Cu(H2O)62+
11
Co(H2O)62+
Ni(H2O)62+
Fe(H2O)62+
Coordination Chemistry III: Electronic Spectra
Wheel of Color
absorption spectrum of [Cu(H2O)6]2+
Beer-Lambert Law
-log(I/I0) = A = elc : Absorbance
I/I0 : transmittance
e : molar absorptivity (Lmol-1cm-1)
Wheel of Color
absorption spectrum of [Cu(H2O)6]2+
Beer-Lambert Law
-log(I/I0) = A = elc : Absorbance
I/I0 : transmittance
e : molar absorptivity (Lmol-1cm-1)
Wheel of Color
absorption spectrum of [Cr(NH3)6]3+ (d3)
eg
t2g
absorption spectrum of [Cu(H2O)6]2+
eg
Why 4 or 2 bands?
t2g
Wheel of Color
Because the transitions occur between states.
An electron configuration can have several states.
Possible states (microstates) of carbon (1s22s22p2)
absorption spectrum of [Cr(NH3)6]3+ (d3)
eg
absorption spectrum of [Cu(H2O)6]2+
and many
others
..... 2
(think
Pc and Pe)
Why
4 or
bands?
t2g
eg
t2g
Strategy to understand the electronic spectra of complexes
1. Determine free-ion (or in uniform field) term symbols.
2. Determine how these terms split in a weak field.
3. Determine how these terms split in a strong field.
4. Correlate these with Tanabe-Sugano diagram.
Terms : energy levels (or states) of a particular configuration
Quantum numbers of single
electron atoms (ions)
Terms (Term Symbols)
Quantum numbers of single electron atoms (ions)
Y = Rnl(r)·Q lm (q)·Flm (f)·ym
l
l
s
n : principal quantum number (n = 1,2,3,4....)
l : (orbital) angular momemtum quantum number (l = 0, 1,...., n-1)
ml : angular momemtum magnetic quantum number (l = -n, -n+1,...., n)
ms : spin magnetic quatum number (ms = -½ , ½ )
Terms (Term Symbols)
Quantum numbers of
multielectron atoms (ions)
Quantum numbers of multielectron atoms (ions)
Two schemes for describing interactions (couplings) between electrons
1. Russell-Saunders coupling (L-S coupling)
a. Orbit-orbit interaction (coupling) :
ML = Sml L : total orbital angular momentum quantum number
b. Spin-spin interaction (coupling) :
MS = Sms  S : total spin angular momentum quantum number
c. L-S coupling :
J = L + S : total angular moment quantum number
2. j-j coupling (spin-orbit interaction)
jn = ln + sn  J = Sjn : total angular moment quantum number
In light atoms, the interactions between the orbital angular momenta of individual electrons is
stronger than the spin-orbit coupling between the spin and orbital angular momenta. These
cases are described by "L-S coupling". However, for heavier elements with larger nuclear
charge, the spin-orbit interactions become as strong as the interactions between individual
spins or orbital angular momenta. We won't study the latter in this course.
Terms (Term Symbols)
Quantum numbers of
multielectron atoms(ions)
Quantum numbers of multielectron atoms (ions)
Russell-Saunders coupling (L-S coupling)
a. Orbit-orbit interaction (coupling) :
ML = Sml L : total orbital angular momentum quantum number
b. Spin-spin interaction (coupling) :
MS = Sms  S : total spin angular momentum quantum number
c. L-S coupling :
J = L + S : total angular moment quantum number
J = |L-S|, |L-S|+1, ... , L+S
Terms (Term Symbols)
Free Ion Term Symbols
Quantum numbers of multielectron atoms (ions)
Russell-Saunders coupling (L-S coupling)
a. Orbit-orbit interaction (coupling) :
ML = Sml L : total orbital angular momentum quantum number
b. Spin-spin interaction (coupling) :
MS = Sms  S : total spin angular momentum quantum number
c. L-S coupling :
J = L + S : total angular moment quantum number
J = |L-S|, |L-S|+1, ... , L+S
Term symbol
2S+1L
J
2S+1 : spin multiplicity
States : L = 0 (S), 1(P), 2(D), 3(F), 4(G), 5(H), 6(I),...
Terms (Term Symbols)
Free Ion Term Symbols
1S
MS = 0
2S
MS = -1/2
MS = +1/2
ML=0
x
ML=0
x
x
1 microstate
2 microstates
3P
MS = 1
MS = 0
MS = -1
ML=1
x
x
x
ML=0
x
x
x
ML=-1
x
x
x
9 microstates
Term symbol
2S+1L
J
2S+1 : spin multiplicity
States : L = 0 (S), 1(P), 2(D), 3(F), 4(G), 5(H), 6(I),...
Terms (Term Symbols)
Free Ion Term Symbols
A systematic approach to term symbols
1. Determine the possible values of ML and MS.
2. Determine the electron configurations that are allowed by the Pauli principle.
3. Set up a chart of microstates.
4. Resolve the chart of microstates into appropriate atomic states (terms).
Possible states (microstates) of carbon (1s22s22p2)
1s
2s
2p
ml
0
0
1
0
ms
+½
-½
+½
-½
+½
+½
(1+, 0+)
-1
1s
2s
2p
0
0
1
+½
-½
+½
-½
+½
-½
0
(1+, 1-)
-1
p2
Terms (Term Symbols)
Free Ion Term Symbols
A systematic approach to term symbols
1. Determine the possible values of ML and MS.
2. Determine the electron configurations that are allowed by the Pauli principle.
3. Set up a chart of microstates.
4. Resolve the chart of microstates into appropriate atomic states (terms).
p2
l1 = l2 = 1
s1 = s 2 = ½
ML = 2, 1, 0, -1, -2
MS = 1, 0, -1
Terms (Term Symbols)
Free Ion Term Symbols
A systematic approach to term symbols
1. Determine the possible values of ML and MS.
2. Determine the electron configurations that are allowed by the Pauli principle.
3. Set up a chart of microstates.
4. Resolve the chart of microstates into appropriate atomic states (terms).
1. Max MS = 0 : S = 0  MS = 0
Max ML = 2 : L = 2  ML = 2,1,0,-1,-2  1D ( 5 microstates)
2. Max MS = 1 : S = 1  MS = 1,0,-1
Max ML = 1 : L = 1  ML = 1,0,-1  3P ( 9 microstates)
3. Max MS = 0 : S = 0  MS = 0
Max ML = 0 : L = 0  ML = 0  1S ( 1 microstate)
Terms (Term Symbols)
Free Ion Term Symbols
A systematic approach to term symbols
1. Determine the possible values of ML and MS.
2. Determine the electron configurations that are allowed by the Pauli principle.
3. Set up a chart of microstates.
4. Resolve the chart of microstates into appropriate atomic states (terms).
p2
1D
1D
2
3P
3P ,3P ,3P
2
1
0
1S
1S
0
mJ = 0
mJ = 0
mJ = 2,1,0,-1,-2
mJ = 1,0,-1
mJ = 2,1,0,-1,-2
How about energy levels?
Terms (Term Symbols)
Free Ion Term Symbols
Hund's rule (for groundstate term symbol)
1. The term with maximum multiplicity lies lowest in energy
2. For a given multiplicity, the term with the largest value of L lies lowest in energy.
3. For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy.
When the shell is more than half full, the opposite rule holds (highest J lies lowest).
p2
1S
1S
0
1S, 1D
1D
1D
1D
2
3P
2
3P
1S
1D
2
p2
3P
3P
3P
1
3P
0
3P ,3P ,3P
2
1
0
1S
0
mJ = 0
mJ = 0
mJ = 2,1,0,-1,-2
mJ = 1,0,-1
mJ = 2,1,0,-1,-2
How about energy levels?
Terms (Term Symbols)
p1
p2
p3
l1 = 1
s1 = ½
L=1
S=½
2P (2P
Free Ion Term Symbols
3/2,
2P
1/2)
1D(1D ), 3P(3P ,3P ,3P ), 1S(1S )
2
2
1
0
0
l1 = l2 = l3 = 1
s 1 = s 2 = s3 = ½
ML = 3, 2, 1, 0, -1, -2, -3
MS = 3/2, 1/2, -1/2, -3/2
2D (2D , 2D ), 2P(2P ,
5/2
3/2
3/2
p3
MS
3/2
ML
2P1/2) 4S (4S3/2)
1/2
-1/2
2
1+,1-,0+
1+,1-,0-
1
(1+,0+,0-) (1+, 1-,-1+)
(1-,0+,0-)(1+,1-,-1-)
1+,0+,-11+,0-,-1+
1-,0+,-1+
1+,0-,-11-,0+,-11-,0-,-1+
-1
xx
xx
-2
x
x
0
1+,0+,-1+
-3/2
1-,0-,-1-
Terms (Term Symbols)
p1
p2
p3
l1 = 1
s1 = ½
L=1
S=½
l1 = l2 = l3 = 1
s 1 = s 2 = s3 = ½
same as p2
p5
same as p1
s1 d1
d1
2P (2P
3/2,
2P
1/2)
1D(1D ), 3P(3P ,3P ,3P ), 1S(1S )
2
2
1
0
0
p4
p6
Free Ion Term Symbols
L =0, S = 0
l1 = 0, l2 = 2
s1 = s 2 = ½
l1 = 2
s1 = ½
ML = 3, 2, 1, 0, -1, -2, -3
MS = 3/2, 1/2, -1/2, -3/2
1S (1S
0)
L=2
S = 1, 0
L=2
S=½
2D (2D , 2D ), 2P(2P ,
5/2
3/2
3/2
3D (3D , 3D 3D )
3
2,
1
1D (1D )
2
2D (2D , 2P )
5/2
3/2
2P1/2) 4S (4S3/2)
Terms (Term Symbols)
d2
l1 = l2 = 2
s1 = s 2 = ½
ML = 4, 3, 2, 1, 0, -1, -2, -3, -4
MS = 1, 0, -1
d2
terms
MS
1
0
-1
1G
2+,2-
4
ML
Free Ion Term Symbols
3
2+,1+
2+,12-,1+
2-,1-
3F
2
2+,0+
2+,0- 2-,0+
1+,1-
2-,0-
3P
1+,0+
2+,-1+
1+,0- 1-,0+
2+,-1- 2-,-1+
1-,02-,-1-
1+,-1+
2+,-2+
0+,01+,-1- 1-,-1+
2+,-2- 2-,-2+
1-,-12-,-2-
1
0
1S
-1
x x
x x x x
x x
-2
x
x x x
x
-3
x
x x
x
-4
x
1D
1S
1D
d2
1G
3P
3F
Terms (Term Symbols)
d2
l1 = l2 = 2
s1 = s 2 = ½
Free Ion Term Symbols
ML = 4, 3, 2, 1, 0, -1, -2, -3, -4
MS = 1, 0, -1
terms
1S
1G
1G
d2
3F
3P
1D
1D
3P
3F
1S
in reality
1S
1D
by Hund's rule
d2
1G
3P
3F
Terms (Term Symbols)
Free Ion Term Symbols
Short-cut to ground-state term symbols : make max S and max L
ml
2
1
0
-1
-2
d1
S = ½ , L=2  2D
d2
S = 1 , L=3  3F
d4
S = 2 , L=2  5D
d7
S = 3/2 , L=3  4F
Strategy to understand the electronic spectra of complexes
1. Determine free-ion (or in uniform field) term symbols.
2. Determine how these terms split in a weak field.
3. Determine how these terms split in a strong field.
4. Correlate these with Tanabe-Sugano diagram.
Terms : energy levels (or states) of a particular configuration
Splittings of free-ion terms
in a chemical environment
2S+1E
eg
d
In Weak Field

g
(doubly degenerate)
spin multiplicity remains the same.
2S+1D
t2g
2S+1T
Oh
Oh
2g
(triply degenereate)
Splittings of free-ion terms
in a chemical environment
In Weak Field
Splitting of One-Electron Levels in Various Symmetries
Levels
Oh
Td
D4h
s
a1g
a1
a1g
p
t1u
t2
a2u+eu
d
eg+t2g
e+t2
a1g+b1g+b2g+eg
f
a2u+t1u+t2u
a2+t1+t2
a2u+b1u+b2u+2eu
g
a1g+eg+t1g+t2g
a1+e+t1+t2
2a1g+a2g+b1g+b2g+2eg
h
eu+2t1u+t2u
e+t1+2t2
a1u+2a2u+b1u+b2u+3eu
i
a1g+a2g+eg+t1g+2t2g
a1+a2+e+t1+2t2
2a1g+a2g+2b1g+2b2g+3eg
Splittings of free-ion terms
in a chemical environment
In Weak Field
Splitting of Multi-Electron Levels in Various Symmetries
Terms
Oh
Td
D4h
S
A1g
A1
A1g
P
T1g
T1
A2g+Eg
D
Eg+T2g
E+T2
A1g+B1g+B2g+Eg
F
A2g+T1g+T2g
A2+T1+T2
A2g+B1g+B2g+2Eg
G
A1g+Eg+T1g+T2g
A1+E+T1+T2
2A1g+A2g+B1g+B2g+2Eg
H
Eg+2T1g+T2g
E+2T1+T2
A1g+2A2g+B1g+B2g+3Eg
I
A1g+A2g+Eg+T1g+2T2g
A1+A2+E+T1+2T2
2A1g+A2g+2B1g+2B2g+3Eg
* Assuming all free-ion terms arising from dn configurations.
Splittings of free-ion terms
in a chemical environment
In Weak Field
Splitting of Multi-Electron Levels in Various Symmetries
Terms
Oh
S
A1g
P
T1g
D
Eg+T2g
F
A2g+T1g+T2g
G
A1g+Eg+T1g+T2g
1S
1G
d2
3P
1D
3F
free-ion terms
H
Eg+2T1g+T2g
I
A1g+A2g+Eg+T1g+2T2g
free-ion electron configuration
in weak field (Oh)
Strategy to understand the electronic spectra of complexes
1. Determine free-ion (or in uniform field) term symbols.
2. Determine how these terms split in a weak field.
3. Determine how these terms split in a strong field.
4. Correlate these with Tanabe-Sugano diagram.
Terms : energy levels (or states) of a particular configuration
Splittings of free-ion terms
in a chemical environment
In Strong Field
eg2
t2geg
d2
t2g2
In extremely (∞) strong field
What will happen when the field relaxes?
(Looking for splittings in strong field)
Splittings of free-ion terms
in a chemical environment
eg2
In Strong Field (Oh)
t2g2
T2g
3
0
1
-1
-1
3
-1
0
-1
1
T2g x T2g 9
0
1
1
1
9
1
0
1
1
T2g x T2g = A1g + Eg + T1g + T2g
t2geg
d2
number of the microstates of t2g2 configuration = 15
assume the spin multiplicities of the irreducible representations as
T2g x T2g = aA1g + bEg + cT1g + dT2g
t2g2
possible combinations of a, b, c, d  number of microstates = a+2b+3c+3d
(1,1,1,3), (1,1,3,1), (3,3,1,1), (2,2,2,1), (2,2,1,2), (1,1,2,2)
In extremely (∞) strong field
t2g2  1A1g + 1Eg + 1T1g +3T2g
1A + 1E + 3 T + 1T
1g
g
1g
2g
3A + 3E + 1 T + 1T
1g
g
1g
2g
2A + 2E + 2 T + 1T
1g
g
1g
2g
2A + 2E + 1 T + 2T
1g
g
1g
2g
2A + 2E + 1T + 2T
1g
g
1g
2g
no spin doublet in the
free-ion terms
 3 possiblities
Splittings of free-ion terms
in a chemical environment
eg2
eg2
In Strong Field (Oh)
Eg
2
-1
0
0
2
2
0
-1
2
0
Eg x Eg
4
1
0
0
4
4
0
1
4
0
Eg x Eg = A1g + A2g + Eg
t2geg
d2
number of the microstates of eg2 configuration = 6
assume the spin multiplicities of the irreducible representations as
Eg x Eg = aA1g + bA2g + cEg
t2g2
possible combinations of a, b, c  number of microstates = a+b+2c
(1,1,2), (2,2,1), (3,1,1), (1,3,1)
In extremely (∞) strong field
eg2  1A1g + 1A2g +
2A + 2A +
1g
2g
3A + 1A +
1g
2g
1A + 3A +
1g
2g
2E
g
1E
g
1E
g
1E
g
no spin doublet in the free-ion terms
 2 possiblities
Splittings of free-ion terms
in a chemical environment
eg2
t2g1 eg1
Eg
2
-1
0
0
2
2
0
-1
2
0
T2g
3
0
1
-1
-1
3
-1
0
-1
1
T2g x Eg
6
0
0
0
-2
6
0
0
-2
0
T2g x Eg = T1g + T2g
t2geg
d2
In Strong Field (Oh)
number of the microstates of t2geg configuration = 24
t2geg  1T1g + 1T2g + 3T1g + 3T2g
t2g2
In extremely (∞) strong field
Splittings of free-ion terms
in a chemical environment
eg2
In Strong Field (Oh)
3A + 1A + 1E
1g
2g
g
1A + 3A + 1E
1g
2g
g
t2geg
1T
1g
d2
t2g2
+ 1T2g + 3T1g + 3T2g
1A + 1E + 1T +3T
1g
g
1g
2g
1A + 1E + 3T + 1T
1g
g
1g
2g
3A + 3E + 1T + 1T
1g
g
1g
2g
In extremely (∞) strong field
in strong field (Oh)
not complete yet but can imagine
how to split in strong field !!
Strategy to understand the electronic spectra of complexes
1. Determine free-ion (or in uniform field) term symbols.
2. Determine how these terms split in a weak field.
3. Determine how these terms split in a strong field.
4. Correlate these with Tanabe-Sugano diagram.
Terms : energy levels (or states) of a particular configuration
Splittings of free-ion terms
in a chemical environment
eg2
Correlation
3A
+ 1A2g + 1Eg
1A + 3A + 1E
1g
2g
g
3A + 1A + 1E
1g
2g
g
1A + 3A + 1E
1g
2g
g
1g
eg2
how to correlate
t2geg
d2
t2g2
1. 1-to-1 correspondence
between the states at weak
field and strong field
1T + 1T + 3T + 3T
1g non-crossing
2g
1grule :2g
2.
states of the same spin
degeneracy and symmetry
cannot cross.
1A + 1E + 1T +3T
1g
g
1g
2g
1A + 1E + 3T + 1T
1g
g
1g
2g
3A + 3E + 1T + 1T
1g
g
1g
2g
In extremely (∞) strong field
in strong field (Oh)
in weak field (Oh)
1T
1g
+
1T
2g
+
3T
1g
+
3T
2g
1A + 1E + 1T +3T
1g
g
1g
2g
1A + 1E + 3T + 1T
1g
g
1g
2g
3A + 3E + 1T + 1T
1g
g
1g
2g
t2geg
t2g2
not complete yet but can imagine
how to split in strong field !!
In extremely (∞) strong field
in strong field (Oh)
Splittings of free-ion terms
in a chemical environment
Correlation
Diagram
Correlation
Tanabe-Sugano Diagrams
d2 (Oh)
(/10)
Tanabe-Sugano Diagrams
d2 (Oh)
The lowest-energy state is plotted along the
horizontal axis.
D : ligand field splitting
B : Racah parameter, a measure of the
repulsion between terms of same multiplicity
E : the energy (of excited state) above the
ground state
15B
(/10)
Tanabe-Sugano Diagrams
d3 (Oh), d4 (Oh)
d3 (Oh)
d4 (Oh)
(/10)
(/10)
Tanabe-Sugano Diagrams
d5 (Oh)
d5 (Oh), d6 (Oh)
d6 (Oh)
(/10)
(/10)
Tanabe-Sugano Diagrams
d7 (Oh), d8 (Oh)
d7 (Oh)
d8 (Oh)
(/10)
(/10)
Electronic Spectra
Data obtained
1. Transition energies (frequency positions in a spectrum)
2. Intensities of the bands
3. Widths of the bands
Selection Rules
d2 (Oh)
Intensities of the bands (Selection rules)
1. Spin selection rule : DS = 0
2. Laporte selection rule : g ↔ u
Relaxation of selection rules
1. Vibronic coupling relaxes Larpote selection rule.
Oh, e ~ 10 ~50 for d-d transitions with g ↔ g
Td, e ~ 500 for d-d transitions
2. Spin-orbit coupling relaxes spin selection rule.
e ≤ 1 for DS≠0
(/10)
Any transition expected?
Electronic Spectra
Selection Rules
[V(H2O)6]2+
3T
1g(F)
 3T2g
3T
1g(F)
d2 (Oh)
3T
1g(F)
 3T1g(P)
 3A2g : UV region
(/10)
Electronic Spectra
Selection Rules
d3 (Oh)
absorption spectrum of [Cr(NH3)6]3+ (d3)
(/10)
Electronic Spectra
[M(H2O)6]3+
Electronic Spectra
[M(H2O)6]2+
Electronic Spectra
[M(H2O)6]2+
Electronic Spectra
Symmetry Labels for Configurations
?
Ex
T designates a triply degenerate
asymmetrically occupied state.
E designates a doubly degenerate
asymmetrically occupied state.
A, B designate a non degenerate
symmetrically occupied state.
Electronic Spectra
d1
Jahn-Teller distortion
[Ti(H2O)6]3+
a1g
2A
1g
b1g
d1 : l1 = 2, s1 = ½  L=2, S = ½  2D
2E
g
2B
2E
g
eg
1g
eg
d

2D
2D
Oh
2E
g
b2g
2T
2g
t2g
2T
2g
Oh
2B
Oh
2E
g
2T
2g

: 1 band ?
D4h
out of visible range
2T
2g
2E
g
2g
2B
2g
2E
g
2B
1g
2A
1g
Electronic Spectra
d9
Jahn-Teller distortion
[Cu(H2O)6]2+
a1g
2E
Ag1g
b1g
2 2, s = ½  L=2, S = ½  2D
d91 : l
1=D
1
22E
Tg2g
2B
2g
1g
22E
Tg2g
eg
eg
d

2D
2D
Oh
2A
Eg1g
b2g
22T
E2g
g
t2g
22T
E2gg
Oh
Oh
2E
g
2T
E2g
22TE2gg
g
D4h
out of visible range
2T
2g
: 1 band ?
2B
1g
2g
22B
B1g2g
22E
Ag1g
2B
1g
2g
2E
Ag1g
Tanabe-Sugano Diagrams
d1 (Oh)
2E
Hole Formalism
d9 (Oh)
2T
2g
g
d1
• the same free-ion terms
• the same splitting pattern in fields but the
energy levels are reversed.
2D
2T
free ion
2g
2E
g
2T
2g
d9
2E
g
dn
hole
d10-n
Tanabe-Sugano Diagrams
Hole Formalism
d2 (Oh)
d8 (Oh)
(/10)
(/10)
Tanabe-Sugano Diagrams
d3 (Oh)
Hole Formalism
d7 (Oh)
(/10)
(/10)
Tanabe-Sugano Diagrams
d4 (Oh)
(/10)
Hole Formalism
d6 (Oh)
(/10)
Tanabe-Sugano Diagrams
d1(Td)
2D
2E
Hole Formalism
d1(Td)
d9(Oh)
hole
(g)
2T
2T
2
2D
Td
2T
2(g)
Terms
Oh
Td
S
A1g
A1
P
T1g
T1
D
Eg+T2g
E+T2
F
A2g+T1g+T2g
A2+T1+T2
G
A1g+Eg+T1g+T2g
A1+E+T1+T2
H
Eg+2T1g+T2g
E+2T1+T2
I
A1g+A2g+Eg+T1g+2T2g
A1+A2+E+T1+2
T2
d9(Oh)
Oh
2E
2E
d1(Td)
2g
g
d9(Oh)
• the same free-ion terms
• the same splitting pattern in fields
dn(Td) = d10-n(Oh)
Tanabe-Sugano Diagrams
d2 (Oh) ◄► d8 (Td)
d3 (Oh) ◄► d7 (Td)
d6 (Oh) ◄► d4 (Td)
Hole Formalism
d4 (Oh) ◄► d6 (Td)
d7 (Oh) ◄► d3 (Td)
d5 (Oh) ◄► d5 (Td)
d8 (Oh) ◄► d2 (Td)
Tanabe-Sugano Diagrams
2E
g
d1
Do
Oh
Applications (Determination of Do)
d1, d9
2T
2g
2D
Do
d1
d9
d9
2E
g
2T
2g
[Ti(H2O)6]3+
Do
[Cu(H2O)6]2+
Do
Tanabe-Sugano Diagrams
d4 (hs)
Oh
Applications (Determination of Do)
d4 (hs), d6 (hs)
d6 (hs)
[Cr(H2O)6]2+
Do
5E
g
5T
2g
5T
2g
5E
g
Do
[Fe(H2O)6]2+
Tanabe-Sugano Diagrams
Applications (Determination of Do)
Orgel Diagram for d1, d4(hs), d6(hs) d9
Orgel diagram
- considers only states with the same spin
multiplicity as that of the ground state.
- plots the energy levels of the states as LFSE.
Do
d4 (hs)
Do
Do
d6 (hs)
Do
Orgel Diagram for free-ion D ground state
[d1, d4(hs), d6(hs), d9]
Applications (Determination of Do)
Orgel Diagram for d2, d3, d7(hs), d8
Tanabe-Sugano Diagrams
d2
LFSE = 1.2Do
LFSE = 0.2Do
15B
LFSE = -0.8Do
Applications (Determination of Do)
Orgel Diagram for d2, d3, d7(hs), d8
Tanabe-Sugano Diagrams
d2
Noncrossing rule
- the states with the same spin
mutiplicity and symmetry cannot cross
but may mix LFSE = 1.2Do
1.2D
0.6D
0.8D
D
0.2D
+ 15B
-0.2D
+ 15B
0.2D
-0.2D
0.8D
D
-1.2D
oct d3, d8
tet d2, d7
-0.6D
LFSE = 0.2Do
15B
oct d2, d7
tet d3, d8
0.8D : for the case of extremely strong field
LFSE = -0.8Do
Applications (Determination of Do)
Orgel Diagram for d2, d3, d7(hs), d8
Tanabe-Sugano Diagrams
1.2D
D
0.6D - x
0.2D
-0.2D
D
-1.2D
oct d3, d8
tet d2, d7
-0.6D - x
oct d2, d7
tet d3, d8
Orgel Diagram for free-ion F ground state
[d2, d3, d7(hs), d8]
Noncrossing rule
- the states with the same spin
mutiplicity and symmetry cannot cross
but may mix
Applications (Determination of Do)
Orgel Diagram for d2, d3, d7(hs), d8
Tanabe-Sugano Diagrams
1.2D
D
0.6D - x
0.2D
-0.2D
D
-1.2D
oct d3, d8
tet d2, d7
-0.6D - x
oct d2, d7
tet d3, d8
Orgel Diagram for free-ion F ground state
[d2, d3, d7(hs), d8]
Tanabe-Sugano Diagrams
Applications (Determination of Do and B)
d2
[V(H2O)6]3+
E/B
Do
42
n1= 17,800 cm-1
3T (F)
1g
 3T2g
3T (F)
1g
n2 = 25,700 cm-1
3T (F)
1g
 3T1g(P)
29
 3A2g : UV region
n2/n1 = 1.44  at Do/B = 31
at Do/B = 31
n1: E/B ~ 29  E = 17,800 cm-1 = 29B  B ~ 610 cm-1
n2: E/B ~ 42  E = 25,700 cm-1 = 42B  B ~ 610 cm-1
 Do = 31B = 19,000 cm-1
Do/B
31
Tanabe-Sugano Diagrams
[Cr(NH3)6]3+
Applications (Determination of Do and B)
d3
E/B
UV
44
33
Do
n2= 28,500 cm-1
n1 = 21,500 cm-1
n2/n1 = 1.33  at Do/B = 33
at Do/B = 33
n1: E/B ~ 33  E = Do = 21,500 cm-1 = 33B  B ~ 650 cm-1
n2: E/B ~ 44  E = 28,500 cm-1 = 44B  B ~ 650 cm-1
Do/B
33
Tanabe-Sugano Diagrams
d4 (Oh)
d5 (Oh)
Applications (Determination of Do and B)
d5(hs), d4-d7(ls)
d6 (Oh)
d7 (Oh)
colorless (for example [Mn(H2O)6]2+)
d4-d7(ls) : difficult to analyze the electronic spectra because of many excited states with the
same spin multiplicity as that of the ground state
Charge-Transfer Band
[Cr(NH3)6]3+ (d3)
LMCT (CTTM) : ligand
to metal charge transfer
- ligand s (or p)-donor
orbital to metal d-orbital
[Cu(H2O)6]2+ (d9)
CT
MLCT (CTTL) :
metal to ligand charge
transfer
- metal d-orbital to
ligand p-acceptor
orbital (CO, CN-, SCN-,
bipy, S2CNR2-)
Both:
very intense : e ~ 50,000
UV/VIS region
LMCT (CTTM) : causes reduction of metal
MLCT (CTTL) : causes oxidation of metal
Charge-Transfer Band
LMCT (CTTM)
[IrBr6]3- (d6, Oh) : strong absorption bands at ~250 nm
[IrBr6]2- (d5, Oh) : strong absorption bands at ~600 nm and ~270 nm
[MnO4]- (do, Td) : intense purple color (pO  empty d)
MLCT (CTTL)
Common for complexes with bipy and phen ligands