Chemistry 481(01) Spring 2014
Instructor: Dr. Upali Siriwardane
e-mail: upali@latech.edu
Office: CTH 311 Phone 257-4941
Office Hours:
M,W 8:00-9:00 & 11:00-12:00 am;
Tu,Th, F 10:00 - 12:00 a.m.
April 10 , 2014: Test 1 (Chapters 1, 2, 3,)
May 1, 2014: Test 2 (Chapters 6 & 7)
May 20, 2014: Test 3 (Chapters. 19 & 20)
May 22, Make Up: Comprehensive covering all Chapters
Chemistry 481, Spring 2014, LA Tech
Chapter 20-1
Chapter 20. d-Metal complexes: electronic
structure and properties
Electronic structure
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
Chemistry 481, Spring 2014, LA Tech
473
473
483
487
487
493
497
499
501
502
502
504
Chapter 20-2
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).
Chemistry 481, Spring 2014, LA Tech
Chapter 20-3
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-4
Chemistry 481, Spring 2014, LA Tech
Chapter 20-5
MO energy levels for an octahedral complex with six
ligands [Cr(CO)6]
Chemistry 481, Spring 2014, LA Tech
Chapter 20-6
Electronic Transition in Transition
metal Complexes
a) Transition between metal-centered orbitals with d-
character (d-d transition).
a) Transition between metal- and ligand-centered MOs
which transfer charge from metal to
• ligand or ligand to metal.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-7
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-8
Spectrum of d2 complex [Cr(NH3)6]3+
Chemistry 481, Spring 2014, LA Tech
Chapter 20-9
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]2Pink
Blue
[Ni(OH2)6]2+ [Ni(NH3)6]2Green
Blue
Chemistry 481, Spring 2014, LA Tech
Chapter 20-10
UV-vis Spectra of Transition Metal
Complexes
Chemistry 481, Spring 2014, LA Tech
Chapter 20-11
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-12
Quantum Numbers for single
Electrons
Chemistry 481, Spring 2014, LA Tech
Chapter 20-13
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-14
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-15
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
Russell-Saunders or
Spin angular momenta interact
LS Coupling
Chemistry 481, Spring 2014, LA Tech
Chapter 20-16
Russell-Saunders or
LS Coupling
• 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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-17
Labelling Term Symbols
Maximum Values of
L = 0, 1, 2, 3, 4 etc…
S P D F G etc…
cf 1 -electron case (orbitals)
Maximum Values of
S = 0, 1/2, 1, 11/2, 2 etc…
2S+1 = 1 2 3 4 5 etc… as superscript
Chemistry 481, Spring 2014, LA Tech
Chapter 20-18
How do we determine the
Microstates for p2?
1. Determine the possible values of ML and MS.
max. ML? 2
Total Orbital Momentum
values of ML? 2, 1, 0, -1, -2 L 0 1 2 3 4 5 6
S P D F G H I
max. MS? 1
values of Ms? 1, 0, -1
Spin multiplicity
2S+1 = 1 2 3 4 5
The Russell Saunders term symbol that results
from these considerations is given by: (2S+1)L
Chemistry 481, Spring 2014, LA Tech
Chapter 20-19
2
l =1; x=2 Microstates for p =15
Determine the electron configurations allowed by
the Pauli principle.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-20
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
3x3 = 9
1D
1x5 = 5
1S
1x1 = 1
15
Chemistry 481, Spring 2014, LA Tech
Chapter 20-21
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-22
d2 term symbols
d2 =45
Nl=2(2l+1)
l=2
10!/2!(8!)
Microstates for
max. ML? 4
values of ML? 4, 3, 2, 1, 0, -1, -2, -3, -4
max. MS? 1
L= 0 1 2 3 4
values of Ms? 1, 0, -1
S P D F G
1S 3S 1 P 3P 1D 3D 1F 3F 1G 3G
S = 1 3
1 3 3 9 5 15 7 21 9 27
For d2 terms: 1S 1D 1G 3P 3F; the lowest is 3F
1S
1x1 = 1
3P
3x3 = 9
1D
1x5 = 5
3F
3x7 = 21
1G
1x9 = 9
45
Chemistry 481, Spring 2014, LA Tech
Chapter 20-23
Chemistry 481, Spring 2014, LA Tech
Chapter 20-24
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 3F ,
4
3 F , 3F
3
2
Chemistry 481, Spring 2014, LA Tech
Chapter 20-25
Spin-orbit coupling constant l or z
Chemistry 481, Spring 2014, LA Tech
Chapter 20-26
Terms for 3dn free ion configurations
n
10-n
Note that d gives the same terms as d
Chemistry 481, Spring 2014, LA Tech
Chapter 20-27
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.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-28
The Crystal Field Splitting of RussellSaunders 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.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-29
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,
Chemistry 481, Spring 2014, LA Tech
Chapter 20-30
Crystal Field Splitting of RS terms in
high spin octahedral crystal fields.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-31
Chemistry 481, Spring 2014, LA Tech
Chapter 20-32
Orgel diagrams
Diagram showing the terms arising from crystal field
splitting The spin multiplicity and the g subscripts
are dropped for simplicity
right
2 (Oh)
7
d ,d
Left
3(Oh)8
d ,d
(Td)
7
d
Chemistry 481, Spring 2014, LA Tech
Chapter 20-33
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.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-34
Tanabe-Sugano Diagrams
Chemistry 481, Spring 2014, LA Tech
Chapter 20-35
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
Chemistry 481, Spring 2014, LA Tech
Chapter 20-36
Tanabe-Sugano Diagrams
d2 in Oh field
Chemistry 481, Spring 2014, LA Tech
Chapter 20-37
Chemistry 481, Spring 2014, LA Tech
Chapter 20-38
Chemistry 481, Spring 2014, LA Tech
Chapter 20-39
Chemistry 481, Spring 2014, LA Tech
Chapter 20-40
Chemistry 481, Spring 2014, LA Tech
Chapter 20-41
The transitions responsible for the
absorption and luminescence of Cr3+
ions in ruby.
Chemistry 481, Spring 2014, LA Tech
Chapter 20-42
Chemistry 481, Spring 2014, LA Tech
Chapter 20-43
Chemistry 481, Spring 2014, LA Tech
Chapter 20-44
Chemistry 481, Spring 2014, LA Tech
Chapter 20-45
Chemistry 481, Spring 2014, LA Tech
Chapter 20-46
Chemistry 481, Spring 2014, LA Tech
Chapter 20-47
Chemistry 481, Spring 2014, LA Tech
Chapter 20-48