Elec Spec of Metal Complexes Flashcards
What is the Beer-Lambert Law?
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)
When is the Beer-Lambert law valid?
Valid only at low absorbance (A < 1)
What is on the axis on an absorption spectra?
Absorbance (y-axis)
Wavenumber or wavelength (x-axis)
How can you convert between wavelength in nm to wavenumbers in cm-1?
λ (nm) = 107 / v (cm-1)
What is an eV in terms of kJ/mol and cm-1?
1 eV = 96.5 kJ/mol
1 eV = 8067 cm-1
where kT = 200 cm-1 @ 298 K
What is the range of visible light in λ and v?
λ: 380 - 750 nm
v = 26,500 - 13,000 cm-1
where the first number is violet and latter is red
What types of elec transitions occur in metal complexes?
d-d transitions
Ligand-to-metal charge transfers (LMCT)
Metal-to-ligand charge transfer (MLCT)
Ligand based
f-f and f-d transitions
When do d-d transitions occur?
- Open-shell dn compounds
- Depends on ligand-field splittings
- Depends on electron repulsion
When do ligand-to-metal charge transfers (LMCTs) occur?
Occurs in all complexes, including d10
Reduces metal
When does metal-to-ligand charge transfer (MLCT) occur?
Requires ligands with low-lying π* orbitals
Such as CO, CN-, NO, bipy and phen
When do ligand-based transitions occur?
n-π* and π-π* transitions in delocalised systems
When do f-f and f-d transitions occur?
In lanthanides and actinides
What is the selection rule for an electric dipole transition to be observable?
∫ ψfinalμψinitial dτ =! 0
Where μ is TDM operator
How can you find the ligand-field ground state of a complex?
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 ψorbital under C4, if anti then is 2
g/u is symm from inversion
How can you find the number of microstates of a state?
Use letter to give the degen of states
Then spin multiplies them
2T suggests 6 (2x from spin and 3 states from T)
What is the ligand field state term for eg1?
s=1/2, S = 2
doubly degen so E
2Eg
When is a shoulder observed in electronic spectra?
(e.g. t2g1 to eg1)
Jahn-Teller distortion of the excited states
This is because some bonds longer than other (eg split further)
What are the term states of Ti3+ (d1) in Oh and Td environments?
What are the term states for hs d6 (such as Fe2+)?
Must look how to pair down spin e-
e- has been added to A1
What are the term states of hs d4 (such as Cr2+)?
Use A1 x “hole” in d5
What are the term states of d9 (such as Cu2+)?
Need to find orbital degen for arranging a hole
How many bands are observed in d-d bands in Oh/Td?
Oh/Td have one d-d band each
Oh: T2 -> E
Td: E -> T2
Any asymm band due to JT dist
What are the relative intensities of d-d bands?
Moderate intensities
What is the assumption of the weak-field approach?
Ligand field is a small perturbation to Russel-Saunders terms of the free ion
Is in the gas-phase
What is the weak-field state of d1?
5x microstates with different ML values
5xequal energy 3d states
Ground state is 2D
What is the weak-field state of d6?
e- added to spherical d5
Causes s=2, S=5, L=2
5D
What is the weak-field state of d4?
s=2, S=5, L=2
5D
What is the weak-field state of d9?
4xe- added to d5 sphere
s=1/2, S = 2, L=2
2D
What is the symmetry of free ions?
Spherical symm - R3
How can you find how a free ion term splits into fields in different fields?
Use descent in symm tables (O includes cubic ligand fields such as Oh and Td)
Look at term under R3 and find the orbitals which they split into
What is an orgel diagram?
Plots splitting of free ion terms and energy of microstates with increasing ligand field splitting (Δ)
How does the electric TDM operator transform as in Oh and Td symm?
x,y,z on RHS
In Oh: T1u
In Td: T2
What is required for an allowed transition wrt symmetry?
Non-zero TDM means integrand must be an even function
Γ(ψfinal) x Γ(μ) x Γ(ψinitial) must contain A1
What is the spin selection rule and when is it not followed?
ΔS = 0
Breaks down when ψspinψorbital cannot be separated due to spin-orbit coupling
This breaks as atoms get heavier
What is the Laporte selection rule and when is it applicable?
ΔL = +/- 1 for Q =! 0
When spin and orbital wavefn can be separated
When centrosymm has parity rule of: g <-> u
What does Laporte rule prevent?
Forbids: p-p / d-d / f-f transitions in atoms and ions
Why do Oh have less intense transitions than Td?
Td is non-centrosymmetroic so doesn’t need to fufill parity part of Laporte rule -> less forbidden
Oh has to follow those rules
What relaxes the parity part of Laporte rule?
Relaxed by vibronic coupling
Co-excite a vib mode of symm
How does covalency effect the amount of vibronic coupling?
Covalency increases vib coupling
How does vib coupling relax parity selec rule?
Separate ψ = ψelecψvib</sup
What dictates band widths of transitions?
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
Why do hs d5 complexes have broad and sharp bands?
Sharp - due to spin flips within the t2g and eg, no change in bonding
Broad due to covalency - large change in bond length from t2g -> eg
So large co-excitation of vib states
What mixing occurs in Td complexes?
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
What is the intensity of π->π* transitions?
v large
as large dipole moment change
How many transitions would you usually predict for d2,3,7,8 ions?
Would expect 3 transitions
(you dont)
What are the free ion terms of d2?
s=1, S= 3
Max ML = 3, which implies 3F
Also see a 3P term
How do d2 free ion terms split in ligand fields?
Within Oh/Td
3F -> 3A2 + 3T2 + 3T1
3P -> 3T1
Means there are 3x spin-allowed, laporte forbidden bands observable due to vib coupling mech
What is the ligand ground state of Oh d2?
s=1, S=3, L=3 so T
9 possible microstates
t2g x t2g = A1g + Eg + [T1g] + T2g
Spin triplet associated with 1T1g
g.s is 3T2g
other states are singlet states
What is the config interaction of d2?
Splitting of F term increases with Δ
Set difference in F and P states is 15B, which is the Racah parameter
What is observed in the elec spectrum of d2?
In this case large Δ which causes A2g to raise above T1g
No band gives Δ
What is the summary for d2,3,7,8 Oh elec spec?
How many bands are observed in different dn?
dn:
0,4,6,9 - gives 1 band
5 - no bands
2,3,7,8 - gives 3 bands
What is the summary Orgel diagram for Oh/Td d2,3,7,8?
When are Orgel diagrams used?
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
What is a Tanabe-Sugano diagram?
Δ (in terms of B) on x-axis
Energy (in terms of B) on y-axis
Quantitative version of Orgel
What units are energies given in Tanabe-Sugano diagram?
In terms of B - the racah parameter
Where the racah term is from e- repulsion
All are relative to ground state
How do Racah parameters B and C relate?
Both measures of e- repulsion
C/B ~ 4
How can you find Racah parameters using Tanabe-Sugano diagrams?
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
What suggests mixing occurs in a Tanabe-Sugano diagram?
Close in energy, around Δ/B = 10
This can give rise to spin-forbidden bands
What is the nephelauxetic effect?
Reduced e- repulsion (and racah parameter) in complexes than free ions
Suggests increased average distance between e-
What is the source of nephelauxetic effect?
Covalence of M-L bonding delocalises e-
So more spread out and lower B
What is the nephelauxetic effect series?
Extent differnet ligands reduce B:
2nd/3rd row deecrease B most
F- < H2O < NH3 < en < ox < SCN- < Cl- < CN- < Br- < I-
What occurs in a LMCT?
Ligand-to-metal charge transfer
Excitation of an e- frommainly ligand-based orbital to mainly metal-based orbital
What are the symmetries in tetrahedral complexes which allow LMCT?
t2 MOs are σ and π in symm and so have contributions of both d and p orbitals
Ligand e- fill up to t1
What are the LMCT transitions in Td complexes?
LMCT of increasing energy:
t1(π) -> e(π*)
t1(π) -> t2(σ*,π*)
t2(σ,π) -> e(π*)
t2(σ,π) -> t2(σ*,π*)
What are the SALCs in Oh complexes?
σ: a1g + eg + t1u
π: t1g + t2g + t1u + t2u
What are the LMCT excitations in Oh complexes?
LMCT transitions:
t1u(σπ) & t2u(π) -> t2g + eg
u x u x g -> g, allowed BUT
t1g(π) -> t2g(π*) is forbidden
How does changing the ligand change frequency of LMCT transitions?
Less χ (electro-ve) ligands have less tightly held t1(π) e- at higher energy
Means v(LMCT) decreases down the group
How does metal oxn state change freq of LMCT?
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)
How does freq of LMCT change across a series?
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
How does freq of LMCT change down the group?
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)
What bands are seen in [MnO4]-?
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
What does J-value size suggest about following Curie law?
Large J suggests follows the Curie law
As ligand-field effects negligible
How does separation of states depend on J?
The separation is proportional to J
So larger values will have larger spacing
Why does Eu(III) have a mag moment when not expected by spin-only?
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
How does mag moment of Er(III) change at low T?
Only below 10K does diff between energy levels is close to kT
So accessible es
What is the 2nd order Zeeman effect?
Seen in Eu(III)
Mixing es into gs, which is proportional to B2/energy separation
Not T dependent, doesnt effect Curie behaviour
When does spin-orbit coupling or term symbols more important?
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
What does L values mean for Curie law?
Curie law when only one state available so L=0
For T dependent, L>0
