Chapter 9
Bonding and
Molecular Structure:
Orbital Hybridization
and Molecular Orbitals
Jeffrey Mack
California State University,
Sacramento
Orbitals & Theories of Chemical
Bonding
• Chapter 6 told us that the location of the valence
electrons in an atom is described by an orbital
model.
• It should seem reasonable that an orbital model
can also be used to describe electrons in
molecules.
• In this chapter, you will explore two common
approaches to rationalizing chemical bonding
based on orbitals:
• Valence Bond (VB) theory and Molecular Orbital
(MO) theory.
Valence Bonding Theory
Developed by Linus Pauling
• Premise: Bonding involves
valence electrons.
• Half-filled atomic orbitals on
bonding atoms overlap to
form bonds.
• Bonds are localized between
atoms (or as lone pairs).
• Leads to prediction of
molecular shape.
Linus Pauling, 1901-1994
Molecular Orbital Theory
Developed by Robert S. Mullikan (1896-1986)
• Bonding electrons reside in Molecular Orbitals that
arise from the original atomic orbitals of the bonding
atoms.
• Bonding electrons are spread over the entire
molecule. (delocalized)
• Explains paramagnetism and electronic
spectroscopy in molecules.
*1s
1s
1s
1s
The Orbital Overlap Model of
Bonding
Overlap of two
s orbitals
In H2 a sigma
() covalent
bond that arises
from the
overlap of two
half filled s
orbitals, one
from each
atom.
A sigma bond is defined as a bond in which electron
density lies along the axis of the bond.
Sigma Bond Formation
Two s
orbitals
overlap
Overlap
of an s &
p orbital
Two p
orbitals
overlap
Valence Bond Theory
The main points of the valence bond approach to
bonding are:
• Orbitals overlap to form a bond between two atoms.
• Overlapping orbitals hold two electrons of opposite
spin. Usually, one electron is supplied by each of
the two bonded atoms.
• The bonding electrons are localized with a higher
probability of being found within a region of space
between the bonding nuclei. Both electrons are
simultaneously associated with both nuclei.
Valence Bond Terminology
Overlap:
two orbitals existing in the same region of space
lp:
lone pair of electrons (non-bonding)
bp:
bonding pair of electrons (result of orbital overlap)
Central atom: the atom of concern in a molecule
hybridization: the linear combination of atomic orbitals
hybrid orbital: bonding orbitals that arise from the mixing of AO’s.
-bond:
(sigma bond) overlap of orbitals along the bond axis
-bond:
(pi bond) overlap of orbitals above and below the bond
axis.
single bond:
one -bond
double bond: one -bond & one -bond
triple bond:
one -bond & two -bonds
Sigma (σ) Bonding
When bonding occurs along a bond axis, it is
referred to as a “sigma” bond: ()
X
:
Y
The electrons occupy space between the
nuclei.
Pi (π) Bonding
:
When bonding occurs above and below a bond
axis, it is referred to as a “pi” bond: ()
X
Y
The electrons occupy space above and below
the nuclei.
Sigma (σ) Bonding & Pi (π) Bonding
:
Sigma () bonding: When bonding occurs along a
bond axis, it is referred to as a “sigma” bond.
X
:
Y
Pi () bonding: When bonding occurs above and
below a bond axis, it is referred to as a “pi” bond.
A double bond is made up of a  and a  bond.
Hybridization of Atomic Orbitals
The simple model of atomic orbital
overlap in H2, HF and F2 breaks
down for more complicated
molecules.
Consider methane: VSEPR theory
predicts bond angles of 109.5°.
These angles can’t be achieved with
the s, px, py & pz orbitals of the
central carbon atoms.
Hybridization of Atomic Orbitals
In order to attain the needed geometry, the atomic orbitals
(AO’s) mix or hybridize to form new valence bond orbitals.
consider carbon as a
central atom in a
molecule:
 
2p

There are 4 valence
electrons:
2s
carbon
The valence orbitals
are the 2s & 2p’s
Hybridization of Atomic Orbitals
This hybridization determines by the electron pair geometry
for the central atom.
Each half-filled orbital is capable of
forming a covalent bond.
 
The new orbitals
2p
are called



carbon

2s

sp3
Valence
bond orbitals
carbon
The 4 valence electrons on carbon fill the orbitals by Hund’s
rule:
Hybridization of Atomic Orbitals
Bonding in methane involves the overlap of the new sp3
hybrid orbitals in carbon with the 1s orbitals in hydrogen.

2
p
Carbon
H


H

H

sp3 hybrid valence
bond orbitals.

2s
Each overlap contains two shared
electrons, one from each bonding nuclei.
Each overlap results in a –bond
H





Bonding in CH4
sp3 Hybridization
Since there are four sp3 hybrid orbitals, they must spread out to
form a tetrahedron about a central atom to minimize repulsion.
It follows then that an central atom that has a “tetrahedral”
EPG must have sp3 hybridization.
sp3 Hybridization
Water must also bond via sp3 hybrid valence bond
orbitals.
Bonding in a Tetrahedron Formation
of Hybrid Atomic Orbitals
4 C atom orbitals
hybridize to form
four equivalent sp3
hybrid atomic
orbitals.
Bonding in a Tetrahedron Formation
of Hybrid Atomic Orbitals
4 C atom orbitals
hybridize to form four
equivalent sp3 hybrid
atomic orbitals.
sp3 Hybridization
Conclusion:
When the central atom in a molecule has
combination of 4 total sigma (single) bonds and
lone pairs, the hybridization at the central atom
is sp3.
sp2 Hybridization
In order to attain the needed geometry, the atomic orbitals
(AO’s) mix or hybridize to form new valence bond orbitals.
The 2s & two of the 2p orbitals mix:
The new hybrid
obitals all have the
same energy:
2p
there is one
p-orbital left
over
sp2
The new orbitals are called sp2 Valence bond orbitals
sp2 Hybridization
sp2 Hybridization
The remaining p-orbital is perpendicular to the three sp2
valence bond orbitals that spread out in a plane.
sp2 Hybridization
Bonding in BF3
The atomic orbitals on the
central B-atom can’t
accommodate 3 bonds!
Bonding in BF3
The 1 s orbital and 2 p orbitals must
mix to form 3 new sp2 hybrid orbitals.
The 3 sp2 hybrid orbitals can now form sigma bonds
with each half-filled p-orbital on each fluorine atom.
This results in a “Trigonal Planar” molecular and
electron pair geometry.
sp2 Hybridization
Bonding in an sp2 hybridized atom is shown below:
Each of the three sp2 orbitals can form a -bond with
another atom.
Two of the orbitals
overlap along the
bond axis:
“end on” overlap
The left over p-orbital can form a -bond with another halffilled p-orbital.
“Sideways” overlap...
results in a -bond!
sp2 Hybridization
Bonding in an sp2 hybridized atom is shown below:
Each of the three sp2 orbitals can form a -bond with
another atom.
Two of the orbitals
overlap along the
bond axis:
“end on” overlap
The left over p-orbital can form a -bond with another halffilled p-orbital.
“Sideways” overlap...
results in a -bond!
sp2 Hybridization
An example of sp2 hybridization is given by C2H4 (ethene)



2p
Carbon




2p
sp2 hybrid valence
bond orbitals.
H
H
C
2s
H
C
H
Trigonal planar EPG
at each carbon: sp2
hybridizaton!
The left over p-orbitals on each carbon overlap to form the bond (second half of the double bond).
Each sp2 orbital can form a -bond, two with each of the H’s
and one with the other carbon.
An Example of sp2 Hybridization:
C2H4
Multiple Bonding in C2H4
 - Bonds in C2H4
-Bonding in C2H4
The unused p orbital on each C atom contains an
electron and this p orbital overlaps the p orbital
on the neighboring atom to form the π bond.
Consequences of Multiple Bonding
There is restricted rotation around C=C bond.
Consequences of Multiple Bonding
Restricted rotation around C=C bond.
Other Examples of Molecules with
sp2: CH2O
Conclusion: When a central atom has a trigonal planar electronic
geometry (EPG), it is most likely to bond through sp2 hybridization.
Compounds containing double bonds ( + ) most often have have
sp2 hybridization.
sp Hybridization
The sp orbitals spread out to form a linear geometry (directed away
from one another) leaving the p orbitals perpendicular to the
molecular axis.
The sp orbitals can form -bonds or hold lone pairs. The two porbitals can form the (2) -bonds in a triple bond.
An example of sp hybridization is given by C2H2 (acetylene)



2p

2s


Carbon

2p
sp hybrid valence bond
orbitals form.
sp Hybridization
Just as with sp2 hybridization, in sp hybridization, the left over
p-orbitals can form -bonds (in this case 2).
In acetylene (C2H2) there is a triple bond. (1 , 2 ’s)
 and  Bonding in C2H2
sp Hybridization
Other examples of molecules with sp hybridization are:
N2
:NN:
CN– (cyanide anion)
[:CN:]–
Conclusion: When a central atom has a linear electronic
geometry (EPG) with no lone pairs , it is most likely to bond
through sp hybridization.
Compounds containing triple bonds ( + 2) or adjacent
double bonds (CO2) have sp hybridization.
sp, sp2, & sp3 hybridization
Bonding in Glycine
Bonding in Glycine
Bonding in Glycine
Bonding in Glycine
Bonding in Glycine
Valence Bond Theory (2): Expanded
Valence
For elements beyond the second period, we found several
examples where the central atom in a Lewis structure had
greater than 8 electrons in the valence shell.
At n = 3
l=
0…
1…
2…
s-orbitals
p-orbitals
d-orbitals
We’ve seen that when four sp3 hybrid orbitals form, a central
atom can accommodate only up to 8 electrons in the valence
(bp & lp).
To place more electrons in the valence, we must bring the d–
orbitals into the “mix”.
Consider a Molecule Like PCl5
Phosphorous:valence electron configuration
of 3s23p3. (5 electrons)
Each of the five electrons forms a single bond
with a chlorine atom.
This means that central atom in the molecule needs 5 bonding
orbitals to achieve the trigonal bipyramidal electronic geometry.
This cannot happen with sp3
hybridization…

3p

3s

mix or
“hybridize”






sp3 hybrid valence
bond orbitals.
Valence Bond Theory (2): Expanded
Valence
The only way to produce 5 half-filled orbitals on phosphorous
is by adding a fifth atomic orbital…
3d
3d




3p

3s
mix the 3s, the
three 3p and one
3d




new sp3d hybrid valence
bond orbitals
Each of these half–filled sp3d
orbitals can form a –bond with a
chlorine atom in PCl5.
Additional example of sp3d hybrid
molecules:
SF4 (sulfur tetrafluoride)
EPG: Trigonal Bipyramidal
MG: See Saw
ClF3 (chlorine trifluoride)
EPG: Trigonal Bipyramidal
MG: T-shape
Valence Bond Theory (2): Expanded
Valence
What about molecules with 12 electrons in the valence?
In order to achieve an expanded valence that can hold six electron
pairs (bp & lp) we need to form 6 new hybrid orbitals.
This requires the mixing of an s, three p’s and two d–atomic orbitals.
3d
3d
3p
mix the 3s, the
three 3p and two
3d’s
3s
new sp3d2 hybrid valence
bond orbitals
sp3d2 Hybridization: SF6
3d
3d




3p

3s
sulfur
mix the 3s, the
three 3p and two
3d’s





six new sp3d2 hybrid
valence bond orbitals
Each of these half–filled
sp3d2 orbitals can form a
–bond with a fluorine
atom.
sp3d2 Hybridization: SF6
Sulfur has a valence electron configuration of 3s23p4
(6 electrons).
Each of the six electrons forms a single bond with a
fluorine atom forming an octahedral MG and EPG.
The bonding can be described in terms of sp3d2
hybrid orbitals.
SF6
Predicting Hybridization
1. Start by drawing the Lewis structure (check
formal charges)
2. Use VSEPR theory the electron group
geometry about the central atom.
3. Relate the central atom electron group
geometry to the corresponding hybridization.
4. Identify and label the orbital overlap in each
bond.
5. Label the bonds with  and  bonds.
Hybridization Practice
• Indicate the central atom hybridization for the
following.
XeF4
CH2O
BrF5
SF6
Br3
Additional Examples of sp3d2
BrF5 (bromine pentafluoride)
EPG: octahedral
MG: Square Pyramidal
XeF4 (xenon tetra fluoride)
EPG: octahedral
MG: Square Planar
Conclusion: Molecules with an octahedral EPG have sp3d2
hybridization at the central atom.
Molecular Orbital Theory
• Molecular Orbital Theory (MO) approaches
bonding between atoms from a different approach
than Valence Bond Theory.
• In Valence Bond theory, the atomic orbitals of a
bonding atom mix or hybridize to form localized
bonds that take on the EPG’s predicted by VSEPR
theory.
• In MO theory, the atomic orbitals are treated like
waves that constructively or destructively add to
form new Molecular Orbitals.
• The electrons of the molecule are distributed over
the entire molecule as a whole. (delocalized)
Molecular Orbital Theory
• Molecular Orbital Theory has several advantages
and differences over VESPR & VB theory:
• MO does a good job of predicting electron pair
spectra and paramagnetism, where VSEPR and the
VB theories don't.
• MO theory like VB theory, predicts the bond order of
molecules, however it does not need resonance
structures to describe molecules.
• The main drawback to our discussion of MO theory
is that we are limited to talking about diatomic
molecules (molecules that have only two atoms
bonded together), or the theory gets very complex.
MO Theory: Considered Hydrogen
When two wave functions (orbitals) on different atoms add
constructively they produce a new MO that promotes bonding
given by:
new Molecular Orbital
atomic orbitals
(1s)H(1) + (1s)H(2)
when two waves add,
the amplitude increases:
“constructive
interference”
+

H-H
=
increased amplitude
MO Theory: Considered Hydrogen
When two wave functions (orbitals) on different atoms add
destructively they produce a new MO that decreases bonding
given by:
atomic orbitals
new Molecular Orbital
(1s)H(1)  (1s)H(2)
when two waves subtract,
the amplitude decreases:
“destructive
interference”
+
*H-H
=
no amplitude
(a node)
Molecular Orbital Theory
Consider hydrogen atoms combining to form H2.
The individual 1s atomic orbitals combine.
When they add, a lower energy -bonding MO forms.
When they subtract, a higher energy *-antibonding MO forms
Molecular Orbital Theory
• Bonding and antibonding sigma MO’s are
formed from 1s orbitals on adjacent atoms.
Molecular Orbital Diagrams
Energy
Molecular orbitals result when atomic orbitals on bonding
atoms constructively and destructively combine:
s1s*
1s
1s
s1s
When they add, lower energy bonding Molecular Orbitals
(MO’s) form, when they subtract, higher energy anti-bonding
MO’s form.
Anti-bonding orbitals are designated by an asterisk (*) called a
star.
Molecular Orbital Diagrams
Once again we consider the simplest
molecule, H2.
When two hydrogen atoms combine the
1s orbitals on each can add or subtract

to form a 1s bonding or *1s
1s
anti-bonding orbital.
H-atom
*1s


1s
H-atom
1s
Each H-atom has one 1s electron that can contribute to the
MO bonding and anti-bonding MO’s.
Just as in the electron configurations of atoms, the electron fill
from the lowest energy MO first (Aufbau principle) only
pairing when forced to (Hund’s rule). Each MO can only hold
two electrons of opposite spin (Pauli principle)
Bond Order in Molecular Orbital
# of Bonding electrons - # antibonding electrons
BO =
2
• Electrons in bonding molecular orbitals add
stability.
• Electrons in anti-bonding molecular orbitals
reduce stability.
Bond Order: The Bonding in H2 is
described by…
0 electrons in an anti-bonding MO
*1s
1s
H-atom

1s
H-atom
1s
2 electrons in a bonding MO
# of Bonding electrons - # antibonding electrons
BO =
2
2-0
=
=1
2
Bond Order = 1 (single bond)
2
(
s
)
MO electron configuration of:
1s
One also sees that the molecule (H2) is diamagnetic
(no unpaired electrons)
Excited States
*1s
What happens to a H2 molecule
if one of the electrons is excited
to the anti-bonding orbital?
1s
H-atom

2-0
Original BO =
=1
2

1s
1s
H-atom
ground state H2
*1s
1s

1s
The molecule falls
1- 1
New BO =
= 0 apart!
1s
excited state H2
2
Photodissociation
Why Doesn’t He2 Exist?

*1s
electrons in AO’s
fill the MO’s
He: 1s2
1s

1s
1s
2-2
BO =
=0
2
Molecular Orbital theory
predicts that the molecule
is unstable!
Sigma Bonding from p-Orbitals
Molecular Orbitals from Atomic pOrbitals
Sideways overlap of atomic 2p orbitals that lie in the same
direction in space give bonding and antibonding MOs.
The MO Correlation Diagram for the
2p Atomic Orbitals
The three 2p orbitals on each side combine to form
six new Molecular Orbitals that can accommodate up
to 12 electrons.
*
s 2p
p*2p
2p
2p
s 2p
p2p
The two  2p and the
two  2* p are degenerate.
This configuration is seen for B, C and N only…
The MO Correlation Diagram for the
2p Atomic Orbitals
The three 2p orbitals on each side combine to form
six new Molecular Orbitals that can accommodate up
to 12 electrons.
*
s 2p
p*2p
2p
2p
p2p
s 2p
This configuration is seen for O and F only…
The overall MO diagram for the
1s, 2s and 2p orbitals:
2p
MO’s
2s
MO’s
1s
MO’s
*1s
1s
Bonding in O2
Since the 1s and 2s MO’s are full, they do not contribute any
net bonding Any net bonding will be determined by the 2p
MO’s.
s*2p
Each O–atom has four 2p
electrons:



p*2p


2p
2p
O - atom

p2p
O - atom
s 2p
The electrons fill the MO’s fill by the Aufbau principle and Hund’s
rule.
Bonding in O2
Since the 1s and 2s MO’s are full, they do not contribute any
net bonding Any net bonding will be determined by the 2p
MO’s.
s*2p
Each O–atom has four 2p
electrons:


p*2p
2p
2p

p2p

O - atom




O - atom
s 2p
The electrons fill the MO’s fill by the Aufbau principle and Hund’s
rule
Bonding in O2
BO =
6-2
=2
2
double bond
This agrees with the Lewis dot structure:
O=O
s*2p


p*2p
2p
2p

p2p





O - atom
s 2p
O - atom
However, VB theory did not
tell us that the molecule is
paramagnetic!
The Paramagnetism of O2
(a) Making liquid O2.
(b) Liquid O2 is a light blue color.
(c) Paramagnetic liquid O2 clings to a magnet.
(d) Diamagnetic liquid N2 is not attracted to a
magnet.