2 etc…
2S+1 = etc… as superscript

19. How do we determine the Microstates for p2?
1. Determine the possible values of ML and MS.
max. ML? 2
values of ML? 2, 1, 0, -1, -2
max. MS? 1
values of Ms? 1, 0, -1
Total Orbital Momentum L
S P D F G H I
Spin multiplicity
2S+1 =
The Russell Saunders term symbol that results from these considerations is given by: (2S+1)L

20. l =1; x=2 Microstates for p2 =15
Determine the electron configurations allowed by the Pauli principle.

21. TERMS SYMBOLS
are referred to as singlet, doublet, triplet etc. according to value of 2S+1. Denotes Spin multiplicity or spin degeneracy of term.
Thus the terms for p2 can be derived as 1D, 3P, 1S
The total degeneracy of each term = (2S+1)(2L+1)
Thus the original set of 15 microstates for p2 has become sub divided into 3 terms :
3P x3 = 9
1D x5 = 5
1S x1 = 1 15

22. d1 configuration As an example, for a d1 configuration:
S= + ½, hence (2S+1) = 2
L=2
and the Ground Term is written as 2D
d9 has the same configuration

23. d2 term symbols Microstates for d2 =45 max. ML? 4
Nl=2(2l+1)
l=2
10!/2!(8!)
Microstates for d2 =45
max. ML? 4
values of ML? 4, 3, 2, 1, 0, -1, -2, -3, -4
max. MS? 1
values of Ms? 1, 0, -1
1S 3S 1P 3P 1D 3D 1F 3F 1G 3G
For d2 terms: 1S 1D 1G 3P 3F; the lowest is 3F
1S x1 = 1
3P x3 = 9
1D x5 = 5
3F x7 = 21
1G x9 = 9 45
L =
S P D F G
S =

25. Spin-Orbit Coupling
In the Russell-Sunders coupling scheme after allowing for the coupling of the individual spins to give a resultant spin (S) and the individual orbital angular momenta to give a resultant value (L) then we can consider spin-orbit coupling (J)
S.L  J (the total angular momentum)
The J values are given by: L + S, L + S - 1,…L - S
The levels then arising are labeled: 2S+1LJ
For example: consider the ground state term 3F for d2
Here S = 1, L = 3; hence J = 4, 3 ,2
3F level into three new closely separated levels 3F4, 3F3, 3F2

26. Spin-orbit coupling constant l or z

27. Terms for 3dn free ion configurations
Note that dn gives the same terms as d10-n

28. Ground Term Symbol Have the maximum spin multiplicity
If there is more than 1 Term with maximum spin multiplicity, then the Ground Term will have the largest value of L.

29. The Crystal Field Splitting of Russell-Saunders terms
Crystal or Ligand Field affect the different orbitals (s, p, d, etc.) will result in splitting into subsets of different energies based on character table.
Octahedral (Oh)field environment will cause the
d orbitals to split to give t2g and eg subsets of 5 states
D term symbol into T2g and Eg(where upper case is used to denote term symbols and lower case orbitals).
f orbitals are split to give subsets known as t1g, t2g and a2g subsets of 7 states.
F term symbol will split by a crystal field will give states known as T1g,T2g, and A2g.

30. Selection rules and intensities
1) spin-forbidden, ∆S ≠ 0, transitions are generally much weaker than spin-allowed transitions. f ↔ f, s ↔ d, p ↔ f etc. 2) Laporte selection rule : Must be a change in parity; Allowed transitions: g ↔u Forbidden transitions: g ↔g u ↔ u 3) Δl = ± 1 So, allowed transitions are s ↔ p, p ↔ d, d ↔ f; Forbidden transitions are s ↔ s, p ↔ p, d ↔ d,

31. Crystal Field Splitting of RS terms in high spin octahedral crystal fields.

33. Orgel diagrams
Diagram showing the terms arising from crystal field splitting The spin multiplicity and the g subscripts are dropped for simplicity
right (Oh)
d2 , d7
Left
(Oh)
d3 , d8
(Td) d7

34. Racah Parameters Racah Parameters
In practice, however, two alternative parameters are used for dn terms:
B = F2 - 5F4
C = 35F4
These are called Racah Parameters; Racah recognised that these relationships appeared frequently and thus it is
more convenient to use B and C.

35. Tanabe-Sugano Diagrams

36. Term reversal on going dn to d10-n
d1 and d9  2D
d2 and d8  3F and 3P
d3 and d7  4F and 4P
d4 and d6  5D

37. Tanabe-Sugano Diagrams d2 in Oh field

42. The transitions responsible for the absorption and luminescence of Cr3+ ions in ruby.