Ligand Field Theory
continued
Spectroscopic Term Symbols
Selection Rules
Orgel Diagrams
Tanabe Sugano Diagrams
LMCT, MLCT
Nephelauxetic Effect
ESR
Magnetic Properties
Octahedral, versus trigonal prismatic d0 and d1 complexes
Some d0 and d1 M prefer
trigonal prismatic,
D3h, rather than Oh
Example:
[Ta(Me)6]-, [Zr(Me)6]is trigonal prismatic
[Mo(Me)6] and [W(Me)6]
distorted prismatic
M-C σ bond: 6e- from M,
6e- from 6CH3 L
Oh:a1g2, eg4, t1u6
Net stabilization of E for D3h
hence many d0 and1d-organometallic
complexes are trigonal prismatic
not octahedral
Electronic Spectra of Transition Metal Complexes
Absorption band of complex:
λmax position of peak
εmax = Amax/c x l (dm3 mol-1 cm-1)
εmax 0-10,000
Color of transition mretal
complex is due to
d-d transitions
d1, d4, d6, d9 complexes →one abs. band
d2, d3, d7, d8 → three abs. bands
d5 complexes → very weak sharp abs.
1. Metal centered d-d
2. CT, charge transfer
M→L or L →M
More intense bands
νλ =c
1/λ = ν
Absorption of photon in 10-18 s molecular vibrations, rotations much slower
breadth of abs. is due to range (many) vibrational and rotational states
different microstates arising from different configuration are Spectroscopic Term Symbols
Spectroscopic Term Symbols
microstates: number of different ways ecan be placed in a given set of orbital
sites
e.g., p2
or
ml
1
0
-1
or
1
0
-1
Etc….there are 15 different ways to put 2 electrons in 3 p orbitals
It is clear that E (ML = 2) > E (ML = 1)
1
0
-1
Spectroscopic Term Symbols
n!
# microstates = -------e! h!
where n = max # electrons in sublevel
(sum of e + h)
e = #e- in case study
h = # "holes" in case study
a site (hole is not occupied by an e-)
e.g., d3 : n = 10, e = 3, h = 7
…….
.
.
ML=Σmli =ml1 + ml2…..
MS = Σms = ms1 +ms2……
We’ll look at ns2, ns1n’s1, and
p2 on next slide!
Are other states possible?
Analogous to:
l =0 1 2 3
s p d f
L=
0 1 2
3
4
2S+1L
J
Total angluar momentum quantum #:
J = L+S, L+S-1, L+S-2….l L-S l
For s,F l = 0, ml = 0; for p l =1, ml = 1, 0, -1; ML = Σml
o
r
Any other terms?
p2
Largest ML=1+1 = 2
L=2, D; S=0, 2S+1 = 1 1D
(2L+1)(2S+1) = 5 states
L=1, S=1; 3P
(2L+1)(2S+1) = 9
L=0, S=0; 1S
(2L+1)(2S+1) = 1
Highest multiplicity: 2S+1
2S+1 = 4
2S+1= 6
d2 Case
10!
9*10
#microstates = ---------- = ---------- = 45
2!*8!
2
Experimentally determined
ordering of energy states
2S+1L
J
Identify the ground term symbol of Fe2+ d6
MS = Σ ms; ML = Σ ml; ML = L, L-1….., -L; MS = S, S-1…, -S
L = 0, 1, 2, 3 4…..
S, P, D, F, G
S = 0, ½, 1, 3/2, 2…..
2S+1 = 1, 2, 3……
What is the ground term symbol of the C atom with 2p2 electronic configuration?
Is the ground state energy (symbol) the same for [Fe(H2O)6]3+ and [Fe(CN)6]3-?
Spin and Orbital Contribution to the magnetic moment
4λ
EJ-(J+1) =(J+1)/λ
λ-spin-orbit coupling constant
large only for lanthanides f elements
At 300 K, RT, kT ≈ 200cm-1
3λ
2J+1 levels; ∆E=gJµBB0
gJ is the Lande splitting factor
these are E levels of epr spectra
hν is in the radio frequency range
Selection Rules
Spin selection:
∆S = 0
Change in spin multiplicity is forbidden
Laporte selection rules:
Allowed transitions: g ↔ u
Forbidden transitions: g ↔ g, u ↔ u
hence,
∆l = ±1
Allowed transitions: s ↔ p, p ↔ d, d ↔ f
Forbidden: s ↔ s, p ↔ p, s ↔ d, f ↔ f, etc..
d ↔d
So why d-d transitions observed?
Spin-forbidden transition becomes
“allowed” by mixing of for example
singlet and triplet states
Electronic Spectra of Octahedral Complexes-HS only
Ti(H2O6]3+
d1 ml=2, L=2; S=1/2
Ground state: 2D
E of transition depends
on ∆oct characteristic of complex
Orgel Diagrams
For Oh and Td
d1, d4, d6, d9
one electronic transition
spin allowed
T2g ← Eg
Cr5+, Fe2+
d0, d5, d10 spherical
Eg ← T2g
Mn3+, Cu2+
What are the multiplicities?
For d1: 2Eg ←2T2g
The others?
Why a doublet?
i.e, why two absorption bands, or two transitions? Can you explain?
3A : t 0
2g 2g
3T : t 1e 1:
1g 2g g
Consider the d2 ion
3F (ground state),
3P next lowest
state
3 possible
transistions:
3T F)← 3T
2g
1g
3A
2g
(F)← 3T1g
3T (P)
1g
← 3T1g
(dxy)1(dx2-y2)1
3T : t 1e 1:
2g 2g g
3T :
1g:
eg2
(dxy)1(dz2)1
t2g2eg0
3A : t 0
2g 2g
3T : t 1e 1:
1g 2g g
Consider the d2 ion
3F (ground state),
3P next lowest
state
3 possible
transistions:
3T F)← 3T
2g
1g
3A
2g
(F)← 3T1g
3T (P)
1g
← 3T1g
(dxy)1(dx2-y2)1
3T : t 1e 1:
2g 2g g
3T :
1g:
eg2
(dxy)1(dz2)1
t2g2eg0
Note shift in E of bands for H2O and NH3 complex
[Ni(H2O)6]2+ and [Ni(NH3)6[2+ d8 Oh complexes
Note E and ∆ in B
A B C are
Racah parameters
take into account
electronic repulsions
∆oct/B = 29
E2/B=40
E2 = 25,600 cm-1
40=25,600/B
Application of Tanabe-Sugano DiagramExample 20.5
[V(H2O)6]3+ d2 complex:
Absorptions at:
17,200 cm-1 3T2g ← 3T1g
25,600 cm-1 3T1g(P)← 3T1g
Estimate B and ∆oct
Important point:
from Tanabe-Sugano diagram
only approx. ∆oct and B possible
Let: E2 = 25,600 cm-1
E1 = 17,200 cm-1
B = 640 cm-1
Proceed with trial and error:
E1/B=26.9 cm-1
E1 = 17,200 cm-1
(E2/B)/(E1/B) = 1.49
B =640 cm-1
When ∆oct/B = 20
(E2/B)/(E1/B)=32/18 = 1.78
∆oct/640 = 29
∆oct = 18,600 cm-1
∆oct/B = 30
(E2/B)/(E1/B)=41/28 = 1.46
∆oct/B = 29
(E2/B)/(E1/B)=40/26.9 = 1.49
d2
d3
d4
d5
Non-crossing Rule: if two states of the same
symmetry are likely to cross as a parameter is changed, they will mix
together and avoid crossing
T-S for d3
Look at E and A states
of same symmetry in d2 Tanabe Sugano diagram
Absorption band width related/clarified by T-S diagram
d3
Note: 4T2 ← 4A2
lines are not parallel
small change in ∆o
large change in E of
transition
CrCl(NH3)5]2+
Effect of L on E of transitions: Cl- vs NH3
[CrCl(NH3)5]2+
Cr(NH3)6]3+
Oh
due to C4v vs
more splitting of d states
Ligand – to - metal charge transfer transition
LMCT in tetraoxoanions, [MO4]nM in high oxidation state, L has non-bonding electrons
Tetraoxoanions of high valent M are highly colored
due to e ← L ( ‫ ׃‬O) (e MO is empty)
Related to E of transition is correlated with electrochemical
series:
oxidation state M
MnO4- < TcO4- < ReO47+
CrO4- < MoO4- < WO4-
6+
VO4- < NbO4- < TaO4-
5+
Note progression of LMCT absorption bands
correlates with ease of reduction of M
Metal-to-ligand transitions
MLCT: especially Mn+ n=0
π* ← M
2,2’-bipyridine
1,10-phenanthroline
orange
tris(2,2’-bipyridyl)ruthenium(II)
Excited state from CT has lifetime
of microsecond, photochemical redox
reagent
Photon driven oxidation system
λ-MnO2 Catalyst
eRuII*(bpy)3
O2 + 4H+
hυ
S2O82-
2H2O
SO4- + SO42-
RuII(bpy)3/RuIII(bpy)3
Eox = 1.4 V
eIllumination was done using 250W industrial light source with UV filtered by Pyrex
and IR with a 12 cm path water filter at intensity of 20 mWcm-2.
Transitions of Cr3+ in ruby (Al2-xCrxO3)
x ~1-2% CrO6 octahedra
Luminescence:
material emits radiation
after electronic excitation
a. fluorescence: no change
iIn multiplicity (τ =nanosec)
b. phosphorescence:
excited state undergoes
interstate crossing
to state of different
Multiplicity (slow, τ = µsec)
and then undergoes
radiative decay
When emission is stimulated
by 627 nm photons reflecting
back and forth between
two mirrors, it gows in intensity
by many orders of magnitudeprinciple of laser by
-Theodore Maiman
t2g2eg1 ← t2g3; 4T2 ← 4A2 ; 4T1 ← 4A2
Evidence of metal-ligand bonding
Nephelauxetic effect (electron “cloud expanding”): evidence that electrons
are shared between M – L
pairing energies are less in complex than in corresponding Mn+, and effective size
of orbitals increases – e- is delocalized over whole molecule,
hence e- repulsions minimized
For complexes with common metal ion, the nephelauxetic effect varies
as:
F- < H2O < en < [ox]2- < [NCS]- < Cl- < [CN]- < Br- < IFor metals:
Mn(II) < Ni(II) ≈ Co(II) < Mo(II) < Re(IV) < Fe(II) < Ir(III) < Co(III) < Mn(IV)
Estimate reduction of e- - e- repulsion
in complex
(B0 – B)/B0 = hligands x kmetal
β ~ B/B0 the smaller β
greater is delocalization
B = Racah parameter
B0 = inter-electronic repulsion in free Mn+ (g)
d1; e.g., Cr5+
∆E=hν = ge µBB0
ge = 2.0023 for free eβe = µB Bohr magneons
B0 = applied magnetic field (H)
in practice, ν is fixed at ~9GHz
and B0 = H is varied to observe
Resonance
Then g is characteristic of dn
Suppose L has nuclear magnetic
moment, I≠ 0
if I = 1
2I+1 levels
(I nuclear magnetic moment)
If M with unpaired electron is linked to L with I ≠ 0, hyperfine splitting of the esr is observed
showing that the orbital occupied by the electron has both M and L character; M-L covalent bonding
∆
∆
∆me=1; ∆mi=0
Observation of esr hyperfine is further evidence of delocalization of e in complex
Exp:
µeff =(3kχMT/Nµ0 µB )1/2
µeff = 2.828 (χMT)1/2
µ (spin only = 2 [S(S +1)]1/2
Magnetic Susceptibility
A Gouy balance
used to measure magnetic
susceptibility of sample; change of
apparent weight when magnet is
turned on is proportional to
magnetic susceptibility,χ =M/H,
which is determined by number of
unpaired e-
Magnetic Properties and Crystal Field Strength
Low Spin & High Spin Complexes
diamagnetic
paramagnetic
low-spin complex
high-spin complex
only electron configurations d4, d5, d6, or d7 can have low or high spin
52
Magnetic interaction