1 PHY 745 Group Theory 111150 AM MWF Olin 102 Plan for Lecture 24 Jahn Teller Effect S ection 77 in DDJ Example of tetrahedral molecule with doubly or triply degenerate electronic states ID: 656244
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PHY 745 Spring 2017 -- Lecture 24
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PHY 745 Group Theory
11-11:50 AM MWF Olin 102
Plan for Lecture 24:
Jahn
-Teller Effect
S
ection 7.7 in
DDJ
Example of tetrahedral molecule with doubly or triply degenerate electronic states.
Ref: Grosso and
Pastori
Parravinci
, SSP, Chap.
8, Wang et al. JCP 93, 6318 (1990) Slide2
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Symmetry analysis of vibrations of
tetrahedral systemSlide5
s
d
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Visualization of symmetry elements
http://symmetry.otterbein.edu/tutorial/methane.html
C
3
C
2
S
4Slide6
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D
z
1
D
x
1
D
y
1
D
z
4
D
x
4
D
y
4
D
z
3
D
x
3
D
y
3
D
z
2
D
x
2
D
y
2
D
z
5
D
x
5
D
y
5
Construct 15-component vector V describing the 3-dimensional motion of the 5 atoms in CH
4Slide7
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D
z
1
D
x
1
D
y
1
D
z
4
D
x
4
D
y
4
D
z
3
D
x
3
D
y
3
D
z
2
D
x
2
D
y
2
D
z
5
D
x
5
D
y
5
D
y
5
D
z
5
D
x
5
D
y
1
D
z
1
D
x
1
D
y
2
D
z
2
D
x
2
D
y
4
D
z
4
D
x
4
D
y
3
D
z
3
D
x
3
Alternate coordinate systemSlide8
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All motions:
A
1
+E+T
1
+3T
2
Translations:
T
2
Rotations
:
T
1
Vibrations:
A
1
+E+2T
2
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Some equations
nuclei
electrons
Nuclear part:Slide13
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Some equations -- continued
Transform coordinates to
q
1
and
q
2
amplitudes of the two
E
symmetry normal modesSlide14
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Some equations -- continued
Diagonalize
nuclear Hamiltonian
More detailed Hamiltonian from JCP paper:Slide16
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Solved numerically
P
4
+Slide17
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As
4
+
Sb
4
+