Problems with Valence Bond Theory

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Problems with Valence Bond Theory

• VB theory predicts many properties better than
  Lewis Theory
• bonding schemes, bond strengths, bond lengths,
  bond rigidity
• however, there are still many properties of
  molecules it doesnt predict perfectly
• magnetic behavior of O2

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Aurora Borealis
Chapter 9 Slide 2
Chapter 9 Slide 2
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Valence Bond Theory

• Valence Bond Model of covalent bonding is easy to
  visualize, but it does have some problems
• Incorrectly assumes that electrons are localized
  and so we have to use resonance to describe some
  molecules.
• Does not do a good job of describing molecules
  containing unpaired electrons
• Does not indicate bond energies

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Valence Bond Theory

• Valence Bond Model does not explain why O2 is
  attracted to a magnetic field while N2 is
  slightly repelled nor accounts for the emission
  of light by molecules in an aurora.
• The need to explain the magnetic behavior seen
  for O2 led to the development of another bonding
  theory called the Molecular Orbital (MO) Theory.

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Molecular Orbital Theory

• in MO theory, we apply Schrödingers wave
  equation to the molecule to calculate a set of
  molecular orbitals
• in practice, the equation solution is estimated
• we start with good guesses from our experience as
  to what the orbital should look like
• then test and tweak the estimate until the energy
  of the orbital is minimized
• in this treatment, the electrons belong to the
  whole molecule so the orbitals belong to the
  whole molecule
• unlike VB Theory where the atomic orbitals still
  exist in the molecule

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LCAO

• the simplest guess starts with the atomic
  orbitals of the atoms adding together to make
  molecular orbitals this is called the Linear
  Combination of Atomic Orbitals (LCAO) method
• weighted sum
• because the orbitals are wave functions, the
  waves can combine either constructively
  (additive) or destructively (subtractive)

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Bonding in H2

• 9.2

Chapter 9 Slide 7
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Molecular Orbitals

• when the wave functions combine constructively,
  the resulting molecular orbital has less energy
  than the original atomic orbitals it is called
  a Bonding Molecular Orbital
• s, p
• most of the electron density between the nuclei

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Molecular Orbitals

• when the wave functions combine destructively,
  the resulting molecular orbital has more energy
  than the original atomic orbitals it is called
  a Antibonding Molecular Orbital
• s, p
• most of the electron density outside the nuclei
• nodes between nuclei

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Molecular Orbital Model

• Molecular electron configurations can be written
  similar to atomic electron configurations.
• Each molecular orbital can hold 2 electrons with
  opposite spins.
• Orbitals are conserved.

Chapter 9 Slide 10
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Sigma Bonding and Antibonding Orbitals
Chapter 9 Slide 11
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Molecular Orbital Theory

• Electrons in bonding MOs are stabilizing
• Lower energy than the atomic orbitals
• Electrons in anti-bonding MOs are destabilizing
• Higher in energy than atomic orbitals
• Electron density located outside the internuclear
  axis
• Electrons in anti-bonding orbitals cancel
  stability gained by electrons in bonding orbitals

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Dihydrogen, H2 Molecular Orbitals
Hydrogen Atomic Orbital
Hydrogen Atomic Orbital
s
1s
1s
s
Since more electrons are in bonding orbitals
than are in antibonding orbitals, net bonding
interaction
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Dihelium, He2 Molecular Orbitals
Helium Atomic Orbital
Helium Atomic Orbital
s
1s
1s
s
Since there are as many electrons in antibonding
orbitals as in bonding orbitals, there is no net
bonding interaction
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MO and Properties

• Bond Order difference between number of
  electrons in bonding and antibonding orbitals
• only need to consider valence electrons
• may be a fraction (partial bond order)
• higher bond order stronger and shorter bonds
• if bond order 0, then bond is unstable compared
  to individual atoms - no bond will form.

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Dilithium, Li2 Molecular Orbitals
Lithium Atomic Orbitals
Lithium Atomic Orbitals
s
2s
2s
s
s
BO ½(4-2) 1
1s
1s
s
Since more electrons are in bonding orbitals
than are in antibonding orbitals, net bonding
interaction
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Diatomic O2

• dioxygen is paramagnetic
• paramagnetic material have unpaired electrons
• neither Lewis Theory nor Valence Bond Theory
  predict this result
• Paramagnetism substance is attracted into the
  inducing magnetic field.
• Diamagnetism substance is repelled from the
  inducing magnetic fiel

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Diatomic Oxygen, O2

• Dioxygen is attracted to a magnetic field!
• Neither Lewis Theory nor Valence Bond Theory
  predict this result.
• Paramagnetism substance is attracted into the
  inducing magnetic field.
• - Unpaired electrons (O2)
• Diamagnetism substance is repelled from the
  inducing magnetic field.
• - Paired electrons (N2)

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Magnetic Properties of Liquid Nitrogen and Oxygen
Chapter 9 Slide 19
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Pi Bonding and Antibonding Orbitals
Chapter 9 Slide 20
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p Atomic Orbitals and the Formation of Molecular
Orbitals
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Molecular Orbital Diagram for B2
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Molecular Orbital Diagram for O2
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s and p Orbital Mixing
No s-p mixing
s-p mixing
B2s 14 eV vs B2p 8.3 eV O2s
32.3eV vs O2p 15.9 eV
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s-p mixing
No s-p mixing
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1 electron volt (eV) 1.60217646 10-19 joules
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Factors that Affect the Formation of Molecular
Orbitals

• Symmetry
• s and s
• pz and pz (pz is along the bonding axis)
• s and pz
• Energy
• Orbitals must have similar energy in order to
  overlap

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Heteronuclear Diatomic Molecules

• the more electronegative atom has lower energy
  orbitals
• when the combining atomic orbitals are identical
  and equal energy, the weight of each atomic
  orbital in the molecular orbital are equal
• when the combining atomic orbitals are different
  kinds and energies, the atomic orbital closest in
  energy to the molecular orbital contributes more
  to the molecular orbital
• lower energy atomic orbitals contribute more to
  the bonding MO
• higher energy atomic orbitals contribute more to
  the antibonding MO
• nonbonding MOs remain localized on the atom
  donating its atomic orbitals

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Molecular Orbital Diagram of Hydrogen Fluoride
H1s 13.6 eV F2s 46.4 eV F2p 18.7 eV
32.8 eV
n.b. - nonbonding orbitals
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Molecular Orbital Diagram of Carbon Monoxide
C2s 19.5 eV O2s 32.3 eV O2p 15.9 eV
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Polyatomic Molecules

• when many atoms are combined together, the atomic
  orbitals of all the atoms are combined to make a
  set of molecular orbitals which are delocalized
  over the entire molecule
• gives results that better match real molecule
  properties than either Lewis or Valence Bond
  theories

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Valence Bond Model of Ozone
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Molecular Orbital Model of Ozone
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Resonance Structures of Benzene
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Molecular Orbital Model of Benzene