Chapter 11 Coordination Chemistry III: Electronic Spectra...electronic spectra of coordination compounds, especially involving heavy metals. Spin-orbit coupling acts to split free-ion

Chapter 11 Coordination Chemistry III: Electronic Spectra

11-3 Electronic Spectra of Coordination Compounds

11-2 Quantum Numbers of Multielectron Atoms

11-1 Absorption of Light

Vivid colors of coordination compound.

Dyes, gems (rubies, emeralds), blood etc.

Transitions between d orbitals of metals.

We will need to look closely at the energies of these orbitals.

The electronic absorption spectrum provides a convenient method for determining the magnitude of the effect of ligands on the d orbitals of the metal.

Chapter 11 Coordination Chemistry III: Electronic Spectra

Complementary colors: if a compound absorbs light of one color, we see the complement of that color.

Absorption of Light

Complementary colors: if a compound absorbs light of one color, we see the complement of that color.

Absorption of Light

600 ~ 1000 nmBlue color

Absorption of Light;Beer-Lambert Absorption Law

Beer-Lambert Law

log(Io/I) = A = εlc

Wavelength, wavenumber→Energy

E = hv = hc/λ= hcν

Absorption of light results in the excitation of electrons from lower to higher energy states.

We observe absorption in band with the energy of each band corresponding to the difference in energy between the initial and final states.

We first need to consider electrons in atoms can interact with each other.

Electrons tend to occupy separate orbitals← ΠcElectrons in separate orbitals tend to have parallel spins ← Πe

Quantum Numbers of Multielectron Atoms

Carbon atomEnergy levels for the p2 electrons → Five energy levelsEach energy levels can be described as a combination of the ml and ms values of the 2p electrons.

The orbital angular momenta and the spin angular momenta of the 2p electrons interact in a manner called Russell-Saunders coupling (LS coupling).

2p electrons

n = 2, l = 1ml = +1, 0, or -1ms = +1/2 or -1/2


How many possible combinations of ml and ms values?

One possible set of values for the two electrons in the p2

configuration would be

First electron: ml = +1 and ms = +1/2Second electron: ml = 0 and ms = -1/2

microstates

Russell-Saunders coupling (LS coupling)

Orbit-orbit couplingML = ∑ml→ L: total orbital angular momentum quantum number

Spin-spin couplingMs = ∑ms→ S: total spin angular momentum quantum number

Spin-orbit couplingJ = L + S : total angular momentum quantum number

2p electrons

n = 2, l = 1ml = +1, 0, or -1ms = +1/2 or -1/2Notation 1+0-

microstate


Electronic quantum # (ml and ms) to atomic quantum #(ML and MS)

microstates

2p electrons

n = 2, l = 1ml = +1, 0, or -1ms = +1/2 or -1/2

Tabulate the possible microstates1. No two electrons in the same microstate have

identical quantum numbers (the Pauli exclusion principle)

2. Count only the unique microstates (1+0- and 0-1+)


Electronic quantum # (ml and ms) to atomic quantum #(ML and MS) → describe states of multielectron atoms

Russell-Saunders coupling (LS coupling)

Orbit-orbit couplingML = ∑ml→ L: total orbital angular momentum quantum number

Spin-spin couplingMs = ∑ms→ S: total spin angular momentum quantum number

Spin-orbit couplingJ = L + S : total angular momentum quantum number


L and S describe collections of microstates.ML and MS describe the microstates themselves.

Atomic States Individual ElectronsML = 0, ±1, ± 2,… ± L ml = , ±1, ± 2,… ± l MS = S, S-1,…. –S ms = +1/2, -1/2

Term symbol

Term Symbol

2S+1LJ

L = 0, 1, 2, 3 → S, P, D, F,


Electronic quantum # (ml and ms) to atomic quantum #(ML and MS) → describe states of multielectron atoms

Free-ion terms are very important in the interpretation of the spectra of coordination compounds.

1S (singlet S) : S → L = 0 → ML = 0, 2S+1 =1 → S =0 → MS = 0

0+0-0

0

ML

MS

The minimum configuration of two electrons


2P (doublet P) : P → L = 1 → ML = +1,0,-1 2S+1 =2 → S =1/2 → MS = +1/2, -1/2

ML

MS

The minimum configuration of one electron

-1+-1--1

0+0-0

1+1-+1

+1/2-1/2

Six microstates


ML

MS

-1+-1--1

0+0-0

1+1-+1

+1/2-1/2

Six microstates

xx-1

xx0

xx+1

+1/2-1/2

The spin multiplicity is the same as the # of microstates


Reduce microstate table into its component free-ion terms.

The spin multiplicity is the same as the # of microstates.

Each terms has different energies; they represent three states with different degrees of electron-electron interactions.

Which term has the lowest energy. This can be done by using two of Hund’s rules.

1. The ground term (term of lowest energy) has the highest spin multiplicity. (Hund’s rule of maximum multiplicity)

2. If two or more terms share the maximum spin multiplicity, the ground term is one having the highest value of L.




d6

l = 2ml = +2, +1 0, -1, -2ms = +1/2 or -1/2

High spin Low spin

5D 1I

Spin-Orbit Coupling

The spin and orbital angular momenta couple each other → spin-orbit coupling

J = L + S : total angular moment quantum number

J may have the following valuesJ = L+S, L+S-1, L+S-2,…. |L-S|

Term Symbol

2S+1LJSpin-orbit coupling can have significant effects on the electronic spectra of coordination compounds, especially involving heavy metals.

Spin-orbit coupling acts to split free-ion terms into states of different energies.

J may have the following valuesJ = L+S, L+S-1, L+S-2,…. |L-S|

Term Symbol

2S+1LJSpin-orbit coupling acts to split free-ion terms into states of different energies.

p2

1S, 1D1S

1D21D

3P 3P

3P2

3P1

3P0

1S0

Spin-Orbit Coupling

p2

1S, 1D1S

1D21D

3P 3P

3P2

3P1

3P0

1S0

Total energy level diagram for the carbon atom. (five energy states)

The state of lowest energy can be predicted from Hund’s third rule.

3. For subshells that are less than half-filled, the state having the lowest J value has the lowest energy.

For subshells that are more than half-filled, the state having the highest J value has the lowest energy.

Half-filled subshells have only one possible J value.

Spin-Orbit Coupling

Electronic Spectra of Coordination Compounds

Microstates and free-ion terms for electron configurations

Identify the lowest-energy term

Identify the lowest-energy term

1. Sketch the energy levels, showing the d electrons.

2. Spin multiplicity of lowest-energy state = number of unpaired electrons + 1.

3. Determine the maximum possible value of ML for the configuration as shown. This determines the type of free-ion term.

4. Combine results of steps 2 and 3 to get ground term.

Spin multiplicity = 3+1=4

Max. of ML: 2+1+0 =3

4F

Electronic Spectra of Coordination Compounds

Electronic Spectra of Coordination Compounds: Selection Rules

On the basis of the symmetry and spin multiplicity of ground and excited electronic states

1. Transitions between states of the same parity are forbidden (symmertywith respect to a center of inversion.: Laporte selection rule

2. Transitions between states of different spin multiplicities are forbidden: spin selection rule

4A2 and 4T1: spin-allowed4A2 and 2T2: spin-forbidden

Between d orbitals are forbiddeng → g transitionBetween d and p orbitals are allowed; g → u transition

Some rules for relaxation of selection rules

1. Vibrations may temporarily change the symmetry(the center of symmetry is temporarily lost: vibronic couplingrelax the first selection rule:d-d transition

2. Tetrahedral complexes often absorb more strongly than Oh complexes. Metal-ligand sigma bonds can be described as involving a combination of sp3 and sd3

hybridization of the metal orbitals: relax the first selection rule

3. spin-orbit coupling provides a mechanism of relaxing the second selection rule

Electronic Spectra of Coordination Compounds: Selection Rules

Electronic Spectra of Coordination Compounds: correlation diagrams

To relate the electronic spectra of transition metal complexes to the ligand field splitting: correlation diagrams and Tanabe-Sugano diagrams

1. Free ions (no ligand field): d2; 3F, 3P, 1G, 1D, 1S.2. Strong ligand field.

t2g2 eg

2t2geg



The free-ion terms will be split into states corresponding to the irreducible representation.

7.5 Splitting of Terms

The possible splitting of S, P, D, F

And S state is nondegenerate; no splittingP term from Eqs. 7.2 ~ 7.6

T1g; in Oh a P term is not split, but becomes a triply degenerate T1gterm

D term has a fivefold orbital degeneratefrom Eqs. 7.2 ~ 7.6

ΓD = Eg + T2g

F term has a sevenfold orbital degeneratefrom Eqs. 7.2 ~ 7.6

ΓF = A2g + T1g + T2g



Irreducible representations may be obtained for the strong-field limit configurations.

Each free-ion irreducible representation is matched with a strong-field irreducible representation.

The spin multiplicity of the ground state.


For the ground-state configuration t2g2 we take the direct product t2g X t2g

Γ(t2g2) = A1g + Eg + T1g + T2g

We need to know spin multiplicities. Here Dt = 15.Three possible ways

The triplet state must have a triply degenerate orbitals term


For the ground-state configuration eg2 we take the direct product eg X eg

Γ(eg2) = A1g + A2g + Eg

We need to know spin multiplicities. Here Dt = 6.Two possible ways

The triplet state must have nondegenerate orbitals term

Γ(eg2) = 3A1g + 1A2g + 1Eg

Γ(eg2) = 1A1g + 3A2g + 1Eg


For the ground-state configuration t2g1eg

1 we take the direct product t2g X eg

Γ = T1g + T2g

We need to know spin multiplicities. Here Dt = 24.The electrons in this configuration are unrestricted by the Pauliexclusion principle. And they can occur as both singlets and triplets

Γ = 1T1g + 1T2g + 3T1g + 3T2g


Electronic Spectra of Coordination Compounds: Tanabe-Sugano diagrams

B = Racah parameter, a measure of the repulsion between terms of the same multiplicity; the energy difference between 3F and 3P is 15B.

E is the energy above the ground state.



High spin vs low spin

Ground state and spin multiplicity changed

High spin Low spin


Jahn-Teller Distortions and Spectra

d1 d9 complexes: might expect each to exhibit one absorption band: excitation from the t2g to the eg levels.

t2g

eg

t2g

eg

Two closely overlapping absorption bands.

To lower the symmetry of the molecule and to reduce the degeneracy.Distortion from Oh to D4h: results in stabilization of the molecule.

The most common distortion observed is elongation along z axis.

Jahn-Teller Distortions and Spectra

Jahn-Teller Distortions and Spectra: Symmetry labels for configurations

Electron configurations have symmetry labels that match their degeneracies.

T

E

A or B

Triply degenerate asymmetrically occupied state

Doubly degenerate asymmetrically occupied state

Nondegeneratestate

the opposite of the order of energies of the orbitals

Too weak

Jahn-Teller Distortions and Spectra: Symmetry labels for configurations

2D term for d9

Lower energy Higher energy

2Eg2T2g

Distortions can be splitting of bands.

Symmetry label

Tanabe-Sugano Diagrams: Determining ∆ofrom Spectra;d1, d4(high spin), d6(high spin), d9

Tanabe-Sugano Diagrams: Determining ∆o from Spectra

Tanabe-Sugano Diagrams: Determining ∆o from Spectra;d3, d8

To find ∆o, we simply find the energy of the lowest-energy transition

Ground state F term

Tanabe-Sugano Diagrams: Determining ∆o from Spectra;d2, d7 (high spin)

Ground state F term

3T1g state arising from the 3P free-ion terms, causing a slight curvature of the both in the Tanabe-Sugano diagram.

An Alternative way.

t2g2

t2geg

eg2

Tanabe-Sugano Diagrams: Determining ∆o from Spectra;d2, d7 (high spin)

t2g2 eg

2t2geg

Tanabe-Sugano Diagrams: Determining ∆o ;d5 (high spin), d4 to d7 (low spin)

d5

Low spin from d4 to d7


Tetrahedral Complexes

The lack of a center of symmetry: makes transitions between d orbitals more allowed; much more intense absorption bands.

Hole formalism: d1 Oh configuration is analogous to the d9 Td configuration: the hole in d9 results in the same symmetry as the single electron in d1.

We can use the correlation diagram for d10-n

configuration in Oh geometry

t2g

egt2

eoctahedral tetrahedral

hole

Charge-Transfer Spectra

Charge-transfer absorptions is much more intensethan d-d transitions.

Involve the transfer of electrons from molecular orbitals that are primarily ligand in character to orbitals that are primarily metal in character (or vice versa)

LMCT

Formal reduction of the metal: Co(III) to Co(II)

IrBr62- (d5): two band

IrBr63- (d6): one band

Why?

LMCT

Formal reduction of the metal: Co(III) to Co(II)


MLCTπ-acceptor ligand (π* orbitals): CO, CN-, SCN-, bipyridine..

Oxidation of the metald-d transitions may be completely overwhelmed and essentially impossible to observe.

MLCT

Formal oxidation of the metal: Fe(III) to Fe(IV)


Homework: Chapter 11

Exercise 11-1~11-9

Problem 1, 6, 8, 11, 14, 20, 24

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Chapter 11 Coordination Chemistry III: Electronic Spectra...electronic spectra of coordination compounds, especially involving heavy metals. Spin-orbit coupling acts to split free-ion