Understanding the Absorption Electronic Spectra of

Understanding the Absorption Electronic Spectra of Coordination Compounds at greater depth

Ligand Field Theory

Chapter 20

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Review of the Previous Lecture

1. Learned how to more specifically define multielectron systems

2. Introduced new quantum numbers (L and S)

3. Defined atomic states and how to label them with Russel-Saunders Term Symbols

4. Characterized the energy of atomic states using Hund’s rules

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1. Ligand Field Theory

Ligand field theory incorporates molecular orbital theory and treats the ligand field not as apurely electrostatic system.

▪ Electronic transitions will be reexamined by considering the atomic states ofmultielectron systems and focusing on transition metals

▪ Allowed transitions will be examined in both weak and strong field coordinations

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2. Orgel diagrams to evaluate d-d electronic transitions

A. Orgel diagrams are correlation diagrams that correlate orbital energies as they vary withligand field strengths

▪ Consider the ground atomic state and examine what happens in the weak field limit

i.e. d1

E

S = ½

Multiplicity = 2S + 1 = 2

L = 2

2D Ground State

+2 +1 0 -1 -2

Absence of ligands

Atomic State L

S 0

P 1

D 2

F 3

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i.e. d1

“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2

Octahedral Field

S = ½

Multiplicity = 2S + 1 = 2; 2T2g

2D

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i.e. d1

“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2

Octahedral Field

S = ½

Multiplicity = 2S + 1 = 2; 2T2g

This single electroncan be in any of thethree t2g orbitals andso this electronicsituation describes atriply degenerate state.

2D

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i.e. d1

“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2

Octahedral Field2T2g

t2g

eg

2Eg

Electron transition

The electron can be in either eg orbital.▪ Double degeneracy.

2D

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“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2


t2g

eg

2Eg

Electron transition

Spin Allowed transition

2D


i.e. d1

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“Δoct”E

t2g

eg

Absence of ligands+2 +1 0 -1 -2


t2g

eg

2Eg

Electron transition

2D

d1 OctahedralOrgel Diagram

Expect one absorbancein the UV-Vis spectrum

A d1 absorbance in reality

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A Z-in Jahn-Teller distortion applies to a d1 electron configuration in an octahedral field:

i.e. [Ti(H2O)6]3+ Ti3+

ElectronicabsorbanceGround State

dx2

– y2

dz2

dxz dyz

dxy

dx2

– y2

dz2

dxz dyz

dxy

dx2

– y2

dz2

dxz dyz

dxy

A B

BA

E

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2B. Different atomic states produce different components in an octahedral field

Atomic State Components in an octahedral field (Splitting)

S A1g

P T1g

D T2g + Eg

F A2g + T2g + T1g


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2C. d2 Octahedral Orgel Diagram (Partial)

E

S = 1

Multiplicity = 2S + 1 = 3

L = (+2x1) + (+1x1) = 3

3F Ground State

+2 +1 0 -1 -2

Absence of ligands

Atomic State L

S 0

P 1

D 2

F 3

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1D

3F

1S

E

For d2 the atomic states are 3F, 3P, 1G, 1D, and 1S

1G

3P

The d2 Orgel Diagram wouldconsist of all of these atomic statesbut we will only focus on theground state and how it splits in anoctahedral field.

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E

3F Ground State

+2 +1 0 -1 -2

Absence of ligands

Atomic State Components in an octahedral field (Splitting)

S A1g

P T1g

D T2g + Eg

F A2g + T2g + T1g

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“Δoct”E

t2g

eg



t2g

eg

3T2g3F

t2g

eg

3A2g

1st Excitation 2nd Excitation

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“Δoct”E

t2g

eg



t2g

eg

3T2g3F

t2g

eg

3A2g

1st Excitation 2nd Excitation

Partiald2 Octahedral

Orgel Diagram

Considering only groundAtomic State

3F

3T1g

3T2g

3A2g

Increasing Δoct

Energy

1st Excitation

2nd Excitation

2D. d3 Octahedral Orgel Diagram (Partial)

E

+2 +1 0 -1 -2

Absence of ligands

Increasing Δoct

4F

4P

For d3 the atomic states are4F, 4P, 2H, 2G, 2F, 2D, 2D, and 2P

2D. d3 Octahedral Orgel Diagram (Partial)

E

+2 +1 0 -1 -2

Absence of ligands

Increasing Δoct

4F

4P

For d3 the atomic states are4F, 4P, 2H, 2G, 2F, 2D, 2D, and 2P

States of the same term symbols cannotcross. Orbital mixing.▪ Lower energy state is stabilized▪ Higher energy state is destabilized

2E. d9 Octahedral Orgel Diagram

“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2

Octahedral Field

t2g

eg

2D

Excitation


“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2

Octahedral Field

t2g

eg

2D

Excitation

2Eg2T2g

Positive Hole Concept


“Δoct”E

t2g

eg

Absence of ligands

+2 +1 0 -1 -2

Octahedral Field

t2g

eg

2D

Excitation

2Eg2T2g

Inverse of d1 Octahedral Orgel Diagram2D

2Eg

2T2g

Increasing Δoct

Energy

2F. Inverse Relationship of Orgel Diagrams

It turns out d10-n (Oh or Td) Orgel diagrams are inverseof dn (Oh or Td) Orgel diagrams.

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2G. Determining Δoct

Determining Δoct can be complicatedusing Orgel Diagrams when there areallowed transitions arising fromdifferent initial atomic states.

- Let’s consider a more detailed

d2 octahedral Orgel Diagram

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2G. Determining Δoct

To determine Δoct, need toapproximate the value of the Racahparameter B:

▪ A measure of the splitting of theinitial atomic states

▪ B accounts for electron-electronrepulsions

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3. Tanabe-Sugano Diagrams

Tanabe-Sugano diagrams provide similar information as Orgel diagrams but allow you toconsider d-d electronic transitions in the weak and strong field limits.


2DΔoct

B

EB

2T2g

2Eg

d1 OctahedralTanabe Sugano Diagram

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3A. Using Tanabe-Sugano Diagrams to determine Δoct

Consider d3 in an octahedral field.

E

t2g

eg


Octahedral Field4A2g

t2g

eg

4T2g4F

t2g

eg

4T1g

1st Excitation 2nd Excitationt2g

eg

3rd Excitation

+2 +1 0 -1 -24P (One microstate example) 4T1g

Hard to Represent

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E

t2g

eg


Octahedral Field4A2g

t2g

eg

4T2g4F

t2g

eg

4T1g

1st Excitation 2nd Excitationt2g

eg

4T1g

Hard to Represent

3rd Excitation

+2 +1 0 -1 -24P (One microstate example)

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To determine Δoct, you first need to perform a trialand error process of determining a value for Δoct/Bon the Tanabe-Sugano diagram that will give youcomparable energy difference ratios for the allowedtransitions as your experimental values.

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3B. Tanabe-Sugano Diagrams provide d-d electronic transition information in the weak and strong field

Consider d5 in an octahedral field.

E

t2g

eg


Weak Field; High SpinS = 5/2

6A1g2T2g

6S

Strong Field; Low SpinS = 1/2

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d5 Octahedral Tanabe-Sugano Diagram

▪ Weak field (high spin)

- 6A1g is the ground state

- No spin-allowed transitions

But they do occur; ϵ < 1 M-1cm-1

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d5 Octahedral Tanabe-Sugano Diagram▪ Strong field (low spin)

- 2T2g is the ground state

- Four allowed transitions2T2g to 2A2g ,

2T2g

2T2g to 2Eg

2T2g to 2T2g (2I)

2T2g to 2A1g

Spin-allowed transitions,ε = 10 - 200 M-1cm-1

- Four absorbances but due to resolution may not actually see them

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Understanding the Absorption Electronic Spectra of