Elec Spec of Metal Complexes

Question 1

What is the Beer-Lambert Law?

Answer 1

A = log₁₀(I₀/I) = εcl

where I = intensity
I = intensity of incident light
c = concentration in M
l = path length of light in cm
ε = extinction coefficient (M^-1cm^-1)

Question 2

When is the Beer-Lambert law valid?

Answer 2

Valid only at low absorbance (A < 1)

Question 3

What is on the axis on an absorption spectra?

Answer 3

Absorbance (y-axis)
Wavenumber or wavelength (x-axis)

Question 4

How can you convert between wavelength in nm to wavenumbers in cm^-1?

Answer 4

λ (nm) = 10⁷ / v (cm^-1)

Question 5

What is an eV in terms of kJ/mol and cm^-1?

Answer 5

1 eV = 96.5 kJ/mol

1 eV = 8067 cm^-1

where kT = 200 cm^-1 @ 298 K

Question 6

What is the range of visible light in λ and v?

Answer 6

λ: 380 - 750 nm

v = 26,500 - 13,000 cm^-1

where the first number is violet and latter is red

Question 7

What types of elec transitions occur in metal complexes?

Answer 7

d-d transitions

Ligand-to-metal charge transfers (LMCT)

Metal-to-ligand charge transfer (MLCT)

Ligand based

f-f and f-d transitions

Question 8

When do d-d transitions occur?

Answer 8

• Open-shell dⁿ compounds
• Depends on ligand-field splittings
• Depends on electron repulsion

Question 9

When do ligand-to-metal charge transfers (LMCTs) occur?

Answer 9

Occurs in all complexes, including d¹⁰

Reduces metal

Question 10

When does metal-to-ligand charge transfer (MLCT) occur?

Answer 10

Requires ligands with low-lying π* orbitals
Such as CO, CN-, NO, bipy and phen

Question 11

When do ligand-based transitions occur?

Answer 11

n-π* and π-π* transitions in delocalised systems

Question 12

When do f-f and f-d transitions occur?

Answer 12

In lanthanides and actinides

Question 13

What is the selection rule for an electric dipole transition to be observable?

Answer 13

∫ ψ_finalμψ_initial dτ =! 0

Where μ is TDM operator

Question 14

How can you find the ligand-field ground state of a complex?

Answer 14

Use electron config
Find max S, then find degen in that state
Then letter is the degen, S is superscript
1/2 is symmetry of ψ^orbital under C4, if anti then is 2
g/u is symm from inversion

Question 15

How can you find the number of microstates of a state?

Answer 15

Use letter to give the degen of states
Then spin multiplies them

²T suggests 6 (2x from spin and 3 states from T)

Question 16

What is the ligand field state term for e_g¹?

Answer 16

s=1/2, S = 2
doubly degen so E

²E_g

Question 17

When is a shoulder observed in electronic spectra?
(e.g. t_2g¹ to e_g¹)

Answer 17

Jahn-Teller distortion of the excited states

This is because some bonds longer than other (e_g split further)

Question 18

What are the term states of Ti³⁺ (d¹) in Oh and Td environments?

Answer 18

Question 19

What are the term states for hs d⁶ (such as Fe²⁺)?

Answer 19

Must look how to pair down spin e-
e- has been added to A1

Question 20

What are the term states of hs d⁴ (such as Cr²⁺)?

Answer 20

Use A1 x “hole” in d5

Question 21

What are the term states of d⁹ (such as Cu²⁺)?

Answer 21

Need to find orbital degen for arranging a hole

Question 22

How many bands are observed in d-d bands in Oh/Td?

Answer 22

Oh/Td have one d-d band each

Oh: T₂ -> E
Td: E -> T₂

Any asymm band due to JT dist

Question 23

What are the relative intensities of d-d bands?

Answer 23

Moderate intensities

Question 24

What is the assumption of the weak-field approach?

Answer 24

Ligand field is a small perturbation to Russel-Saunders terms of the free ion

Is in the gas-phase

Question 25

What is the weak-field state of d¹?

Answer 25

5x microstates with different M_L values 5xequal energy 3d states Ground state is ²D

Question 26

What is the weak-field state of d⁶?

Answer 26

e- added to spherical d⁵ Causes s=2, S=5, L=2 ⁵D

Question 27

What is the weak-field state of d⁴?

Answer 27

s=2, S=5, L=2 ⁵D

Question 28

What is the weak-field state of d⁹?

Answer 28

4xe- added to d5 sphere s=1/2, S = 2, L=2 ²D

Question 29

What is the symmetry of free ions?

Answer 29

Spherical symm - R₃

Question 30

How can you find how a free ion term splits into fields in different fields?

Answer 30

Use descent in symm tables (O includes cubic ligand fields such as O_h and T_d) Look at term under R₃ and find the orbitals which they split into

Question 31

What is an orgel diagram?

Answer 31

Plots splitting of free ion terms and energy of microstates with increasing ligand field splitting (Δ)

Question 32

How does the electric TDM operator transform as in Oh and Td symm?

Answer 32

x,y,z on RHS In O_h: T_1u In T_d: T₂

Question 33

What is required for an allowed transition wrt symmetry?

Answer 33

Non-zero TDM means integrand must be an even function Γ(ψ_final) x Γ(μ) x Γ(ψ_initial) must contain A₁

Question 34

What is the spin selection rule and when is it not followed?

Answer 34

ΔS = 0 Breaks down when ψ_spinψ_orbital cannot be separated due to spin-orbit coupling This breaks as atoms get heavier

Question 35

What is the Laporte selection rule and when is it applicable?

Answer 35

ΔL = +/- 1 for Q =! 0 When spin and orbital wavefn can be separated When centrosymm has parity rule of: g <-> u

Question 36

What does Laporte rule prevent?

Answer 36

Forbids: p-p / d-d / f-f transitions in atoms and ions

Question 37

Why do Oh have less intense transitions than Td?

Answer 37

Td is non-centrosymmetroic so doesn't need to fufill parity part of Laporte rule -> less forbidden Oh has to follow those rules

Question 38

What relaxes the parity part of Laporte rule?

Answer 38

Relaxed by vibronic coupling Co-excite a vib mode of symm

Question 39

How does covalency effect the amount of vibronic coupling?

Answer 39

Covalency increases vib coupling

Question 40

How does vib coupling relax parity selec rule?

Answer 40

Separate ψ = ψ^elecψ^vib

Question 41

What dictates band widths of transitions?

Answer 41

Co-excitation of vib modes Progressions depends on Franck-Condon principle Sharper - no change in r(M-L) Broader - large change in r(M-L), more vib co-excitation

Question 42

Why do hs d⁵ complexes have broad and sharp bands?

Answer 42

Sharp - due to spin flips within the t_2g and e_g, no change in bonding Broad due to covalency - large change in bond length from t_2g -> e_g So large co-excitation of vib states

Question 43

What mixing occurs in Td complexes?

Answer 43

d/p mixing: t₂ from metal nd and (n+1)p orbitals e is purely d e -> t₂ has some g -> u character, means the intensity is increased

Question 44

What is the intensity of π->π`*` transitions?

Answer 44

v large as large dipole moment change

Question 45

How many transitions would you usually predict for d^2,3,7,8 ions?

Answer 45

Would expect 3 transitions (you dont)

Question 46

What are the free ion terms of d²?

Answer 46

s=1, S= 3 Max M_L = 3, which implies ³F Also see a ³P term

Question 47

How do d² free ion terms split in ligand fields?

Answer 47

Within Oh/Td ³F -> ³A₂ + ³T₂ + ³T₁ ³P -> ³T₁ Means there are 3x spin-allowed, laporte forbidden bands observable due to vib coupling mech

Question 48

What is the ligand ground state of Oh d²?

Answer 48

s=1, S=3, L=3 so T 9 possible microstates t_2g x t_2g = A_1g + E_g + [T_1g] + T_2g Spin triplet associated with ¹T_1g g.s is ³T_2g other states are singlet states

Question 49

What is the config interaction of d²?

Answer 49

Splitting of F term increases with Δ Set difference in F and P states is 15B, which is the Racah parameter

Question 50

What is observed in the elec spectrum of d²?

Answer 50

In this case large Δ which causes A2g to raise above T1g No band gives Δ

Question 51

What is the summary for d^2,3,7,8 Oh elec spec?

Answer 51

Question 52

How many bands are observed in different dn?

Answer 52

dⁿ: 0,4,6,9 - gives 1 band 5 - no bands 2,3,7,8 - gives 3 bands

Question 53

What is the summary Orgel diagram for Oh/Td d^2,3,7,8?

Answer 53

Question 54

When are Orgel diagrams used?

Answer 54

Determine # of spin-allowed bands and symm of states in transitions Weak field, high spin only, not for d⁵ high-spin No info for spin-forbidden transitions Qualtitative

Question 55

What is a Tanabe-Sugano diagram?

Answer 55

Δ (in terms of B) on x-axis Energy (in terms of B) on y-axis Quantitative version of Orgel

Question 56

What units are energies given in Tanabe-Sugano diagram?

Answer 56

In terms of B - the racah parameter Where the racah term is from e- repulsion All are relative to ground state

Question 57

How do Racah parameters B and C relate?

Answer 57

Both measures of e- repulsion C/B ~ 4

Question 58

How can you find Racah parameters using Tanabe-Sugano diagrams?

Answer 58

Find 2 transition wavenumbers and their ration Use difference in diagram (which is in terms of B) to git to best ratio Then find B, Δ, and any other transition wavenumbers

Question 59

What suggests mixing occurs in a Tanabe-Sugano diagram?

Answer 59

Close in energy, around Δ/B = 10 This can give rise to spin-forbidden bands

Question 60

What is the nephelauxetic effect?

Answer 60

Reduced e- repulsion (and racah parameter) in complexes than free ions Suggests increased average distance between e-

Question 61

What is the source of nephelauxetic effect?

Answer 61

Covalence of M-L bonding delocalises e- So more spread out and lower B

Question 62

What is the nephelauxetic effect series?

Answer 62

Extent differnet ligands reduce B: 2nd/3rd row deecrease B most F^- < H₂O < NH₃ < en < ox < SCN^- < Cl^- < CN^- < Br^- < I^-

Question 63

What occurs in a LMCT?

Answer 63

Ligand-to-metal charge transfer Excitation of an e- frommainly ligand-based orbital to mainly metal-based orbital

Question 64

What are the symmetries in tetrahedral complexes which allow LMCT?

Answer 64

t₂ MOs are σ and π in symm and so have contributions of both d and p orbitals Ligand e- fill up to t₁

Question 65

What are the LMCT transitions in Td complexes?

Answer 65

LMCT of increasing energy: t₁(π) -> e(π`*)` t₁(π) -> t₂(σ`*`,π`*`) t₂(σ,π) -> e(π`*`) t₂(σ,π) -> t₂(σ`*`,π`*`)

Question 66

What are the SALCs in Oh complexes?

Answer 66

σ: a_1g + e_g + t_1u π: t_1g + t_2g + t_1u + t_2u

Question 67

What are the LMCT excitations in Oh complexes?

Answer 67

LMCT transitions: t_1u(σπ) & t_2u(π) -> t_2g + e_g u x u x g -> g, allowed BUT t_1g(π) -> t_2g(π`*`) is forbidden

Question 68

How does changing the ligand change frequency of LMCT transitions?

Answer 68

Less χ (electro-ve) ligands have less tightly held t₁(π) e- at higher energy Means v(LMCT) decreases down the group

Question 69

How does metal oxn state change freq of LMCT?

Answer 69

Increased oxn state lowers energy of d and e(π`*`) orbitals (where the orbitals promoted to) Means v(LMCT) decreases from Fe(II) to Fe(III)

Question 70

How does freq of LMCT change across a series?

Answer 70

v(LMCT) decreases across a series as metal d orbitals stabilised by increasing nuclear charge However at Zn(II) they have to promote to next orbital

Question 71

How does freq of LMCT change down the group?

Answer 71

v(LMCT) increase down group as metal d-orbital increases This is due to 1/n² factor in orbital energy Can lead to higher elements being coloured and down the group being colourless (in UV)

Question 72

What bands are seen in [MnO₄]^-?

Answer 72

4xLMCT bands expected and observed Mn-O lengthened in LMCT, co-excites A₁ mode This causes a progression with spacing the freq of A₁ mode in excited state

Question 73

What does J-value size suggest about following Curie law?

Answer 73

Large J suggests follows the Curie law As ligand-field effects negligible

Question 74

How does separation of states depend on J?

Answer 74

The separation is proportional to J So larger values will have larger spacing

Question 75

Why does Eu(III) have a mag moment when not expected by spin-only?

Answer 75

1st es (excited state) v slightly higher in E than gs This causes secondary zeeman effect and they gain angular momentum Stat mech assumption not followed as gs not thermally isolated so doesnt follow Curie

Question 76

How does mag moment of Er(III) change at low T?

Answer 76

Only below 10K does diff between energy levels is close to kT So accessible es

Question 77

What is the 2nd order Zeeman effect?

Answer 77

Seen in Eu(III) Mixing es into gs, which is proportional to B²/energy separation Not T dependent, doesnt effect Curie behaviour

Question 78

When does spin-orbit coupling or term symbols more important?

Answer 78

Term symbol - Lanthanides, with s-s coupling > l-l > s-l > LFE SO coupling - 1st row TM, as s-s > l-l > LFE > s-l

Question 79

What does L values mean for Curie law?

Answer 79

Curie law when only one state available so L=0 For T dependent, L>0