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 doesn’t predict perfectly
– magnetic behavior of O2
1
Aurora Borealis
Chapter 9 | Slide 2
Chapter 9 | Slide 2
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
3
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.
4
Molecular Orbital Theory
• in MO theory, we apply Schrödinger’s 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
5
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)
6
Bonding in H2
9.2
Chapter 9 | Slide 7
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
8
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
9
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
Sigma Bonding and Antibonding
Orbitals
Chapter 9 | Slide 11
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
12
Hydrogen
Atomic
Orbital
Dihydrogen, H2
Molecular
Orbitals
Hydrogen
Atomic
Orbital
s*
1s
1s
s
Since more electrons are in
bonding orbitals than are in antibonding orbitals,
net bonding interaction
13
Helium
Atomic
Orbital
Dihelium, He2
Molecular
Orbitals
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
14
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.
# Bond Elec. - # Antibond Elec.
Bond Order 
2
15
Lithium
Atomic
Orbitals
Dilithium, Li2
Molecular
Orbitals
s*
2s
Lithium
Atomic
Orbitals
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
16
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
17
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)
18
Magnetic Properties of Liquid
Nitrogen and Oxygen
Chapter 9 | Slide 19
Pi Bonding and Antibonding
Orbitals
Chapter 9 | Slide 20
p Atomic Orbitals and the Formation of Molecular Orbitals
Molecular Orbital Diagram for B2
Molecular Orbital Diagram for O2
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
s-p mixing
No s-p mixing
1 electron volt (eV) = 1.60217646 × 10-19 joules
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
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
28
Molecular Orbital Diagram of Hydrogen Fluoride
H1s = 13.6 eV
32.8 eV
F2s = 46.4 eV
F2p = 18.7 eV
n.b. - nonbonding orbitals
Molecular Orbital Diagram of Carbon Monoxide
C2s = 19.5 eV
O2s = 32.3 eV
O2p = 15.9 eV
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
31
Valence Bond Model of Ozone
Molecular Orbital Model of Ozone
Resonance Structures of Benzene
Molecular Orbital Model of Benzene