Part 2.9: Electronic Transitions
Outline
• Absorption spectroscopy
• Types of transitions
– atomic
– molecular
•
•
•
•
•
•
d-d transitions
Transition moment
Microstates
Correlation diagrams
Tanabe-Sugano diagrams
Selection rules
Interaction of Light with Matter
Rainbows
Glasses
Mirage
Refractometer
Moon Light
Butterfly Wings
Sea Shells
Soap Bubbles
Two-slit exp
Holograms
Shadow Blur
Sand in Water
Sunsets
3
Absorption Spectrosocpy
hn
hn
Sample
We don’t measure absorbance. We measure transmittance.
Sample
P0
(power in)
P
(power out)
• Transmittance:
T = P/P0
• Absorbance:
A = -log T = log P0/P
Beer’s Law
The Beer-Lambert Law (l specific):
A=ecl
A = absorbance (unitless, A = log10 P0/P)
e = molar absorptivity (L mol-1 cm-1)
l = path length of the sample (cm)
c = concentration (mol/L or M)
Sample
P0
P
(power in)
(power out)
l in cm
Concentration
Absorbance
Path length
Absorbance
Molar Abs.
Absorbance
Beer’s Law
The Beer-Lambert Law (l specific):
A=ecl
A = absorbance (unitless, A = log10 P0/P)
e = molar absorptivity (L mol-1 cm-1)
Sample
P0
P
(power in)
l = path length of the sample (cm)
c = concentration (mol/L or M)
(power out)
l in cm
e
What are we actually
measuring/observing?
100 200 300 400
Wavelength (nm)
500
Electronic Transitions
• Interaction between an electromagnetic wave and the wave function of a
molecule/atom/material.
• Transition between quantized energy states of an atom/molecule/material.
• Exciting an electron from one quantum state to another.
hn
hn
Ground
State (S0)
First Excited
State (S1)
Electronic Transitions
e
Spectral Features:
• Number of transitions.
• Energy of the transitions.
• Intensity of the transitions.
100
200
300
Wavelength (nm)
400
500
Electronic Transitions
Spectral Features:
• Number of transitions.
• Energy of the transitions.
• Intensity of the transitions.
hn
e
hn
100
200
300
Wavelength (nm)
400
500
hn
Electronic Transitions
Spectral Features:
• Number of transitions.
• Energy of the transitions.
• Intensity of the transitions.
• Shape of the transition.
e
hn
100
200
300
400
Wavelength (nm) DE
500
Transition Probability
Atomic Transition
hn
Energy
hn
Ground State
Excited State
11
Hydrogen Absorption
H
H
H H
H
H
white light source
H
Hydrogen Sample
Prism
Line
Spectrum
Rydberg Formula
 1 1 
E  RH  2  2 
 nl nh 
12
Increasing Complexity
1 e-
10 e80 e-
250 e-
Atomic Transitions
(movement of electrons)
+
Molecular Transitions
(movement of electron density)
13
Types of Molecular Transitions
σ - σ*
lmax < 150 nm
p - p*
n - p*
Absorption
lmax 200 - 800 nm
p - p*
s - s*
n - p*
lmax 150 - 300 nm
100
400
300
200
Wavelength (nm)
500
14
Types of Molecular Transitions
[Co(H2O)6]2+
Metal Centered (MC)
Focus on Metal
Centered
Transitions
lmax 200 –800 nm
MnO4-
MLCT
lmax 300 –1000 nm
LMCT
lmax 300 –1000 nm
MMCT
lmax 300 –800 nm
15
Colors of Metal Ions
Alexandrite
Cr3+ doped
BeAl2O4
Colors of Metal Ions
Cr3+ doped
BeAl2O4
Uniform White Light
~400 nm = 4A2g to 4T1g
~600 nm = 4A2g to 4T2g
Sunlight
Candle Light
http://www.chemistry-blog.com/2013/08/22/alexandrite-effect-not-all-white-light-is-created-equal/
Colors of Metal Ions
Ruby
~1% Cr3+ doped Al2O3
Absorbs yellow-green region
Emits red
Most expensive ruby (1.6 cm3) = $6.7 million
Al2O3 (1.5 cm3) = ~$500
Intensity
Absorption Spectra of Metal Ions
Energy
Electronic Transitions
A=ecl
e
A = absorbance (unitless, A = log10 P0/P)
e = molar absorptivity (L mol-1 cm-1)
l = path length of the sample (cm)
100 200 300 400
Wavelength (nm)
500
c = concentration (mol/L or M)
Transition probability –the probability of a particular transition
taking place.
Depends on:
1) Energy of the transition/incident light.
2) Orientation of the molecule/material.
3) Symmetry of the initial and final states.
4) Angular momentum (spin).
States vs. Orbitals
S2
S1
Second Excited
State (S2)
Energy
First Excited
State (S1)
S0
Single Orbital
Sum of Orbitals
and electron
occupations
Ground
State (S0)
21
Transition Moment
S2
S1
Y2
Energy
The transition probability of one molecule from
one state (Y1) to another state (Y1) is given by
|M⃗21|, the transition dipole moment, or
transition moment, from Y1 to Y2.
Transition moment:
S0
Y1
where m⃗ is the electric dipole moment operator:
where Qn is charge, x⃗ n is the position vector
operator.
For an electronic transition to be allowed, the transition moment
integral must be nonzero.
Transition Moment
e
e
100 200 300 400
Wavelength (nm)
≈
500
x
Y1
hn
Y2
hn
Transition Moment
e
e
100 200 300 400
Wavelength (nm)
≈
500
If M⃗21 = 0, then the transition probability is 0 and the transition from
Y1 to Y2 is “forbidden” or electric-dipole “forbidden.”
M⃗21 = 0, e = 0
If M⃗21 ≠ 0, then the transition probability is not 0 and the transition
from Y1 to Y2 is not “forbidden.”
M⃗21 ≠ 0, e ≥ 0
Does not tell you definitively that it is
allowed or how intense it will be. Only
that it is not electric-dipole forbidden.
Transition Moment
Y1
Y2
allowedness of a
transition
hn
Irr. Rep. for the
excited state
=
Irr. Rep. for the
linear basis
(x, y, and z)
Irr. Rep. for the
ground state
If the direct product DOES NOT contain the totally symmetric representation
(A, A1, A1g…), then the transition is FORBIDDEN by symmetry arguments.
If the direct product DOES contain the totally symmetric representation (A,
A1, A1g…), then the transition is ALLOWED by symmetry arguments.
The integral
will be exactly zero if the Irr. Rep. of the direct
product does not contain A, A1, Ag , A1g or A’.
Direct Product
Direct product: The representation of the product of two
representations is given by the product of the characters of the
two representations.
26
Direct Product Table
27
Example (dz2 to pz)
allowedness of a
transition
Irr. Rep. for the
excited state
=
Irr. Rep. for the
linear basis
(x, y, and z)
Irr. Rep. for the
ground state
(z) (x) (y)
D2h
p
s
B1u B3u B2u
B1u
B1u
hn
Ag
(z2) (xy) (xz) (yz) (x2-y2)
d
(pz)
Ag B1g B2g B3g Ag
(dz2)
Ag
Ag
Example (dz2 to pz)
Irr. Rep. for the
excited state
Irr. Rep. for the
ground state
Irr. Rep. for the
linear basis
(x, y, and z)
=
(pz)
B1u
B1u
x basis
B1u
B3u
Ag
= B2g
y basis
B1u
B2u
Ag
= B3g
z basis
B1u
B1u
Ag
= Ag
hn
(dz2)
Ag
D2h
allowedness of
a transition
Ag
Example (dz2 to pz)
(pz)
B1u
B1u
hn
(dz2)
x basis
B1u
B3u
Ag
= B2g
y basis
B1u
B2u
Ag
= B3g
z basis
B1u
B1u
Ag
= Ag
Ag
Ag
The transition is forbidden if the direct product does not contain A, A1, Ag , A1g or A’.
The transition is allowed if the direct product does contains A, A1, Ag , A1g or A’.
z polarized =
allowed
hn
hn
pz
dz2
Allowed
y polarized =
forbidden
x polarized =
forbidden
Example (dxy to pz)
allowedness of a
transition
Irr. Rep. for the
excited state
=
Irr. Rep. for the
linear basis
(x, y, and z)
Irr. Rep. for the
ground state
(z) (x) (y)
D2h
p
s
B1u B3u B2u
B1u
B1u
hn
Ag
(z2) (xy) (xz) (yz) (x2-y2)
d
(pz)
Ag B1g B2g B3g Ag
(dxy)
B1g
B1g
Example (dxy to pz)
Irr. Rep. for the
excited state
Irr. Rep. for the
linear basis
(x, y, and z)
=
(pz)
B1u
B1u
D2h
B1g
allowedness of
a transition
x basis
B1u
B3u
B1g = B3g
y basis
B1u
B2u
B1g = B2g
z basis
B1u
B1u
B1g = B1g
hn
(dxy)
Irr. Rep. for the
ground state
B1g
Example (dxy to pz)
(pz)
B1u
B1u
hn
(dxy)
x basis
B1u
B3u
B1g = B3g
y basis
B1u
B2u
B1g = B2g
z basis
B1u
B1u
B1g = B1g
B1g
B1g
The transition is forbidden if the direct product does not contain A, A1, Ag , A1g or A’.
The transition is allowed if the direct product does contains A, A1, Ag , A1g or A’.
z polarized =
forbidden
hn
hn
pz
dxy
Forbidden
y polarized =
forbidden
x polarized =
forbidden
Example (dx2-y2 or dxy,yz to px,y)
allowedness of a
transition
=
Irr. Rep. for the
excited state
Irr. Rep. for the
ground state
Irr. Rep. for the
linear basis
(x, y, and z)
dx2-y2 to px,y
(px,y)
E
(z) (x) (y)
C4v
p
E
A1
s
(dx2-y2)
A1 B 2
B1
E
B1
dx2-y2 to px,y
A1
(px,y)
E
(z2) (xy) (xz) (yz) (x2-y2)
d
hn
E
B1
(dxz,yz)
E
hn
E
E
Example (dx2-y2 or dxy,yz to px,y)
dx2-y2 to px,y
(px,y)
(dx2-y2)
E
hn
B1
E
B1
E
A1
E
Forbidden (z)
B1
Allowed (x,y)
dx2-y2 to px,y
(px,y)
(dxz,yz)
C4v
E
E
hn
= E
A1 + A 2 + B 1 + B2
E
E
E
A1
E
Allowed (z)
E
A 1 + A 2 + B 1 + B2
1 + A 2 + B 1 + B2
= A
E
Forbidden (x,y)
One Electron Octahedral
Eg
T2g
Eg
T1u
T2g =
One Electron Octahedral
Eg
Eg
Forbidden (x, y, z)
T1u
T2g
A2u + Eu + T1u + T2u
Eu + A1u + A2u + Eu + T1u + T2u + T1u + T2u
Six Electron Octahedral (Low spin)
Ground State
A1g
Excited State
T2g
Eg
T1g + T2g
Six Electron Octahedral (Low spin)
Ground State
Excited State
A1g
T2g
Eg
T1g + T2g
T1g
T2g
T1u
A1g =
Six Electron Octahedral (Low spin)
Ground State
Excited State
A1g
T2g
Eg
T1g + T2g
T1g
T2g
Forbidden (x, y, z)
T1u
A1g =
A1u + Eu + T1u + T2u
A2u + Eu + T1u + T2u
Simple Cases
1 electron (two states)
Eg
T1u
T2g
T1u
A1g
5 electron (two states)
T1g
T2g
More Complex Case (Oh d3)
Excited States
Eg
T2g
Ground State
More Complex Case (Oh d2, d3, d2, d8)
Ground State
d2
Excited States
eg
t2g
eg
d3
t2g
eg
d7
t2g
eg
d
8
t2g
There has to be an easier way to
describe transitions between states!
Tanabe-Sugano Diagrams
d3
Useful for:
Electronic States
Relative Energies
Ligand Field Affects
Optical Transitions
Spin Multiplicities
High-Spin to Low-Spin Transitions
Estimate Do
Getting to Tanabe-Sugano Diagrams
Electronic States
Term symbols
Microstate tables
Correlation diagrams
Tanabe-Sugano diagrams
Selection rules
Quantum Numbers
• PRINCIPAL (n): energy level, the distance the orbital is from the
nucleus
n = 1, 2, 3, 4…
• ANGULAR MOMENTUM: l, shape of the orbital
s = 0, p = 1, d = 2, f = 3
•
MAGNETIC: ml , spatial orientation
ml = 0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.
• SPIN: ms spin
ms = +1/2 or -1/2)
Quantum Numbers
F atom
1s
2s
2p
The third electron is in the 2s orbital.
n= 2
l= 0
ml = 0
ms= +1/2
The eighth electron is in a 2p orbital.
n=
2
l= 1
ml = -1
ms= -1/2
Only describes single electron states!
What about multielectron states?
Many Electron States
Many electron interactions are described by
Russel-Saunders or L-S coupling scheme
ML = total orbital angular momentum =Σml
MS = total spin angular momentum = Σms
Summarized by term symbols that contain:
- spin multiplicity (2S+1)
- angular momentum quantum number (L)
- the total angular momentum (J )
2S+1L
J
The interactions produce atomic states called microstates.
Term Symbols
S represents the total spin angular momentum
S = total spin angular momentum = Σms
2S+1L
+1/2
S = 1/2
2L
J
S=1
3L
J
J
+1/2
+1/2
-1/2
+1/2
L specifies the total orbital angular momentum
L = angular momentum = Σml
For D orbitals
L=2
ml =
ml =
J = Total angular momentum
J = L+S, L+S-1, L+S-2,….L-S|
Spin Orbit Coupling
+2
+2
+1
+1
0
0
-1
-1
L=3
3F
J
L=0
3S
J
-2
-2
L=
0 1 2 3 4
Term Symbol S P D F G
Term Symbols
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
Term Symbols
We are only assigning one state at a time!
To assign all the states we turn to a microstate table!
Microstate Table
•
•
•
•
A microstate table contains all possible combinations of ml and ms.
Each microstate represents a possible electron configuration.
It includes both ground and excited states.
Must obey the Pauli Exclusion Principle.
p2
total spin angular momentum
ML
+1
-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:
total orbital
angular momentum
0
-2:
-1+-1-
Microstates
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-
Microstate Table Notation
p2 electron configuration
Two electrons in px, py and pz orbitals.
ml =
Ground State
Configurations:
ml =
A few Excited State
Configurations:
+1
0 -1
___ ___ ___
___ ___ ___
___ ___ ___
microstate:
(1+,0+)
(0+,-1+)
(1+,-1+)
+1
0 -1
___ ___ ___
___ ___ ___
___ ___ ___
microstate:
(1+,1-)
(0+,0-)
(-1+,-1-)
e- spin
e- ml
Microstate Table Notation
(1+,1-)
(-1+,-1-)
(0+,0-)
(1+,-1+)
(1+,0+)
(1-,0-)
(0+,-1+)
(0-,-1-)
(1-,-1-)
(1+,-1-)
(1+,0-)
15 total possible states
(1-,0+)
(0+,-1-)
(0-,-1+)
(1-,-1+)
Microstate Table
15 total possible states
(1+,1-)
(-1+,-1-)
(0+,0-)
(1+,-1+)
(1+,0+)
(1-,0-)
(0+,-1+)
(0-,-1-)
(1-,-1-)
(1+,-1-)
(1+,0-)
total spin angular momentum
total orbital
angular momentum
(1-,0+)
(0+,-1-)
(0-,-1+)
(1-,-1+)
Microstate Table
15 total possible states
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Group Energetically equivalent states.
Microstate Table
15 total possible states
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Group Energetically equivalent states.
Microstate Table
15 total possible states
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Group Energetically equivalent states.
Microstate Table
15 total possible states
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Group Energetically equivalent states.
Term Symbol from Microstate Tables
2S+1L
S = highest Ms
L = highest Ml
1D
3P
5 equivalent states
9 equivalent states
1S
1 state
Relative Energies
1S
1D
3P
5 E equivalent states
9 E equivalent states
1 state
1. For a given electron configuration, the term with the greatest
multiplicity lies lowest in energy. (Hund’s rule.)
2. For a term of a given multiplicity, the greater the value of L, the
lower the energy.
Lowest E
3P
Highest E
<
1D
<
1S
Note: The rules for predicting the ground state always work, but they
may fail in predicting the order of energies for excited states.
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
ml =
+2
___
___
Configurations: ___
___
___
+1
___
___
___
___
___
0
___
___
___
___
___
-1
___
___
___
___
___
-2
___
___
___
___
___
microstate
(2+, 1+)
(1+, 0+)
(2+, 2-)
(1+, -2-)
(2+, -1+)
etc.
45 microstates (ML = 4-4, and MS=1, 0 or -1)
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
X
X
XX
XX
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
X
XX
XX
XX
X
X
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
X
X
XX
XX
XX
X
X
X
X
X
2S+1L
S = highest Ms
L = highest Ml
L=
0 1 2 3 4
Term Symbol S P D F G
1G
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
X
X
XX
XX
XX
X
X
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
X
X
XX
XX
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
2S+1L
S = highest Ms
L = highest Ml
L=
0 1 2 3 4
Term Symbol S P D F G
1G
3F
X
X
X X
X
X
X
X
XX
XX
XX
X
X
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
X
X
XX
XX
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
3F
1D
2S+1L
S = highest Ms
L = highest Ml
L=
0 1 2 3 4
Term Symbol S P D F G
1G
X
X
XX
XX
XX
X
X
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
X
X
XX
XX
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
3F
1D
X
X
XX
XX
XX
X
X
2S+1L
S = highest Ms
L = highest Ml
L=
0 1 2 3 4
Term Symbol S P D F G
1G
3P
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
X
X
XX
XX
XX
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X
3F
1D
X
X
XX
XX
XX
X
X
2S+1L
S = highest Ms
L = highest Ml
L=
0 1 2 3 4
Term Symbol S P D F G
1G
3P
1S
Microstate Table Notation
d2 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
1G
3F
1D
3P
1S
1. For a given electron configuration, the term with the greatest
multiplicity lies lowest in energy. (Hund’s rule.)
2. For a term of a given multiplicity, the greater the value of L,
the lower the energy.
Lowest E
3F
Highest E
< 3P < 1G < 1D < 1S
Note: The rules for predicting the ground state always work, but they
may fail in predicting the order of energies for excited states.
Lowest E
Real Order
3F
< 1D <
Highest E
3P
< 1G < 1S
Microstate Table
d3 electron configuration
Three electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
ml = +2 +1
0 -1 -2 microstate
___ ___ ___ ___ ___ (2+,2-,1+)
Microstate Table Notation
d1 electron configuration
Two electrons in dxy, dxz, dxy, dz2 and dx2-y2 orbitals.
ml =
+2
___
___
Configurations: ___
___
___
+1
___
___
___
___
___
0
___
___
___
___
___
-1
___
___
___
___
___
-2
___
___
___
___
___
microstate
(2+)
(1+)
(0+)
(-1+)
(-2+)
(2+)
(1+)
(0+)
(0+)
(0+)
2S+1L
S = highest Ms
L = highest Ml
2D
Ligand Field Dependence
One d electron (d1)
___ ___
___ ___ ___
dxy, dxz, dxy, dz2 and dx2-y2
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
___
2D
eg ___ ___
t2g ___ ___ ___
___ ___
___ ___ ___
Degenerate
symmetric field
Absence of ligand field.
Free-ion term.
All d orbitals are E equal.
___ ___
___ ___ ___
Real molecules
Correlation Diagram
Orgel Diagram
___ ___
___ ___ ___
Infinite
Oh field
Strong ligand field.
Coord Complex.
d orbitals not degenerate
dz2 and dx2-y2 higher E
dxy, dxz and dyz lower E
Correlation Diagram
d1 Term symbols
= 2D
d2 Term symbols
= 3F, 1D, 3P, 1G, 1S
Correlation Diagram
Term # of States
S
1
P
3
D
5
F
7
G
9
Terms in Oh Field
A1g
T1g
T2g + Eg
T1g + T2g + A2g
A1g + Eg+T1g+T2g
___ ___
___ ___ ___
___ ___
___ ___ ___
___ ___
___ ___ ___
___ ___
___ ___ ___
___ ___
___ ___ ___
___ ___
___ ___ ___
Correlation vs. Tanabe-Sugano Diagrams
Correlation Diagram
Tanabe-Sugano Diagram
d2
Number of states.
General sense of field effects.
Only qualitative.
Number of states.
Field effects.
Quantitative.
Tanabe-Sugano Diagrams
d2
Relative energies.
Ligand field affects.
Energy
Electronic states with the same
symmetry can not cross (noncrossing rule).
Curvature (1E and 1E).
Ground state on the x-axis.
Transitions between states.
Ligand Field
Tanabe-Sugano Diagrams
d2
Excited
States
10 possible transitions
Energy
Not all transition
probabilities are equal!
Ground
State
Ligand Field
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final
wavefunctions must change in parity. Parity is related to the
orbital angular momentum summation over all elections Σli, which
can be even or odd; only even ↔ odd transitions are allowed.
Transitions between the orbitals of the same sub shell are
forbidden.
Spin Selection Rule: There must be no change in the spin
multiplicity (DS = 0) during the transition.
i.e. the spin of the electron must not change during the transition.
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final wavefunctions must
change in parity. Only even (g) ↔ odd (u) transitions are allowed. Transitions
between the orbitals of the same sub shell are forbidden.
g→g u→u
g→u u→g
Forbidden
Allowed
For Oh complexes
allowedness of a
transition
= T1u
=
u =
Forbidden u =
g
u
u
u
g
u
Allowed
g =
g
u
u
Allowed
g =
u
u
g
Forbidden
Direct Product Rules
g
g
u
u =u
g =g
u =g
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final wavefunctions must
change in parity. Only even (g) ↔ odd (u) transitions are allowed. Transitions
between the orbitals of the same sub shell are forbidden.
g→g u→u
g→u u→g
Forbidden
Allowed
For Oh complexes
d→d
t2g → eg
Forbidden
d→p
t2g → t1u
Allowed
p→p
t1u → t1u
Forbidden
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final
wavefunctions must change in parity. Parity is related to the
orbital angular momentum summation over all elections Σli, which
can be even or odd; only even ↔ odd transitions are allowed.
Transitions between the orbitals of the same sub shell are
forbidden.
Spin Selection Rule: There must be no change in the spin
multiplicity (DS = 0) during the transition.
i.e. the spin of the electron must not change during the transition.
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Spin Selection Rule: There must be no change in the spin multiplicity (DS = 0) during
the transition. i.e. the spin of the electron must not change during the transition.
hn
hn
1L*
1L
Allowed
1T
1
→ 1T2
1T
1
→
3T
1
Forbidden
3T
1
→ 1A2
Forbidden
3L*
1L
Forbidden
Allowed
Conservation of
angular momentum.
Tanabe-Sugano Diagrams
Complete Diagram
d2
Spin Only Diagram
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final
wavefunctions must change in parity.
Spin Selection Rule: The spin of the electron must not change
during the transition.
Transition
εmax (M1cm1)
Spin and Symmetry forbidden "d-d" bands
0.02 - 1
Spin allowed and Symmetry forbidden "d-d" bands
1 - 10
Spin and Symmetry allowed CT bands
103 - 5 x 104
Tanabe-Sugano Diagrams
All d-d transitions are
symmetry (Laporte)
“forbidden”
d2
Energy
Spin-allowed transitions
3T → 3T
1g
2g
Ligand Field
3T
1g
→ 3T1g
3T
1g
→ 3A2g
d1 and d9 Tanabe-Sugano Diagram
d1
[Ti(H2O)6]3+
d9
d3 Tanabe-Sugano Diagram
d3
Ruby
~1% Cr3+ doped Al2O3
d3 Tanabe-Sugano Diagram
d8
d6 Tanabe-Sugano Diagram
d6
Low
Spin
Energy
High
Spin
Low
Spin
High
Spin
5T
2g
1A
1g
Ligand Field
Smaller Do
The Spectrochemical Series
Larger Do
I- < Br- < Cl- < OH- < RCO2- < F- < H2O < NCS- < NH3 < en < NO2- < phen < CO, CN-
91
Tanabe-Sugano Diagram
d4
d5
d7
d6 Tanabe-Sugano Diagram
Smaller Do
Complex Ion
labs (nm)
[Co(H2O)6] 3+
600, 400
[Co(NH3)6] 3+
475, 340
[Co(en)3] 3+
470, 340
The Spectrochemical Series
Larger Do
I- < Br- < Cl- < OH- < RCO2- < F- < H2O < NCS- < NH3 < en < NO2- < phen < CO, CN-
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final
wavefunctions must change in parity.
Spin Selection Rule: The spin of the electron must not change
during the transition.
Transition
εmax (M1cm1)
Spin and Symmetry forbidden "d-d" bands
0.02 - 1
Spin allowed and Symmetry forbidden "d-d" bands
1 - 10
Spin and Symmetry allowed CT bands
103 - 5 x 104
Why do we see “forbidden” transitions at all?
Allowing “Forbidden” Transitions
Mechanisms that make “forbidden” electronic transitions to be
“allowed”
1) Vibronic Coupling: Electronic states coupled to vibrational
states help overcome the Laporte selection rule.
2) Spin-orbit Coupling: Spin and orbital angular momenta can
interact to make spin “forbidden” transitions allowed.j
3) Mixing of states: π-acceptor and π-donor ligands can mix with
the d-orbitals transitions are no longer purely d-d.
Vibronic Coupling
Oh symmetry
Ground State
Excited State
A1g
T1g + T2g
The transition probability of one molecule from
one state (Y1) to another state (Y1) is given by
|M⃗21|, the transition dipole moment, or
transition moment, from Y1 to Y2.
T1g
T2g
T1u
A1g =
A1u + Eu + T1u + T2u
A2u + Eu + T1u + T2u
allowedness of a
transition
=
Electronically Forbidden (x, y, z)
Vibronic Coupling
Oh symmetry
Ground State
Excited State
A1g
T1g + T2g
For octahedral complex, there are 15 vibrational normal modes with
irreducible representations:
Vibrational transition couple with electronic transition:
Vibronic Coupling
excited state
vibrational wavefunction
ground state
vibrational wavefunction
Vibronic Coupling
For Oh
Gev
(A1g, Eg , T1u , T2g , T2u)
Ggv
T1g
T2g
T1u
A1g
A1g
T1uand T2u vibrations can couple with the electronic
transition to form allowed transitions.
Vibronic Coupling
excited state
vibrational wavefunction
ground state
vibrational wavefunction
T1uand T2u vibrations can couple
with the electronic transition to
form the allowed vibronic
transition.
Spin-Orbit Coupling
Lower
Energy
Nicholas J. Turro, Principles of Molecular Photochemistry
101
Spin-Orbit Coupling
Spin Selection Rule: There must be no change in the spin multiplicity (DS = 0) during
the transition. i.e. the spin of the electron must not change during the transition.
hn
hn
3L*
1L
1L*
Allowed
Forbidden
Spin-orbit Coupling
Conservation of
angular momentum.
Spin-Orbit Coupling
Heavy Atoms
Pt, Ir, Os, I...
Ru(bpy)3
Os(bpy)3
Nicholas J. Turro, Principles of Molecular Photochemistry
103
Mixing of States
d2
Energy
Tunabe-Sugano
diagram assumes
pure d-d transitions
Mixing of states: π-acceptor and
π-donor ligands can mix with the
d-orbitals transitions are no
longer purely d-d.
Ligand Field
Selection Rules
Selection rules determine the probability (intensity) of the transition.
Symmetry (Laporte) Selection Rule: The initial and final
wavefunctions must change in parity.
Spin Selection Rule: The spin of the electron must not change
during the transition.
Transition
εmax (M1cm1)
Spin and Symmetry forbidden "d-d" bands
0.02 - 1
Spin allowed and Symmetry forbidden "d-d" bands
1 - 10
Spin and Symmetry allowed CT bands
103 - 5 x 104
Outline
• Absorption spectroscopy
• Types of transitions
– atomic
– molecular
•
•
•
•
•
•
d-d transitions
Transition moment
Microstates
Correlation diagrams
Tanabe-Sugano diagrams
Selection rules