Chapter 9
Orbitals and Covalent Bond
1
Molecular Orbitals
The overlap of atomic orbitals from
separate atoms makes molecular
orbitals
 Each molecular orbital has room for two
electrons
 Two types of MO
– Sigma (  ) between atoms
– Pi (  ) above and below atoms

2
Sigma bonding orbitals

From s orbitals on separate atoms
+
+
s orbital s orbital
3
+ +
+ +
Sigma bonding
molecular orbital
Sigma bonding orbitals

From p orbitals on separate atoms


p orbital

4

p orbital


Sigma bonding
molecular orbital
Pi bonding orbitals





p orbitals on separate atoms


Pi bonding
molecular orbital
5
Sigma and pi bonds
All single bonds are sigma bonds
 A double bond is one sigma and one pi
bond
 A triple bond is one sigma and two pi
bonds.

6
Atomic Orbitals Don’t Work
to explain molecular geometry.
 In methane, CH4 , the shape is
tetrahedral.
 The valence electrons of carbon should
be two in s, and two in p.
 the p orbitals would have to be at right
angles.
 The atomic orbitals change when
making a molecule

7
Hybridization
We blend the s and p orbitals of the
valence electrons and end up with the
tetrahedral geometry.
 We combine one s orbital and 3 p
orbitals.


8
sp3 hybridization has tetrahedral
geometry.
9
10
In terms of energy
2p
Energy
Hybridization
2s
11
sp3
How we get to hybridization
We know the geometry from experiment.
 We know the orbitals of the atom
 hybridizing atomic orbitals can explain
the geometry.
 So if the geometry requires a tetrahedral
shape, it is sp3 hybridized
 This includes bent and trigonal pyramidal
molecules because one of the sp3 lobes
holds the lone pair.

12
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.

13
14
15
In terms of energy
2p
Energy
Hybridization
2s
16
2p
sp2
Where is the P orbital?
Perpendicular
 The overlap of
orbitals makes a
sigma bond (
bond)

17
Two types of Bonds
Sigma bonds from overlap of orbitals.
 Between the atoms.
 Pi bond ( bond) above and below atoms
 Between adjacent p orbitals.
 The two bonds of a
double bond.

18
H
H
C
H
19
C
H
sp2 hybridization
When three things come off atom.
 trigonal planar
 120º
 One  bond,  + lp =3

20
What about two
When two things come off.
 One s and one p hybridize.
 linear

21
sp hybridization
End up with two lobes 180º
apart.
 p orbitals are at right
angles
 Makes room for two 
bonds and two sigma
bonds.
 A triple bond or two double
bonds.

22
In terms of energy
2p
Energy
Hybridization
2s
23
2p
sp
CO2
C can make two  and two 
 O can make one  and one 

O
24
C O
N2
25
N2
26
Breaking the octet
PCl5
 The model predicts that we must use
the d orbitals.
 dsp3 hybridization
 There is some controversy about how
involved the d orbitals are.

27
dsp3
Trigonal
bipyrimidal
 can only  bond.
 can’t  bond.
 basic shape for
five things.

28
PCl5
Can’t tell the
hybridization of Cl
Assume sp3 to
minimize repulsion of
electron pairs.
29
d2sp3
gets us to six things
around
 Octahedral
 Only σ bond

30
Molecular Orbital Model
Localized Model we have learned explains
much about bonding.
 It doesn’t deal well with the ideal of
resonance, unpaired electrons, and bond
energy.
 The MO model is a parallel of the atomic
orbital, using quantum mechanics.
 Each MO can hold two electrons with
opposite spins
31
 Square of wave function tells probability

What do you get?

Solve the equations for H2
HA HB
 get two orbitals

32

MO2 = 1sA - 1sB

MO1 = 1sA + 1sB
The Molecular Orbital Model
• The molecular orbitals are centered on
a line through the nuclei
– MO1 the greatest probability is
between the nuclei
– MO2 it is on either side of the nuclei
– this shape is called a sigma molecular
orbital
33
The Molecular Orbital Model
• In the molecule only the molecular
orbitals exist, the atomic orbitals are gone
• MO1 is lower in energy than the 1s
orbitals they came from.
– This favors molecule formation
– Called an bonding orbital
• MO2 is higher in energy
– This goes against bonding
– antibonding orbital
34
The Molecular Orbital Model
Energy
MO2
1s
1s
MO1
35
H2
The Molecular Orbital Model
• We use labels to indicate shapes, and
whether the MO’s are bonding or
antibonding.
– MO1 = 1s
– MO2 = 1s* (* indicates antibonding)
• Can write them the same way as atomic
orbitals
– H2 = 1s2
36
The Molecular Orbital Model
• Each MO can hold two electrons, but
they must have opposite spins
• Orbitals are conserved.
• The number of molecular orbitals
must equal the number atomic
orbitals that are used to make them.
37
-
H2
Energy
1s*
1s
1s
1s
38
Bond Order

The difference between the number of
bonding electrons and the number of
antibonding electrons divided by two
# bonding-#antibonding
Bond Order =
2
39
Only outer orbitals bond
The 1s orbital is much smaller than the
2s orbital
 When only the 2s orbitals
are involved in bonding
 Don’t use the 1s or 1s*
for Li2

Li2 = (2s)2
 In order to participate in bonds the
40 orbitals must overlap in space.

Bonding in Homonuclear Diatomic
Molecules






41 
Need to use Homonuclear so that we know the
relative energies.
Li2(2s)2 (2s*)1
Be2
(2s)2 (2s*)2
What about the p orbitals? How do they form
orbitals?
Remember that orbitals must be conserved.
B2
42
B2
2p*
2p
2p*
2p
43
Expected Energy Diagram
2p
2p*
2p*
2p*
2p
2p
2p
2p
2s*
2s
44
2s
2s
B2
45
2p
2p
2s
2s
B2
(2s)2(2s*)2 (2p)2
 Bond order = (4-2) / 2
 Should be stable.
 This assumes there is no interaction
between the s and p orbitals.
 Hard to believe since they overlap
 proof comes from magnetism.

46
Magnetism
Magnetism has to do with electrons.
 Remember that spin is how an electron
reacts to a magnetic field
 Paramagnetism attracted by a magnet.
– associated with unpaired electrons.
 Diamagnetism repelled by a magnet.
– associated with paired electrons.
 B2 is paramagnetic.

47
Magnetism
The energies of of the 2p and the 2p
are reversed by p and s interacting
 The 2s and the 2s* are no longer
equally spaced.
 Here’s what it looks like.

48
Correct energy diagram
2p*
2p*
2p*
2p
2p
2p
2p
2p
2s*
2s
2s
2s
49
B2
2p
2p*
2p*
2p
2p
2p
2s*
2s
2s
2s
50
Patterns
As bond order increases, bond energy
increases.
 As bond order increases, bond length
decreases.
 Supports basis of MO model.
 There is not a direct correlation of bond
order to bond energy.
 O2 is known to be paramagnetic.
 Movie.

51
Magnetism
Ferromagnetic strongly attracted
 Paramagnetic weakly attracted
– Liquid Oxygen
 Diamagnetic weakly repelled
– Graphite
– Water Frog

52
Examples
C2
 N2
 O2
 F2
 P2

53
Heteronuclear Diatomic Species
Simple type has them in the same
energy level, so can use the orbitals we
already know.
 Slight energy differences.
 NO

54
NO
2p
2p
2s
2s
55
You try
NO+
 CN
 What if they come from completely
different orbitals and energy?
 HF
 Simplify first by assuming that F only
uses one if its 2p orbitals.
 F holds onto its electrons, so they have
low energy

56
*
1s
2p
57

Consequences
Paramagnetic
 Since 2p is lower in energy, favored by
electrons.
 Electrons spend time closer to fluorine.
 Compatible with polarity and
electronegativity.

58
Names
sp orbitals are called the Localized
electron model
  and  Molecular orbital model
 Localized is good for geometry, doesn’t
deal well with resonance.
 seeing  bonds as localized works well
 It is the  bonds in the resonance
structures that can move.

59
 delocalized bonding

C6H6
H
H
H
H
H
H
H
H
H
H
H
60
H
C2H6
61
NO3-
62