Electronic Absorption Spectroscopy

1
Electronic Absorption Spectroscopy

• Lesley J. Yellowlees

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Absorption Spectra

• Ground State
• Excited State
• Energy Difference
• Visible
• 400 nm 700 nm
• 14 000 cm-1 25 000 cm-1
• Colour
• TM Compounds
• d-d transitions

hn
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Cobalt (II)
CoCl2

• CoCl42-
• Cobalt(II)
• d7
• Tetrahedral
• Dark blue
• Co(H2O)62
• Cobalt(II)
• d7
• Octahedral
• Pink

xsHCl (conc)
CoCl42-
xsH2O
Co(H2O)62
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Cobalt (II)

• Different colours
• Different ligands
• Spectrochemical series
• Different geometries

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Titanium
Ti4(aq)

• Ti4
• d0
• Colourless
• Ti3
• d1
• Purple
• NB Ti4 and Ti3, octahedral, 6 x H2O ligands

Zn/Hg
Ti3(aq)
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Titanium

• Ti3
• 1 x d-d transition
• Expect
• Simple
• Bell shaped
• Single absorption

A /
n /cm-1
7
Cobalt

• Co2
• Complicated

A /
n /cm-1
8
Question Why are the d-d spectra so
complicated? Answer Interelectronic repulsions
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Example p2

• 3 p orbitals
• 2 electrons
• 15 ways
• MICROSTATES
• ml, ms
• p orbital
• ml - 1, 0, 1
• Electron
• ms -½, ½

1 0 -1
½ -½
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Example p2

• Ignore electronic repulsion
• All same energy
• Clearly wrong!

(ml,1ms,1,ml,2ms,2)
(1,1-) (1,0) (1,0-) (1-,0) (1-,0-) (0,0-)
(1,-1-) (1,-1-) (1-,-1) (1-,-1-) (0,-1)
(0,-1-) (0-,-1) (0,-1-) (-1,-1-)
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Example p2

• Group microstates
• Same energy
• Terms
• Term symbol
• 2s1L
• p2
• Spherical symmetry

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Example p2

• L 2
• D
• ML -2, -1, 0, 1, 2
• L 5
• H
• ML -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

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Example p2

• Group into terms
• Start at top
• Highest ML
• 2
• MS 0
• 1D
• Includes all
• ML 2 to -2
• MS 0

1D
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Example p2

• 10 Left
• Next highest ML
• 1
• MS 1
• 3P
• Includes
• ML 1 to -1
• MS 1 to -1

1D
3P
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Example p2

• 1 Left
• Next highest ML
• 0
• MS 0
• 1S
• Only one microstate

1D
3P
1S
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Example p2

• p2 configuration
• Consider e- repulsion
• 3 term symbols
• 1D, 3P, 1S

1D
3P
1S
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Example p2

• GS and ES?
• Hunds rules
• Term with greatest spin multiplicity lies at
  lowest energy
• For a given multiplicity, the greater the value
  of L of a term, the lower the energy
• GS 3P

1D
3P
1S
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Example d2

• 5 d orbitals
• 2 electrons
• 45 ways
• d orbital
• ml -2, -1, 0, 1,2
• Electron
• ms -½, ½

-2 -1 0 1 2
½ -½
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Example d2

1G
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Example d2

1G 3F
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Example d2

1G 3F 1D
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Example d2

1G 3F 1D 3P
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Example d2

1G 3F 1D 3P 1S
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Example d2

• Multiplicity
• No. microstates in each term
• e.g. 1G
• MS 0, ML 4
• 9 microstates
• Ground State
• Hunds rules
• 3F

(2MS1)(2ML1)


1G 3F 1D 3P 1S
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Free Ion terms

• 1G 3F 1D 3P 1S
• Naked metal
• Spherical geometry
• Free Ion Terms

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Racah Parameters

• Free ion terms
• Different energies
• Interelectronic repulsions
• Coulomb integrals
• J(ab)
• Exchange integrals
• K(ab)
• Giulio Racah (1909-1965)

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Racah Parameters

• Racah Parameters
• A, B and C
• Numeric
• Energy differences
• C 4B
• B important
• Measure of interelectonic repulsion

Energies of Free Ion Terms for d2 configuration
in terms of Racah Parameters E(1S) A 14B
7C E(1G) A 4B 2C E(1D) A 3B 2C E(3P)
A 7B E(3F) A 8B
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Racah Parameters
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Racah Parameters
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Correlation Diagrams

• Complexes
• Remove degeneracy
• Molecular terms
• e- e- repulsion
• Complicated
• Weak field limit
• Strong field limit
• Correlation Diagram

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Correlation Diagrams

• Weak field limit
• No Field
• Interelectronic repulsions important
• Important parameter
• B

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Correlation Diagrams

• Strong field limit
• Strong ligand field
• Interelectronic repulsions not important
• Important parameter
• D
• Real cases
• Intermediate
• Correlation diagram

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Correlation Diagrams
eg

• e.g. d2, octahedral
• Term symbols
• Octahedral
• Character table
• A singly degenerate
• E doubly degenerate
• T triply degenerate

Do
t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• Ground state
• t2g2eg0
• Triply degenerate

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• Ground state
• t2g2eg0
• Triply degenerate

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• Ground state
• t2g2eg0
• Triply degenerate
• T
• S 1
• 2S 1 3
• 1g
• g centre of inversion

t2g
T
1g
3
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways

t2g
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways
• Not all the same energy
• Why not?

dx2-y2
dz2
t2g
dxz
dyz
dxy
Same plane Higher energy
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Correlation Diagrams
eg

• e.g. d2, octahedral
• First excited state
• t2g1eg1
• 6 ways
• Not all the same energy
• Why not?
• 3T1g 3T2g

dx2-y2
dz2
t2g
dxz
dyz
dxy
Orthogonal planes Lower energy
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Correlation Diagrams
eg

• e.g. d2, octahedral
• Second excited state
• t2g0eg2
• Singly degenerate
• A
• S 1
• 2S 1 3
• 2g
• g centre of inversion

t2g
A
2g
3
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Correlation Diagrams
E(3P) A 7B E(3F) A 8B E(3P)-E(3F) A
7B A 8B E(3P)-E(3F) 15B

• Weak field terms
• 3F, 3P
• Strong field terms
• 3T1g, 3T1g 3T2g, 3A2g
• Relative energies
• Strong to weak field
• LFSE
• 3T1g -4/5Do

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Correlation Diagrams
E(3P) A 7B E(3F) A 8B E(3P)-E(3F) A
7B A 8B E(3P)-E(3F) 15B

• Weak field terms
• 3F, 3P
• Strong field terms
• 3T1g, 3T1g 3T2g, 3A2g
• Relative energies
• Strong to weak field
• LFSE
• 3T1g -4/5Do
• 3T1g 3T2g 1/5Do

eg
3/5Do
-2/5Do
t2g
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Correlation Diagrams
E(3P) A 7B E(3F) A 8B E(3P)-E(3F) A
7B A 8B E(3P)-E(3F) 15B

• Weak field terms
• 3F, 3P
• Strong field terms
• 3T1g, 3T1g 3T2g, 3A2g
• Relative energies
• Strong to weak field
• LFSE
• 3T1g -4/5Do
• 3T1g 3T2g 1/5Do
• 3A2g 6/5Do

eg
3/5Do
-2/5Do
t2g
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Correlation Diagrams
Energy
1/5Do
Weak field limit
Strong field limit
15B
1/5Do
Increasing Do
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Correlation Diagrams
Energy

• NB
• Spin conserved
• Angular momentum conserved
• 3F 7 (2L1)
• 2 x T, 1 x A 7

3P
1/5Do
Weak field limit
Strong field limit
6/5Do
15B
3F
1/5Do
-4/5Do
Increasing Do
51
Correlation Diagrams
Energy
3 d-d transitions
1/5Do
Weak field limit
Strong field limit
15B
1/5Do
Increasing Do