chapter 11 coordination chemistry iii: electronic spectra...electronic spectra of coordination...
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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
Quantum Numbers of Multielectron Atoms
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
Quantum Numbers of Multielectron Atoms
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+)
Quantum Numbers of Multielectron Atoms
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
Quantum Numbers of Multielectron Atoms
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,
Quantum Numbers of Multielectron Atoms
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
Quantum Numbers of Multielectron Atoms
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
Quantum Numbers of Multielectron Atoms
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
Quantum Numbers of Multielectron Atoms
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.
Quantum Numbers of Multielectron Atoms
Quantum Numbers of Multielectron Atoms
Quantum Numbers of Multielectron Atoms
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
Electronic Spectra of Coordination Compounds: correlation diagrams
Electronic Spectra of Coordination Compounds: correlation diagrams
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
Electronic Spectra of Coordination Compounds: correlation diagrams
Electronic Spectra of Coordination Compounds: correlation diagrams
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.
7.5 Splitting of Terms
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
7.5 Splitting of Terms
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
7.5 Splitting of Terms
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: correlation diagrams
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.
Electronic Spectra of Coordination Compounds: Tanabe-Sugano diagrams
Electronic Spectra of Coordination Compounds: Tanabe-Sugano diagrams
High spin vs low spin
Ground state and spin multiplicity changed
High spin Low spin
Electronic Spectra of Coordination Compounds: Tanabe-Sugano diagrams
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
Electronic Spectra of Coordination Compounds: Tanabe-Sugano diagrams
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)
Charge-Transfer Spectra
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)
Charge-Transfer Spectra
Homework: Chapter 11
Exercise 11-1~11-9
Problem 1, 6, 8, 11, 14, 20, 24