Molecular orbital MO theory for engineers

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Molecular orbital (MO) theory for engineers

• Applications of wave cancellation
• Automobile mufflers
• Audio (and other) amplifier electrical feedback
• Noise cancelling headphones
• MO theory for diatomic molecules (2 atoms)
• Band theory - MO theory for covalently bonded
  solids (?) atoms
• Metals
• Electrical insulators
• Semiconductors
• Photoconductors
• Xerography
• Laser diodes (my laser pointer, your CD/DVD
  players
• Photovoltaic cells (converting sunlight into
  electricity

NEXT TIME
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• ?
• ? (- sign flips phase of the sound wave function)
• ? - ? 0

Auto mufflers use destructive interference of
sound waves to reduce engine noises.
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Amplifier noise is reduced by adding
destructively Interference (reversed phase
noises).
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Bose is 200. Want to do it yourself? See Web
site.
http//www.headwize.com/projects/noise_prj.htm
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The Central Themes of MO Theory

• A molecule is viewed on a quantum mechanical
  level as a collection of nuclei surrounded by
  delocalized molecular orbitals MOs).

Atomic orbital wave functions are added and
subtracted to obtain molecular orbital (MO) wave
functions.
The combinations result in e-wave constructive
interference and produce bonding MOs i.e.
regions of high electron density between nuclei).
The combinations result in e-wave destructive
interference and produce antibonding MOs which
show node - regions of zero electron density
between the nuclei).
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An analogy between light waves and atomic wave
functions.
Figure 11.13
NOTE /- signs show PHASES of waves,
NOT CHARGES!
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Figure 11.14
Contours and energies of the bonding and
antibonding molecular orbitals (MOs) in H2.
Axially symmetric
OUT OF PHASE
E-density blue
IN PHASE
Axially symmetric
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Figure 11.15
The MO diagram for H2
ANTIBONDING es 0
BONDING es 2
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Figure 11.16
MO diagram for He2 and He2
s1s
Energy
s1s
MO of He
MO of He2
He2 bond order 0
He2 bond order 1/2
He2 does not exist!
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2 H.
HH
Lower curve like Fig. 9.11
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Antibonding MO ?-
Energy
?1S(A)
?1S(B)
Bonding MO ?
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SAMPLE PROBLEM 11.3
Predicting Species Stability Using MO Diagrams
SOLUTION
bond order 1/2(1-0) 1/2
bond order 1/2(2-1) 1/2
H2 does exist
H2- does exist
configuration is (s1s)2(s?2s)1
MO of H2-
MO of H2
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Figure 11.17
Bonding in s-block homonuclear diatomic molecules.
Be2
Li2
Energy
Li2 bond order 1
Be2 bond order 0
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Contours and energies of s and p MOs through
combinations of 2p atomic orbitals
Figure 11.18
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Figure 11.19
Relative MO energy levels for Period 2
homonuclear diatomic molecules.
without 2s-2p mixing
with 2s-2p mixing
MO energy levels for O2, F2, and Ne2
MO energy levels for B2, C2, and N2
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Figure 11.20
MO occupancy and molecular properties for B2
through Ne2
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Figure 11.21
The paramagnetic properties of O2
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SAMPLE PROBLEM 11.4
Using MO Theory to Explain Bond Properties
Explain these facts with diagrams that show the
sequence and occupancy of MOs.
SOLUTION
N2 has 10 valence electrons, so N2 has 9.
O2 has 12 valence electrons, so O2 has 11.
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SAMPLE PROBLEM 11.4
Using MO Theory to Explain Bond Properties
continued
N2
N2
O2
O2
??2p
antibonding e- lost
bonding e- lost
??2p
?2p
?2p
s?2s
s2s
bond orders
1/2(8-2)3
1/2(7-2)2.5
1/2(8-4)2
1/2(8-3)2.5
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Figure 11.24
The lowest energy p-bonding MOs in benzene and
ozone.
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The MO diagram for HF
Figure 11.22
Two non-bonding orbitals are the lone pairs on
F seen in The Lewis structure for HF
Energy
Note the H1S is less stable than the F2P
MO of HF
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The MO diagram for NO
Figure 11.23
PARAMAGNETIC
Energy
possible Lewis structures
MO of NO