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

CH 4 Absorption Brown Dwarfs: Gliese 229B Geballe, et al. 1995

Planetary Atmospheres ISO Spectrum of Jupiter CH 4 CH 3 D PH 3 NH 3 C2H6C2H6 C2H2C2H2 Voyager, NASA

Comets: Hale-Bopp HCN J=4-3 D. Jewitt, U. Hawaii

Evolved Stars: IRC10216 HCN BIMA ImageC 4 H BIMA Image

Why do molecules form? Classical Argument Stable molecule has e - with HIGH PROBABILITY of being found between nuclei ++ R e-

The Born-Oppenheimer Approximation The H 2 + Hamiltonian Since the mass(p + ) >> mass(e - ), we can ignore nuclear motion (the 1 st term) and solve Schroedinger’s Eq. assuming a fixed nucleus. ++ R e-e- rArA rBrB ignore p+p+ p+p+

Quantum Calculations of H 2 Structure

Molecular Orbitals - LCAO BONDING ANTI-BONDING

e - binding Energy Bonding Anti-bonding eV eV p + repulsion Symmetric Anti- symmetric Energy Distance (nm) K. Krane, Modern Physics

L LzLz E Electronic State in a molecule Electronic orbital angular momenta precess about internuclear axis due to strong electric field. Symbol: , , 

 Molecular Orbitals AOMO +  g 1s  u 1s 1s -+ Z Z

 Molecular Orbitals  g 2p z +-+-  u 2p z p z AOMO

Z Z  Molecular Orbitals  u 2p x  g 2p x AOMO 2p x

Correlation of Molecular Orbitals - Homonuclear G. Herzberg, Molecular Spectra & Molecular Strucutre, vol I. Unified AtomSeparated Atom

Total Electronic Term of a Linear Molecule O L S   Total 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  g 1s H2+H2+  = 0 S = ½ 2g+2g+

E  g 1s H2H2  = 0 S = 0 1g+1g+

E  g 1s He 2 +  = 0 S = ½ 2u+2u+  u 1s

E  g 1s C2C2  = 0 S = 0 1g+1g+  u 1s  g 2s  u 2s  u 2p

E  g 1s N2N2  = 0 S = 0 1g+1g+  u 1s  g 2s  u 2s  u 2p  g 2p

E  g 1s O2O2  = 0 S = 1 3g-3g-  u 1s  g 2s  u 2s  u 2p  g 2p  = 2 S = 0 1g1g  = 0 S = 0 1g+1g+ Ground State  g 2p

O 2 (  g 2p) 2 Configurations s1s1 s2s2  11 33 11

D. McQuarrie, Quantum Chemistry Bond Order Bond Energy Bond Length B2B2 C2C2 N2N2 O2O2 F2F2 Ne 2

G. Herzberg, Molecular Spectra & Molecular Strucutre, vol I. Correlation of Molecular Orbitals - Heteronuclear Unified Atom Separated Atom

E ss OH  = 1 S = ½ 22 ss pp pp

E  1s A CO  = 0 S = 0 1g+1g+  1s B  2s A  2s B  2p A  2p A

Photoelectron Spectrum CO  s   s   p   p  # e - ejected Binding Energy D. McQuarrie, Quantum Chemistry

MO Notation D. McQuarrie, Quantum Chemistry

Ground Electronic State of a few Linear Molecules 22 H 2 +, CN, CO +, CCH 33 O 2, NH, SO, CCS, C 2 O 22 CH, OH, NO 11 H 2, CH +, CO, CS, SiO, HCN, HCO +, N 2 H +, CO 2, HCNH +, HC 3 N

E  g 1s Excited States of H 2  = 0 S = 0 X1g+X1g+  u 1s  g 2s  u 2s  u 2p  g 2p  = 0 S = 1 b3u+b3u+  = 0 S = 0 B1u+B1u+  = 0 S = 0 C1uC1u

Lyman Band Werner Band UV Electronic Transitions: H 2 Shu, Radiation

Electronic Transitions: C 2 Phillips Band