Transcript Slide 1

Lecture 28
Electronic Spectra of Coordination Compounds MLx (x = 4,6)
1) Terms of a free d2 metal atom
•
The total number of microstates for an isolated metal of d2 configuration is
(10!)/(8!2!) = 45. The whole set of terms includes:
3F
(S=1, L=3)
3P (S=1, L=1)
1G (S=0, L=4)
1D (S=0, L=2)
1S (S=0, L=0)
TOTAL:
(2·1+1)·(2·3+1)=21 microstates,
(2·1+1)·(2·1+1)=9 microstates,
(2·0+1)·(2·4+1)=9 microstates,
(2·0+1)·(2·2+1)=5 microstates and
(2·0+1)·(2·0+1)=1 microstate
45 microstates
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The calculated term energy sequence is 3F (lowest), 1D, 3P, 1G, 1S (highest).
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The wavefunctions for S, P, D, F etc. terms are of the same symmetry as for s, p, d, f
etc orbitals. Therefore the terms will be split by a ligand field in the same way as the
corresponding orbitals are (check the appropriate character table!).
2) Term splitting for octahedral d2 metal complexes
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•
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When placed in a ligand field, the five
terms of d2 atom will be split. The
splitting is a function of the ligand field
symmetry and strength.
Each term is split so that the energy
loss of the destabilized terms is
compensated by the energy gain of
the stabilized terms.
At the infinitely strong ligand field
electron – electron interactions are
negligible. The resulting energy levels
will be eg and t2g. Three
configurations will be possible: (eg)2,
(eg)1(t2g)1 and (t2g)2.
no field
weak field
very strong field
1
1
A1
S
1
G
1
E
1
T1
1
T
1 2
A1
3
3
P
T1
1
1
D
E
T2
(e)2
1
T1
1
T2
3
T1
3
T2
(t2)(e)
1
A1g
x2+y2+z2
Eg
(2z2-x2-y2, x2-y2)
T2g
(xz, yz, xy)
A2u
T2u
A1
1
E
3
A2
1
Oh
T1u
1
3
xyz
(x,y,z)
x3, y3, z3
x(z2-y2),…
F
3
A2
3
T2
3
T1
states of identical designation never cross
labels "g" for octahedral field terms are omitted
A1
1
E
1
T2
3
T1
(t2)2
3) The number of bands: octahedral d2 and d8 complexes
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Often correlation diagrams for dn, d10-n Oh and Td complexes are combined. The “bottom”
part of the diagram for octahedral and tetrahedral d2 and d8 complexes looks like:
5
3
(t2) (e)
(t2)1(e)1
1
T
1 1
T
3 2
T1
3
T2
3
3
T1
P
1
1
T2
1
D
(e)2
(t2)6(e)2
A1
1
E
3
A2
3
T1
3
T2
3
A2
octahedral d8 and tetrahedral d2
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T1
1
E
T2
1
T
1 1
T (t )(e)
3 2 2
T1
(t2)4(e)4
3
T2
1
E
1
3
3
F
3
A
3 2
T2
3
T1
1
A1
1
E
1
T2
3
T1
(t2)2
(t2)4(e)4
octahedral d2 and tetrahedral d8
To find the number of the spin-allowed absorption bands it will be enough to find all
terms which have the same multiplicity as the ground state term.
Note that the multiplicity of the ground state terms for d2 and d8 configurations is the
same at any field strength. It is true for certain configurations only (octahedral d1, d2, d3,
d8, d9)
For d2 and d8 metal complexes there are three more terms of the same multiplicity as
the ground state term (triplet). Therefore, we expect three bands in the electronic
absorption spectra of these complexes.
4) High spin complexes of d1-4, d6-9 configurations: Orgel diagrams
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The information about the number and the relative energy of available terms of the same
multiplicity as the multiplicity of the ground state for the case of high spin complexes is
given by Orgel diagrams.
It is enough to have two diagrams for the cases of d1 and d2 metal configurations to find spinallowed transitions for any high spin octahedral or tetrahedral d1-4, d6-9 complexes: dn behaves
as d5+n and opposite to d10-n and d5-n.
With the help of Orgel diagrams: 1) the observed absorption bands can be assigned to certain
transitions; 2) one can predict blue or red shifts for each of the absorption bands as the ligand
field changes.
Energy
d1, d6 Oh
d4, d9 Td
d4, d9 Oh
d1, d6 Td
Eg
T2
Energy d3, d8 O
h
2 7
d , d Td
d2, d7 Oh
d3, d8 Td
A2g
T1(P)
T1g(P)
T1(F)
T2g
T2
E
T2g

0

T1g(F)
A2

0

5) Qualitative analysis of electron absorption spectra: Oh d8
complexes
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According to the Orgel diagram for octahedral d8 metal complexes, such
complexes exhibit 3 absorption bands due to d-d transitions.
, L/mol cm
14
Energy d3, d8 O
h
d2, d7 Td
2
7
d , d Oh
d3, d8 Td
12
3
3
T1g(P)
A2g
A2
T1(P)
10
T1g(P)
T1(F)
T2g
3
A2g
8
3
T1g(F)
3
A2g
3
T2g
6
T2
T1g(F)
A2

Ni(NH 3)62+
0

4
2
400
600
800
1000
1200
, nm
6) Qualitative analysis of electron absorption spectra: Oh d4 and d6
complexes
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For an octahedral high-spin d4 metal complex, Cr(OH2)62+, a single absorption band is
observed at 14000 cm-1 (5Eg  5T2g) as expected (see Orgel diagram below).
Energy
d1, d6 Oh
d4, d9 Td
d4 , d 9 O h
d1, d6 Td
Eg
T2
E
T2g

0

7) Qualitative analysis of electron absorption spectra: Oh d3 and d7
complexes
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For an octahedral d3 metal complex, CrF63-, three absorption bands are observed: 14900
(4A2g  4T2g), 22700 (4A2g  4T1g(F)), and 34400 (4A2g  4T1g(P)) cm-1 as expected (see
Orgel diagram below, left half).
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For an octahedral d7 high-spin complex, Co(OH2)62+, three observed absorption bands are
8100 (4T1g(F)  4T2g), 22700 (4T1g(F)  4A2g), and 34400 (4T1g(F)  4T1g(P)) cm-1 as
expected (see Orgel diagram below, right half).
Energy d3, d8 O
h
d 2, d7 T d
d2, d7 Oh
d3, d8 Td
A2
T1(P)
T1g(P)
T1(F)
T2g
T2
T1g(F)
A2

0
