Introduction to Molecular Orbital Theory

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Introduction to Molecular Orbital Theory

• Allyn Ontko, Ph.D.
• University of Wyoming
• School of Pharmacy

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Molecular Orbital (MO) Theory

• Diagram of molecular energy levels
• Magnetic and spectral properties
• Paramagnetic vs. Diamagnetic
• Electronic transitions
• Solid State - Conductance
• Predicts existence of molecules
• Bond Order

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Molecular Orbital (MO) Theory

• Two atomic orbitals combine to form
• a bonding molecular orbital
• an anti-bonding molecular orbital
• e- in bonding MOs stability
• e- in anti-bonding MOs instability
• atomic orbitals combined equals of molecular
  orbitals formed

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Central Themes

• Quantum mechanical level
• Molecule viewed as a collection of nuclei
  surrounded by delocalized molecular orbitals
• Atomic wave functions are summed to obtain
  molecular wave functions.
• If wave functions reinforce each other, a bonding
  MO is formed (region of high electron density
  exists between the nuclei).
• If wave functions cancel each other, an
  antibonding MO is formed (a node of zero electron
  density occurs between the nuclei).

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An Analogy
Amplitudes of wave functions added
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MO Molecular Hydrogen
The bonding MO is lower in energy than an AO The
anti- bonding MO is higher in energy than an AO
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Considerations

• Bond Order 1/2( bonding e- antibonding
  e- )
• Higher bond order stronger bond
• Molecular electron configurations
• Highest Occupied Molecular Orbital HOMO
• Lowest Unoccupied Molecular Orbital LUMO
• An Example H2 (?1s)2

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MO Molecular Hydrogen
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Predicting Stability H2 H2-
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?1s)1
configuration is (s1s)1
MO of H2
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Helium He2 vs He2
s1s
Energy
s1s
MO of He
MO of He2
He2 bond order 0
He2 bond order 1/2
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Bond Length vs. Bond Order
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Next Row 2s 2p orbitals
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Combinations for p-orbitals
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P orbital Complications

• Results in one ? one ? MO
• One pair from 2pz
• Results in two ? two ? MOs
• One pair for 2px and one pair for 2py
• gt half filled p orbitals (O, F, Ne)
• energy ?2p lt 2?2p lt 1?2p lt 2?2p
• ? half filled p orbitals (B, C, N)
• energy 2?2p lt ?2p lt 2?2p lt 1?2p

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MO Now with S P
X 2
X 2
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P orbital Complications

• Results in one ? one ? MO
• One pair from 2pz
• Results in two ? two ? MOs
• One pair for 2px and one pair for 2py
• gt half filled p orbitals (O, F, Ne)
• energy ?2p lt 2?2p lt 1?2p lt 2?2p
• ? half filled p orbitals (B, C, N)
• energy 2?2p lt ?2p lt 2?2p lt 1?2p

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S-P Energy Separation
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E(2p)-E(2s) N 12.4 eV O 16.5 eV F 31.6 eV
For N small 2p/2s separation big ?(2s) /
?(2pz) repulsion
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S - P orbital mixing
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Relative Energy Levels for 2s 2p
WITHOUT big 2s-2p repulsion
WITH big 2s-2p repulsion
MO energy levels for O2, F2, and Ne2
MO energy levels for B2, C2, and N2
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Triumph for MO Theory?
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Can MO Theory Explain Bonding?
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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Can MO Theory Explain Bonding?
N2
N2
O2
O2
antibonding e- lost
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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Real World Applications

• Most molecules are heteroatomic
• What needs to be considered?
• Orbitals involved
• Electronegativity (Orbital energies)
• Hybridization (Group Theory)
• Mixing

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Lets Start Slowly HF

• Valence electrons
• H 1s1
• F 1s2 2s2 2p5
• Focus on the valence interactions
• Accommodate for differences in electronegativity
• Allow mixing between symmetry-allowed states

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Lets Start Slowly HF
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possible Lewis structures
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For Next Lecture

• Generate an MO Diagram for CO
• What is the bond order?
• What is the HOMO?
• What is the LUMO?
• Draw a corresponding Lewis dot structure
• Bonus Based on your answers above, what can you
  envision for the bonding interaction of CO with a
  transition metal (like Fe)?

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HOMO is lone pair on C. CO always binds to metals
via the C end
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Energy Diagram
2 H.
HH