Electronic Structure of Molecules

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Electronic Structure of Molecules AST380E Yancy
L. Shirley
2
Where do we find molecules ?
Orion in CO J2-1
Molecular Clouds Star Formation Regions
VLT, Japan
3
Brown Dwarfs Gliese 229B
CH4 Absorption
Geballe, et al. 1995
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Planetary Atmospheres
ISO Spectrum of Jupiter
Voyager, NASA
C2H2
C2H6
CH3D
NH3
CH4
PH3
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Comets Hale-Bopp
HCN J4-3
D. Jewitt, U. Hawaii
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Evolved Stars IRC10216
HCN BIMA Image
C4H BIMA Image
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Why do molecules form? Classical Argument
e-


R
Stable molecule has e- with HIGH PROBABILITY of
being found between nuclei
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The Born-Oppenheimer Approximation
e-
rA
rB


p
p
R
The H2 Hamiltonian
ignore
Since the mass(p) gtgt mass(e-) , we can ignore
nuclear motion (the 1st term) and solve
Schroedingers Eq. assuming a fixed nucleus.
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Quantum Calculations of H2 Structure
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Molecular Orbitals - LCAO

ANTI-BONDING
BONDING




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Anti-bonding
p repulsion
Bonding
-13.6 eV
Anti-symmetric
Energy
e- binding Energy
Symmetric
-54.4 eV
Distance (nm)
K. Krane, Modern Physics
12
Electronic State in a molecule
L
Lz
E
Electronic orbital angular momenta precess about
internuclear axis due to strong electric field.
Symbol s , p , d
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s Molecular Orbitals
AO
MO



Z
1s
sg1s
-

-

Z
su1s
1s
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s Molecular Orbitals
AO
MO

-

-

-
-
2pz
sg2pz

-

-

-
-

su2pz
2pz
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p Molecular Orbitals
AO
MO



Z
-
-
-
pu2px
2px
-

-

Z
-


-
pg2px
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Correlation of Molecular Orbitals - Homonuclear
Unified Atom
Separated Atom
G. Herzberg, Molecular Spectra Molecular
Strucutre , vol I.
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Total Electronic Term of a Linear Molecule
O
L
S
L
S
W L S
Total electronic term
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Symmetries of electronic state
z
-z
Inversion
y y g
y
-y
y - y u
x
-x
ONLY Applies to homonuclear linear molecules
z
z
Reflection
y y
y
-y
y - y -
x
x
ONLY Applies to linear molecules in S states
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H2
E
L 0 S ½
2Sg
sg1s
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H2
E
L 0 S 0
1Sg
sg1s
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He2
E
su1s
L 0 S ½
2Su
sg1s
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(No Transcript)
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C2
E
pu2p
su2s
sg2s
L 0 S 0
su1s
1Sg
sg1s
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N2
E
sg2p
pu2p
su2s
sg2s
L 0 S 0
su1s
1Sg
sg1s
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O2
E
pg2p
L 0 S 0
sg2p
1Sg
pu2p
L 2 S 0
su2s
1Dg
sg2s
L 0 S 1
su1s
3Sg-
sg1s
Ground State
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O2 (pg2p)2 Configurations
l1
l2
s1
s2
L
S
1 1 - 2 0
1 1 - 2 0
-1 -1 - -2 0
-1 -1 - -2 0
1 -1 0 1
-1 1 0 1
1 -1 - - 0 -1
-1 1 - - 0 -1
1 -1 - 0 0
1 -1 - 0 0
1D
3S
1S
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Bond Order
Bond Energy
Bond Length
B2
C2
N2
O2
F2
Ne2
D. McQuarrie, Quantum Chemistry
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Correlation of Molecular Orbitals - Heteronuclear
Separated Atom
Unified Atom
G. Herzberg, Molecular Spectra Molecular
Strucutre , vol I.
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OH
E
2pp
2ps
2ss
L 1 S ½
2P
1ss
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CO
E
s2pA
p2pA
s2sB
s2sA
L 0 S 0
s1sB
1Sg
s1sA
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Photoelectron Spectrum CO
s2sB
s2sA
p2pA
s2pA
e- ejected
Binding Energy
D. McQuarrie, Quantum Chemistry
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MO Notation
D. McQuarrie, Quantum Chemistry
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Ground Electronic State of a few Linear Molecules
1S
H2, CH, CO, CS, SiO, HCN, HCO, N2H, CO2,
HCNH, HC3N
2S
H2, CN, CO, CCH
3S
O2, NH, SO, CCS, C2O
2P
CH, OH, NO
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Excited States of H2
E
sg2p
L 0 S 0
C1Pu
pu2p
L 0 S 0
su2s
B1Su
sg2s
L 0 S 1
su1s
b3Su
sg1s
L 0 S 0
X1Sg
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UV Electronic Transitions H2
Lyman Band
Werner Band
Shu, Radiation
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Electronic Transitions C2
Phillips Band