Electronic Structure of Molecules AST380E Yancy L. Shirley
36
Electronic Structure of Molecules AST380E Yancy L. Shirley
description
Electronic Structure of Molecules AST380E Yancy L. Shirley. Where do we find molecules ?. Orion in CO J=2-1. Molecular Clouds & Star Formation Regions. VLT, Japan. Brown Dwarfs: Gliese 229B. CH 4 Absorption. Geballe, et al. 1995. Planetary Atmospheres. Voyager, NASA. - PowerPoint PPT Presentation
Transcript of Electronic Structure of Molecules AST380E Yancy L. Shirley
Electronic Structure of Molecules
AST380E
Yancy L. Shirley
Where do we find molecules ?
Molecular Clouds &Star Formation Regions
Orion in CO J=2-1
VLT, Japan
CH4 Absorption
Brown Dwarfs:Gliese 229B
Geballe, et al. 1995
Planetary Atmospheres
ISO Spectrum of Jupiter
CH4
CH3D
PH3
NH3
C2H6
C2H2
Voyager, NASA
Comets:Hale-Bopp
HCN J=4-3
D. Jewitt, U. Hawaii
Evolved Stars:IRC10216
HCN BIMA Image C4H BIMA Image
Why do molecules form?
Classical Argument
20
2
2/42Re
F attractive
20
2
4 Re
F repulsive
FF repulsiveattractive
Stable molecule has e- with HIGH PROBABILITY of being found between nuclei
+ +
R
e-
The Born-Oppenheimer Approximation
R
e
r
e
r
e
mmH
BAe
eBA
p 044422
ˆ2
0
2
0
22
222
2
The H2+ Hamiltonian
Since the mass(p+) >> mass(e-) , we can ignore nuclear motion (the 1st term) and solve Schroedinger’s Eq. assuming a fixed nucleus.
+ +
R
e-
rA rB
ignore
p+p+
Quantum Calculations of H2 Structure
ear
sa 0/2/101
sBsAsym 11
sBsAasym 11
Molecular Orbitals - LCAO
+
+ + + +
BONDING ANTI-BONDING
e- binding Energy
Bonding
Anti-bonding
-13.6 eV
-54.4 eV
p+ repulsion
Symmetric
Anti-symmetric
En
erg
y
Distance (nm) K. Krane, Modern Physics
L
Lz
E
Electronic State in a molecule
lllm
ml
l
lz
,...,1,
Electronic orbital angular momenta precess about internuclear axis due to strong electric field.
Symbol: , ,
2,1,0: lm
Molecular Orbitals
+ +
+ -
AO MO
+
g1s
u1s
1s
-+
1s
Z
Z
Molecular Orbitals
+- + - +- -
g2pz
+- +-
u2pz
+ +- -
2pz
2pz
AO MO
+
-
+
-
+
-
+
- +
-
Z
Z
+
+
-
-
Molecular Orbitals
u2px
g2px
AO MO
2px
Correlation of Molecular Orbitals - Homonuclear
G. Herzberg, Molecular Spectra & Molecular Strucutre , vol I.
Unified Atom Separated Atom
Total Electronic Term of a Linear Molecule
O
LS
i
ilm
i
ismS
12STotal electronic term:
Symmetries of electronic state
x
y
z
Inversion
-x
-y
-z
g
- u
ONLY Applies to homonuclear linear molecules
x
y
z
Reflection
x
-y
z
+
- -
ONLY Applies to linear molecules in states
E
g1s
H2+
= 0
S = ½ 2g
+
E
g1s
H2
= 0
S = 0 1g
+
E
g1s
He2+
= 0
S = ½ 2u
+
u1s
E
g1s
C2
= 0
S = 0 1g
+u1s
g2s
u2s
u2p
E
g1s
N2
= 0
S = 0 1g
+u1s
g2s
u2s
u2p
g2p
E
g1s
O2
= 0
S = 1 3g
-u1s
g2s
u2s
u2p
g2p
= 2
S = 0 1g
= 0S = 0 1g
+
Ground State
g2p
O2 (g2p)2 Configurations
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
1 2 s1 s2
1
3
1
D. McQuarrie, Quantum Chemistry
Bond Order
Bond Energy
Bond Length
B2 C2 N2 O2 F2 Ne2
G. Herzberg, Molecular Spectra & Molecular Strucutre , vol I.
Correlation of Molecular Orbitals - Heteronuclear
Unified AtomSeparated Atom
E
s
OH
= 1
S = ½ 2
s
p
p
E
1sA
CO
= 0
S = 0 1g
+1sB
2sA
2sB
2pA
2pA
Photoelectron Spectrum CO
s
s
p
p
# e- e
ject
ed
Binding Energy D. McQuarrie, Quantum Chemistry
MO Notation
D. McQuarrie, Quantum Chemistry
Ground Electronic State of a few Linear Molecules
2 H2+, CN, CO+, CCH
3 O2, NH, SO, CCS, C2O
2 CH, OH, NO
1 H2, CH+, CO, CS, SiO, HCN, HCO+, N2H+, CO2, HCNH+, HC3N
E
g1s
Excited States of H2
= 0
S = 0 X1g
+
u1s
g2s
u2s
u2p
g2p
= 0S = 1 b3u
+
= 0S = 0 B1u
+
= 0S = 0 C1u
Lyman Band
Werner Band
UV Electronic Transitions:
H2
Shu, Radiation
Electronic Transitions:
C2Phillips Band
