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Chapter 7
Electronic spectra of transition metal complexes
or
The interaction is called Russel-Saunders
L-S coupling. The interactions produce
atomic states called microstates that are
described by a new set of quantum numbers.
ML = total orbital angular momentum
=Σml
MS = total spin angular momentum = Σms
A microstate table that contains all
possible combinations of ml and ms is
constructed.
Each microstate represents a possible
electron configuration. Both ground state
and excited states are considered.
Microstates would have the same energy
only if repulsion between electrons is
negligible. In an octahedral or tetrahedral
complex, microstates that correspond to
different relative spatial distributions of the
electrons will have different energies. As a
result, distinguishable energy levels, called
terms are seen.
To obtain all of the terms for a given
electron configuration, a microstate table is
constructed. The table is a grid of all
possible electronic arrangements. It lists all
of the possible values of spin and orbital
orientation. It includes both ground and
excited states, and must obey the Pauli
Exclusion Principle.
Consider an atom of carbon. Its highest
occupied orbital has a p2 electron
configuration.
Microstates correspond to the various
possible occupation of the px, py and pz
orbitals.
ml =
+1
0
-1
Configurations: ___ ___ ___
___ ___ ___
___ ___ ___
microstate:
(1+,0+)
(0+,-1+)
(1+,-1+)
These are examples of some of the
ground state microstates. Others would have
the electrons (arrows) pointing down.
ml =
+1
0
-1
Configurations: ___ ___ ___
___ ___ ___
___ ___ ___
microstate:
(1+,1-)
(0+,0-)
(-1+,-1-)
These are examples of some of the
excited state microstates.
For the carbon atom, ML will range from
+2 down to -2, and MS can have values of +1
(both electrons “pointing up”), 0 (one electron
“up”, one electron “down”), or -1 (both
electrons “pointing down”).
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
The table
includes all
possible
microstates.
Once the microstate table is complete, the
microstates are collected or grouped into
atomic (coupled) energy states.
For two electrons,
L = l1+ l2, l1+ l2-1, l1+ l2-2,…│l1- l2│
For a p2 configuration, L = 1+1, 1+1-1, 1-1.
The values of L are: 2, 1 and 0.
L is always positive, and ranges from the
maximum value of Σl.
For two electrons,
S = s1+ s2, s1+ s2-1, s1+ s2-2,…│s1- s2│
For a p2 configuration, S = ½ + ½ , ½ + ½ -1.
The values of S are: 1 and 0.
Quantum numbers L and S describe
collections of microstates, whereas ML and MS
describe the individual microstates
themselves.
The microstate table is a grid that includes
all possible combinations of L, the total
angular momentum quantum number, and S,
the total spin angular momentum quantum
number.
For two electrons,
L = l1+ l2, l1+ l2-1, l1+ l2-2,…│l1- l2│
S = s1+ s2, s1+ s2-1, s1+ s2-2,…│s1- s2│
Once the microstate table is complete, all
microstates associated with an energy state
with specific value of L and S are grouped.
It doesn’t matter which specific
microstates are placed in the group.
Microstates are grouped and eliminated until
all microstates are associated with a specific
energy state or term.
Each energy state or term is represented
by a term symbol. The term symbol is a
capitol letter that is related to the value of L.
L=
0
1
2
3
4
Term
Symbol
S
P
D
F
G
The upper left corner of the
term symbol contains a number
called the multiplicity. The
multiplicity is the number of
unpaired electrons +1, or 2S+1.
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
Eliminate
microstates
with
ML=+2-2,
with Ms=0.
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
These
microstates
are
associated
with the term
1D.
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
Eliminate
microstates
with
ML=+1-1,
with
Ms=+1-1
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
Eliminate
microstates
with
ML=+1-1,
with
Ms=+1-1
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
These
microstates
are
associated
with the term
3P.
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
One
microstate
remains. It
is
associated
with the term
1S.
The term states for a p2 electron
configuration are 1S, 3P, and 1D.
The term symbol with the greatest
multiplicity and highest value of ML will be
the ground state. 3P is the ground state term
for carbon.
1. For a given electron configuration, the term
with the greatest multiplicity lies lowest in
energy. (This is consistent with Hund’s rule.)
2. For a term of a given multiplicity, the
greater the value of L, the lower the energy.
For a p2 configuration, the
term states are 3P, 1D and 1S.
The terms for the free atom
should have the following relative
energies:
3P< 1D
<1S
The rules for predicting the
ground state always work, but
they may fail in predicting the
order of energies for excited
states.
A microstate table for a d2 electron
configuration will contain 45 microstates (ML
= 4-4, and MS=1, 0 or -1) associated with
the following terms:
1S, 1D, 1G, 3P, and 3F

Problem: Determine the ground state of a
free atom with a d2 electron configuration,
and place the terms in order of increasing
energy.
1S, 1D, 1G, 3P,
and 3F
We only need to know the ground state
term to interpret the spectra of transition
metal complexes. This can be obtained
without constructing a microstate table.
The ground state will
a) have the maximum multiplicity
b) have the maximum value of ML for the
configuration obtained in part (a).
a) Wavelength
Energy of electronic transition
b) Shape.
Gaussian Band Shape - coupling of electronic and
vibrational states
c) Intensity.
Molar absorptivity,  (M1cm1) due to probability
of electronic transitions.
d) Number of bands
Transitions between States of given dn configuration.
Electronic transitions are controlled by quantum mechanical selection rules
which determine the probability (intensity) of the transition.
Transition
Spin and Symmetry forbidden "d-d" bands
Spin allowed and Symmetry forbidden "d-d" bands
Spin and Symmetry allowed LMCT and MLCT bands
εmax (M1cm1)
0.02 - 1
(Oh) 1 - 10
(Td) 10 – 103
103 - 5 x 104
Spin Selection Rule: There must be no change in the spin multiplicity (2S + 1)
during the transition.
i.e. the spin of the electron must not change during the transition.
Symmetry (Laporte) Selection Rule: There must be a change in parity (g ↔ u)
during the transition
Since s and d orbitals are g (gerade) and p orbitals are u(ungerade), only
s ↔ p and p ↔ d transitions are allowed and d → d transition are formally
forbidden. [i.e. only transitions for which Δl = ± 1 are allowed].
d → d bands are allowed to the extent that the starting or terminal level of the
transition is not a pure d-orbital. (i.e. it is a molecular orbital of the complex
with both metal and ligand character).
States for dn configurations
Russel-Saunders Coupling
• Angular momentum of individual electrons couple to give total angular
momentum for dn configuration ML = ∑ml
• Spin momentum of individual electron spins couple together to give total
spin, S = ∑s
• Inter-electronic repulsions between the electrons in the d orbitals give rise to
ground state and excited states for dn configurations.
• States are labeled with Tern Symbols
• Electonic transitions between ground and excited states are summarized in
Orgel and Tanabe-Sugano diagrams .
• Term Symbols (labels for states) contain information about L and S for state
Hund’s Rules. i) Ground state has maximum spin, S
ii) For states of same spin, ground state has maximum L.
Number of d-d bands in electronic spectrum
Excitation from ground state to excited stated of dn configuration
Ground State
Triple degeneracy of a d2 ion’s 3T2g
ground state due to three possible sites
for hole in t2g level
Singly degenerate 3T2g ground state.
Only one possible arrangement for
three electrons in t2g level
Triple degenerate ground state for d7
Three possible sites for hole in t2g level
d2
eg
t2g
eg
d
3
t2g
eg
d
7
t2g
Singly degenerate 3T2g ground state.
Only one possible arrangement for
six t2g electrons.
eg
d
8
t2g
Excited States
Labeling of d-d bands in electronic spectrum.


Consider states of dn configuration
Determine free ion ground state Term Symbol (labels
for states)

Assign splitting of states in ligand field

Spectroscopic labeling of bands.


Orgel diagrams (high-spin)
Tanabe-Sugano diagrams (high-spin and low-spin)
Individual electron l = 2, ml = 2, 1, 0, -1, -2
Maximum ml = l
l =
0, 1, 2, 3,
Orbital: s, p, d , f
_______________________________
dn configuration, L = 0, 1, 2, 3, 4
Term Symbol
S, P, D, F, G
ML = Σ ml, maximum ML = L
Spin Multiplicity = 2 S +1
M L = m l
L = M L( m ax)
l = 2,
ml =
2
1
S = s
0
-1
-2
Te rm
2 S + 1 s ym bo l
L
S
2
1/2
2
3
1
3
3
3 3/2
4
4
2
2
5
5
0
5/2
6
6
2
D
F
F
D
S
Ground state determined by inspection of degeneracy of terms for given dn
Orgel Diagrams
3
3
2
Eg
3
P
A2g
D
4
F
d1
2
T2g
Ti3+
3
T2g
o
d2
2
4
Eg
3
P
3
T1g
3
T1g
V2+
5
T1g
4
F
T2g
d3
3
5
T2g
D
5
T1g
o
T1g
T1g(P)
T2g
3
2
4
4
3
2
T1g(P)
4
o
A2g
Eg
d4 o
T2g
3
A2g
3
T1g(P)
Cr3+
Mn3+
The d-d bands of the d 2 ion [V(H2O) 6]3+
Racah Inter-electronic Repulsion Parameters (B, C)
1
S
1
G
3
P
E(3P) = A+7B
1
D
E(1D) = A - 3B + 2C
3
F
E(3F) = A - 8B
d2
3
F
3
F
3
P
= 15B
1
D
= 5B + 2C
The Tanabe-Sugano diagram for the d2 ion
Reduction in electron-electron repulsion upon complex formation
Racah Parameter, B: electron-elctronic repulsion parameter
Bo is the inter- electronic repulsion in the gaseous Mn+ ion.
B is the inter- electronic repulsion in the complexed MLxn+ ion.
The smaller values for B in the complex compared to free gaseous
ion is taken as evidence of smaller inter-electronic repulsion in the
complex due to a larger “molecular orbital” on account of overlap
of ligand and metal orbital, i.e. evidence of covalency (cloud
expansion”).
Nephelauxetic Ratio, β = B
Bo
Nephelauxetic Ligand Series
I < Br < CN < Cl < NCS < C2O42- < en < NH3 < H2O < F
Small β
Covalent
Large β
Ionic
Nephelauxetic Metal Series
Pt4+ < Co3+ < Rh3+~Ir3+ < Fe3+ < Cr3+ < Ni2+ < V4+< Pt2+~ Mn2+
Small β
Large β
Large overlap
Small overlap
Covalent
Ionic
Cr(NH3)63+
β = 1 –hk
β = 1 –(1.4)(0.21)
= 0.706
Cr(CN)63-
β = 1 –hk
β = 1 –(2.0)(0.21)
= 0.580
Bo - B = hligands x kmetal ion
Bo
Typical Δo and λmax values for octahedral (ML6) d-block metal complexes
__________________________________________________________________
Complex
Δo cm-1
~ λmax (nm)
Complex
Δo cm-1
λmax
(nm)
___________________________________________________________________________________
[Ti(H2O)6]3+
20,300
493
[Fe(H2O)6]2+
9,400
1064
3+
3+
[V(H2O)6]
20,300
493
[Fe(H2O)6]
13,700
730
[V(H2O)6]2+
12,400
806
[Fe(CN)6]335,000
286
[CrF6]315,000
667
[Fe(CN)6]433,800
296
3+
3[Co(H2O)6] , l.s. 20,700
483
[Fe(C2O4)3]
14,100
709
[Cr(H2O)6]2+
14,100
709
[Co(CN)6]3- l.s.
34,800
287
[Cr(H2O)6]3+
17,400
575
[Co(NH3)6]3+ l.s. 22,900
437
3+
2+
[Cr(NH3)6]
21,600
463
[Ni(H2O)6]
8,500
1176
[Cr(en)3]3+
21,900
457
[Ni(NH3)6]2+
10,800
926
[Cr(CN)6]326,600
376
[Ni(en)3]2+
11,500
870
___________________________________________________________________________________
1.
Assign the metal oxidation state in the following compounds.
a.
b.
c.
K2[PtCl6]
Na2[Fe(CO)4]
[Mn(CH3)(CO)5]
2.
Account for the following:
The manganous ion, [Mn(H2O)6]2+, reacts with CN- to form [Mn(CN)6]4- which has
m = 1.95 B.M., but with I- to give [MnI4]2- which has m = 5.93 B. M.
[Co(NH3)6]Cl3 is diamagnetic, whereas Na3[CoF6] is paramagnetic (m = 5.02 B.M).
[PtBr2Cl2]2 is diamagnetic and exists in two isomeric forms, whereas [NiBr2Cl2]2
has a magnetic moment, m = 3.95 B.M., and does not exhibit isomerism.
Copper(II) complexes are typically blue with one visible absorption band in their
electronic spectra whereas copper(I) complexes are generally colorless.
Assign a spectroscopic label to the Cu2+ transition.