Covalent Bonding: orbitals

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Chapter 9

• Covalent Bonding orbitals

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Topics

• Hybridization and the localized electron model
• The molecular orbital model
• Bonding in homonuclear diatomic molecules
• Bonding in heteronuclear diatomic molecules
• Combining the localized electron and molecular
  orbital models

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9.1 Hybridization and localized electron model
How do atoms share electrons between their
valence shells?

• The localized electron bonding model

• A covalent bond is formed by the
• pairing of two electrons with opposing
• spins in the region of overlap of atomic
• orbitals between two atoms

• Overlap the two orbitals share a
• common region in space

• This overlap region has high
• electron charge density

• The more extensive the overlap
• between two orbitals, the stronger
• is the bond between two atoms

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• According to the model
• For an atom to form a covalent bond it must have
  an unpaired electron
• Number of bonds formed by an atom should be
  determined by its number of unpaired electrons

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How does Lewis theory explain the bonds in H2 and
F2?
Sharing of two electrons between the two atoms.
H2
(1s1)
(1s1)
F2
(1s22s22p5)
(1s22s22p5)
Localized electron model bonds are formed by
sharing of e- from overlapping atomic orbitals.
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Hybridization of Atomic Orbitals
Based on ground-state electron configuration,
carbon should have only two bonds
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Hybridization of Atomic Orbitals
Most of the electrons in a molecule remain in the
same orbital locations that they occupied in the
separated atoms
Bonding electrons are localized in the region of
atomic orbital overlap
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Hybridization ?

• Two or more atomic orbitals are mixed to produce
  a new set of orbitals (blended orbitals)
• Number of hybrid orbitals number of atomic
  orbitals mixed

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sp3 Hybridization
Occurs most often for central atom only
The total number of hybrid orbitals is equal to
the number of atomic orbitals combined
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sp3 Hybridization

• s and p orbitals of the valence electrons are
  blended.
• one s orbital is combined with 3 p orbitals.
• sp3 hybridization has tetrahedral geometry.

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sp3 Hybridization
The carbon atom in methane (CH4) has bonds that
are sp3 hybrids Note that in this molecule
carbon has all single bonds
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In terms of energy
2p
Hybridization
Energy
2s
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Methane building blocks
H
C
H
H
C
H
H
VSEPR
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1s
2s
2px
2pz
2py
sp3 sp3 sp3 sp3
y
Promote
Hybridize
x
109.5o
z
Methane Carbon
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sp3 Orbital Hybridization in NH3
7N

• 3 Equivalent half-filled orbitals are used to
  form bonds with 3H atoms. The 4th sp3 holds the
  lone pair

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Bonding in Ammonia
Ammonia (NH3) is similar to CH4 except the lone
pair of electrons occupies the 4th hybrid orbital
7N 1s2 2s2 2p3
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How about hybridization in H2O?
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sp2 Hybridization
Consider BF3
5B
The empty 2p orbital remains unhybridized
sp2 is comprised of one 2s orbital and two 2p
orbitals to produce a set of three sp2 hybrid
orbitals
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Formation of sp2 Hybrid Orbitals
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Hybrid orbitals and geometry
The geometric distribution of the three sp2
hybrid orbitals is within a plane, directed at
120o angles
This distribution gives a trigonal planar
molecular geometry, as predicted by VSEPR
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sp2 Hybridization scheme is useful in describing
double covalent bonds, e.g. Ethylene
in CH2CH2
Unhybridized orbital
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10.5
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Nonhybridized p-orbitals
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sp2 Hybridization scheme is useful in describing
double covalent bonds, e.g. Ethylene
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Sigma ? and pi ? bonds

• Sigma bond is formed when two orbitals each with
  a single electron overlap
• (Head-to-head overlap). Electron density is
  concentrated in the region directly between the
  two bonded atoms
• Pi-bond is formed when two parallel p-orbitals
  overlap side-to-side
• The orbital consists of two lopes one above the
  bond axis and the other below it.
• Electron density is concentrated in the lopes
• Electron density is zero along the line joining
  the two bonded atoms

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H
H
C
C
H
H
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sp2 hybridization

• C2H4
• Double bond acts as one pair.
• trigonal planar
• Have to end up with three blended orbitals.
• Use one s and two p orbitals to make sp2
  orbitals.
• Leaves one p orbital perpendicular.

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In terms of energy
2p
Energy
2s
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sp Hybridization
H-Be-H
1s2 2s2
4Be
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In terms of energy
2p
Energy
2s
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This hybridization scheme is useful in
describing triple covalent bonds
in acetylene
Hybridization in
Unhybridized orbitals
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CarbonCarbon Triple Bonds
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Hybridization in molecules containing multiple
bonds

• The extra electron pairs in double or triple
  bonds have no effect upon the geometry of
  molecules
• Extra electron pairs in multiple bonds are not
  located in hybrid orbitals
• Geometry of a molecule is fixed by the electron
  pairs in hybrid orbitals around the central atom
• All unshared electron pairs
• Electron pairs forming single bonds
• One (only one) electron pair in a multiple bond

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CO2
C
O
O

• C can make two s and two p
• O can make one s and one p

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dsp3/sp3d Hybridization
A 3s electron can be promoted to a 3d subshell,
which gives rise to a set of five sp3d hybrid
orbitals
Central atoms without d-orbitals, N, O, F, do not
form expanded octet
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PCl5
Phosphorus Pentachloride
Cl
P
Cl
Cl
Cl
P
Cl
Cl
VSEPR
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sp3d sp3d sp3d sp3d sp3d
Neon
3s
3px
3pz
3py
2
dxz dyz dxy dx2-y2 dz2
Hybridized
90o
Promoted
120o
TrigonalBipyrimidal
120o
Phosphorus Pentachloride Phosphorus
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d 2sp3/sp3d2 hybridization
This hybridization allows for expanded valence
shell compounds typically group 6A elements,
e.g., S
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Predicting Hybridization Schemes
In hybridization schemes, one hybrid orbital is
produced for every simple atomic orbital involved
Write a plausible Lewis structure for the
molecule or ion

• Use the VSEPR method to predict the
• electron-group geometry of the central atom

• Count of e-pairs around the atom
• Multiple bond is counted as one pair

• Choose the hybrid set having same
• number of orbitals

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Success of the localized electron model

• Overlap of atomic orbitals explained the
  stability of covalent bond
• Hybridization was used to explain the molecular
  geometry predicted by the localized electron
  model
• When lewis structure was in adequate, the concept
  of resonance was introduced to explain the
  observed properties

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Weakness of the localized electron model

• It incorrectly assumed that electrons are
  localized and so the concept of resonance was
  added
• Inability to predict the magnetic properties of
  molecules like O2 (molecules containing unpaired
  electrons)
• No direct information about bond energies

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9.2 Molecular Orbital Theory

• Molecular orbitals (MOs) are mathematical
  equations that describe the regions in a molecule
  where there is a high probability of finding
  electrons
• Atomic orbitals of atoms are combined to give a
  new set of molecular orbitals characteristic of
  the molecule as a whole
• The number of atomic orbitals combined equals the
  number of molecular orbitals formed.
• (Two s-orbitals Two molecular
  orbitals)

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Molecular orbitals

• Two atomic orbitals combine to form a bonding
  molecular orbital and an anti-bonding MO.
• Electrons in bonding MOs stabilize a molecule
• Electrons in anti-bonding MOs destabilize a
  molecule
• For the orbitals to combine, they must be of
  comparable energies. e.g., 1s(H) with 2s(Li) is
  not allowed
• The molecular orbitals are arranged in order of
  increasing energy.
• The electronic structure of a molecule is derived
  by feeding electrons to the molecular orbitals
  according to same rule applied for atomic
  orbitals

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Molecular orbitals

• Each molecular orbital can hold a maximum of two
  electrons with opposite spins
• Electrons go into the lowest energy molecular
  orbital available
• Hunds rule is obeyed

Molecular orbital model will be applied only to
the diatomic molecules of the elements of the
first two periods of the Periodic Table
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Formation of molecular orbitals by combination of
1s orbitals
Antibonding MO2 region of diminished electron
density
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Energy level diagram in hydrogen (H2).
Bonding molecular orbital has lower energy and
greater stability than the atomic orbitals from
which it was formed.
antibonding molecular orbital has higher energy
and lower stability than the atomic orbitals from
which it was formed.
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The Molecular Orbital Model

• We use labels to indicate shapes, and whether the
  MOs are bonding or antibonding.
• MO1 s1s
• MO2 s1s ( indicates antibonding)
• We can write them the same way as atomic orbitals
• H2 s1s2

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Bond order

• Bond Order 1/2 (bonding e antibonding e)
• (number of bonds)
• Higher bond order stronger bond

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Bond order for H2
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Bond order for He2 and He2
s1s
Energy
s1s
MO of He
MO of He2
He2 bond order 0
He2 bond order 1/2
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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
1s
AO of H
configuration is (s1s)2(s?1s)1
MO of H2-
MO of H2
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bond order
½
1
0
½
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9.3 Bonding in homonuclear diatomic molcules

• For atomic orbitals to participate in molecular
  orbitals, they must overlap in space
• Thus only valence orbitals of atoms contribute
  significantly to the molecular orbitals of the
  molecule
• Inner orbitals are too small to overlap and thus
  their electrons are assumed to be localized and
  not participate in bonding

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Only outer orbitals bond

• The 1s orbital is much smaller
• than the 2s orbital
• When only the 2s orbitals
• are involved in bonding
• Dont use the s1s or s1s
• for Li2
• Li2 (s2s)2
• In order to participate in
• bonds the orbitals must
• overlap in space.

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Bonding in s-block homonuclear diatomic molecules.
Be2
Li2
Energy
Be2 bond order 0
Li2 bond order 1
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Possible interactions between two equivalent p
orbitals and the corresponding molecular orbitals
-
-

Head-to-head overlap
High e- density

- Low e- density
Side-to-side overlap
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Molecular Orbital (MO) Configurations

• The number of molecular orbitals (MOs) formed is
  always equal to the number of atomic orbitals
  combined.
• The more stable the bonding MO, the less stable
  the corresponding antibonding MO.
• The filling of MOs proceeds from low to high
  energies.
• Each MO can accommodate up to two electrons.
• Use Hunds rule when adding electrons to MOs of
  the same energy.
• The number of electrons in the MOs is equal to
  the sum of all the electrons on the bonding atoms.

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Expected Energy Diagram
s2p
p2p
p2p
2p
2p
p2p
p2p
s2p
Energy
s2s
2s
2s
s2s
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B2
2p
2p
Energy
2s
2s
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B2

• (s2s)2(s2s)2 (s2p)2
• Bond order (4-2) / 2
• Should be stable.

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Magnetism

• Magnetism has to do with electrons.
• Paramagnetism substance is attracted by a
  magnet.
• associated with unpaired electrons.
• Diamagnetism substance is repelled by a magnet.
• associated with paired electrons.
• Experimentally, B2 was found to be paramagnetic
• However, Orbital diagram shows that it is
  diamagnetic?

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Magnetism

• The energies of of the p2p and the s2p are
  reversed by p and s interacting
• The s2s and the s2s are no longer equally
  spaced.
• Heres what it looks like.

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Correct energy diagram
s2p
p2p
p2p
2p
2p
s2p
p2p
p2p
s2s
2s
2s
s2s
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B2
s2p
p2p
2p
2p
s2p
p2p
s2s
2s
2s
s2s
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Note that for O2 and F2 ?2p orbital is lower in
energy than ?2p orbitals
MO energy level digrams for diatomic molecules of
B2 through F2
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Patterns

• As bond order increases, bond energy increases.
• As bond order increases, bond length decreases.
• Direct correlation of bond order to bond energy
  is not always there
• O2 is known to be paramagnetic.

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SAMPLE PROBLEM
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
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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9.4 Bonding in heteronuclear diatomic molecules

• Will deal with molecules of atoms adjacent to
  each other in the Periodic Table
• Simple type has them in the same energy level, so
  can use the orbital diagrams used for
  homonuclear molecules already known to us
• Slight energy differences.
• NO

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The MO diagram for NO
Energy
possible Lewis structures
Bond order
Experimentally NO is paramagnetic
MO of NO
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Nitric oxide, NO
valence e- 5(N) 6(O) 11
2p
2p
2s
2s
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The MO diagram for HF
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
2p
MO of HF
AO of F
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Partial molecular orbital energy-level diagram
for HF

• Other valence electrons of F are
• assumed to be localized

F binds its valence electrons more tightly than H
Energy
1s
Note the H1S is less stable (has more energy)
than the F2P
2p
Since both electrons are lowered in energy, HF
molecule is more stable Than individual atoms.
This is the Driving force for bond formation
MO of HF
AO of H
AO of F
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Partial molecular orbital energy-level diagram
for HF

• The ? molecular orbital containing the bonding
  electron pair shows greater electron probability
  close to F
• Thus, F atom will have a slight excess of ve
  charge, i.e., electron sharing is not equal
• Consequently, MO diagrams accounts for bond
  polarity

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The MO Energy-level diagram for both the NO and
CN- ions
valence e in NO 10
Same order as homonuclear atoms
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9.5 Combining the localized electron and
molecular orbital models

• sp orbitals are called the Localized electron
  model
• s and p Molecular orbital model
• Localized is good for geometry, doesnt deal well
  with resonance.
• seeing s bonds as localized works well
• It is the p bonds in the resonance structures
  that can move.
• ? molecular orbital can be considered to be
  spread over the entire molecule rather than being
  concentrated between the two atoms
• Electrons occupying the ? molecular orbital
  belong to the whole molecule they are described
  as Delocalized

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The resonance structures for O3 and NO3-

• The two extra electrons in the double bond are
  found in the
• delocalized ?-orbital associated with the whole
  molecule
• Also, there are 3 ?-bonds localized between S
  and O atoms
• Thus bond distances are the same

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Bonding in Benzene
The structure of benzene, C6H6, discovered by
Michael Faraday in 1825, was not figured out
until 1865 by F. A. Kekulé
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Benzene
This kind of structure gives rise to two
important resonance hybrids and leads to the idea
that all three double bonds are delocalized
across all six carbon atoms
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Benzene

• A better description of bonding in benzene
  results when a combination of the two models is
  used for interpretation
• Six p-orbitals can be used to ?-molecular
  orbitals
• The electrons in the resulting ?-molecular
  orbitals are delocalized above and below the
  plane of the ring.
• Thus, C-C bonds are equivalent as obtained from
  experiment

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p delocalized bonding

• C6H6

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The lowest energy p-bonding MOs in benzene and
ozone.
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Delocalized molecular orbitals are not confined
between two adjacent bonding atoms, but actually
extend over three or more atoms.