Homework Problems
Chapter 9 Homework Problem: 4, 7, 10, 16, 20, 22, 28, 30, 36, 40, 52,
56, 66, 81, 84, 92, 104, 107
CHAPTER 9
Chemical Bonding II: Molecular
Geometry and Bonding Theories
Shapes of Molecules and Ions
Molecules and ions have a three dimensional shape. This shape
can be important in determining the chemical behavior of a substance.
We will discuss two types of geometries:
1) electron domain geometry - The arrangement of electron
containing regions about a central atom. This is sometimes called
electron cloud geometry.
2) molecular geometry - The arrangement of atoms about a
central atom.
The number of electron containing regions about a central atom is
equal to the number of lone pair regions + the number of covalent bonds.
Note that in counting electron containing regions a single, double, or
triple bond counts as one region.
Examples of Counting Electron Containing Regions
How many electron containing regions are
there for central atoms in each of the molecules at left?
N 3 regions (two bonds, one lone pair)
C 3 regions (three bonds, no lone pairs)
C at left 4 regions (four covalent bonds)
C at right 3 regions (three covalent bonds)
Note the bond order does not matter in
counting electron containing regions.
VSEPR Theory
We may predict both electron cloud geometry and molecular
geometry using VSEPR (Valence Shell - Electron Pair Repulsion) theory.
The idea behind this theory is that electron containing regions will
arrange themselves about a central atom in such a way as to put those
regions as far apart as possible. This is due to the repulsive force
existing between particles of the same charge (in this case electrons).
The various common cases for electron and molecular geometry
are given in Figure 9.2 (page 368) or Table 9.2 (page 369).
Two Regions
If we have two electron containing regions around a central atom,
then placing them opposite one another keeps them as far apart as
possible.
In this case, both the electron geometry and the molecular
geometry are linear.
Three Regions
For three regions about a central atom the electron geometry is
trigonal planar (120 angle between the regions). There are two possible
molecular geometries:
If all three regions are bonds - trigonal planar
If two of the three regions are bonds, and one is a lone pair of
electrons - nonlinear (bent)
Four Regions
For four regions about a central atom the electron geometry is
tetrahedral (109 angle between the regions). There are three possible
molecular geometries:
4 bonds - tetrahedral
3 bonds - trigonal pyramid
2 bonds - nonlinear (bent)
Five Regions
For five regions about a central atom the electron geometry is
trigonal bipyramid. In this case not all of the angles between electron
containing regions are the same. Instead, we may divide the regions into
equitorial regions and axial regions.
Five Regions
There are four possible molecular geometries:
5 bonds - trigonal bipyramid
3 bonds - T-shape
4 bonds - “see-saw”
2 bonds - linear
Six Regions
For six regions about a central atom the electron geometry is
octahedral. The bond angles between adjacent regions are all 90.
Six Regions
There are three common molecular geometries:
6 bonds - octahedral
5 bonds - square pyramid
4 bonds - square planar
Example: What are the electron geometries and molecular geometries
around the central atom in BrF3, POCl3, and H2SO3?
Example: What are the electron geometries and molecular geometries
around the central atom in BrF3, POCl3, and H2SO3?
BrF3
5 regions, so electron cloud geometry is trigonal bipyramid.
3 bonds, so molecular geometry is T-shape.
POCl3 4 regions, so electron cloud geometry is tetrahedral.
4 bonds, so molecular geometry is also tetrahedral.
H2SO3 4 regions, so electron cloud geometry is tetrahedral.
3 bonds, so molecular geometry is trigonal pyramid.
Summary
electron cloud
bonds
regions
electron
molecular
geometry
geometry
2
2
linear
linear
3
3
trigonal planar
trigonal planar
2
4
4
nonlinear (bent)
tetrahedral
tetrahedral
3
trigonal pyramid
2
nonlinear (bent)
Summary
electron cloud
bonds
regions
5
6
5
electron
molecular
geometry
geometry
trig. bipyramid
trig. bipyramid
4
see-saw
3
T-shape
2
linear
6
octahedral
octahedral
5
square pyramid
4
square planar
Geometry in Large Molecules
For large molecules we can discuss the electron cloud and
molecular geometry around each one of the interior atoms.
Example: Give the electron cloud and molecular geometry for
each interior atom in the molecule glycine (NH2CH2COOH).
Example: Give the electron and molecular geometry for each
interior atom in the molecule glycine (NH2CH2COOH).
Atom
electron geometry
N atom
tetrahedral
Left C atom
tetrahedral
molecular geometry
trigonal pyramid
tetrahedral
Right C atom trigonal planar
trigonal planar
O atom
nonlinear (bent)
tetrahedral
Deviations From “Pure” Geometries
We have assumed that the angles observed in molecular
geometries do not depend on how many bonds and lone pair regions
there are. In fact, the number of regions containing lone pair electrons
has a small effect on the observed bond angles.
In general we may say the repulsive forces between electron
containing regions in a molecule or ion are stronger for lone pair
electrons than for bonding electrons. So
lone pair - lone pair >
lone pair - bonding >
bonding - bonding
This is due to the fact that bonding electrons are more localized than lone
pair electrons, as they must appear between bonded atoms.
In the molecules at left (all of which have
four electron containing regions around a central
atom) the bond angle decreases from 109.5  in
CH4 (pure tetrahedral geometry) to 107.0  in NH3
to 104.5  in H2O.
In CH2O (below) all of the bond angles
would be 120. ° in pure trigonal planar geometry.
Representing Three Dimensional Structure
Molecules have a three dimensional structure. We need a
systematic method for representing these structures in two dimensions.
We do this as follows
For convenience, we will sometimes used a dashed line to replace the
hatched wedge for a bond going into the page.
Example: Give the three dimensional structures for CH3Cl and PF5.
Example: Give the three dimensional structures for CH3Cl and PF5.
CH3Cl
PF5
tetrahedral
trigonal bipyramid
Polar Molecule
A polar molecule is a molecule where the center of positive and
negative charge do not coincide. Two things are required for a molecule
to be polar
1) The molecule must have at least one polar bond.
2) The contributions from the polar bonds cannot cancel.
For a polar covalent bond the difference in electronegativity
between the bonded atoms should be about 0.5 or greater. This means
that carbon-carbon bonds are completely nonpolar, and carbon-hydrogen
bonds are only slightly polar.
EN(C) = 2.5
EN(H) = 2.1
The table of electronegativities and the molecular geometry for
the molecule can be used to determine whether the molecule is polar or
nonpolar.
The polarity of a molecule is expressed in terms of the dipole
moment of the molecule. The symbol for dipole moment is . Dipole
moments are measured in units of Debye (D).
Example
Consider the following molecules: H2O, CF4, NH3, and
CH3COCH3. Which of these molecules is expected to have a permanent
dipole moment?
H2O  = 1.85 D
CF4  = 0. D
NH3  = 1.47 D
CH3COCH3  = 2.88 D
EN Values: H = 2.1; C = 2.5; N = 3.0; O = 3.5; F = 4.0
1 Debye = 3.336 x 10-30 C.m
Theories For Molecular Bonding
The Lewis dot structure method predates quantum mechanics.
While it is a good qualitative description of covalent bonding it fails to
work well in some cases (resonance structures are one example).
There are two general methods that use quantum mechanics to
improve on the Lewis dot structure method:
Valence Bond theory - Discusses bond formation in terms of
overlap of atomic orbitals (often hybrid orbitals).
Molecular Orbital theory - Uses quantum mechanics to solve the
Schrodinger equation for a molecule or ion. This is a very mathematical
approach.
Valence Bond Theory For H2
In valence bond theory bond formation is pictured as occurring
due to the overlap of atomic orbitals of the atoms that are bonded
together. Each of the orbitals contains one electron. When the orbitals
overlap, the electron from each atomic orbital is shared by the two atoms.
Notice the electrons need to be opposite spin.
The covalent bond forms from the overlap of the two 1s atomic orbitals
of the hydrogen atoms that are bonded together. This places the
electrons between the two hydrogen nuclei, which holds the molecule
together.
Bond Formation and Energy
The formation of a covalent bond between two atoms occurs
because it leads to a lower energy than exists for separate atoms. This
can be seen in the bonding of two H atoms to form an H2 molecule.
Shortcoming of Simple Valence Bond Theory
The above picture breaks down when you need to form several
different valence bonds for the same atom out of orbitals of different
types.
Example: Be in BeH2
Be 1s2 2s2
H 1s1
We want the beryllium atom to contribute one electron to each bond
between Be and an H atom, but the 2s orbital of beryllium is full, with no
unpaired electron.
So what do we do?
Hybrid Orbitals
In this case, before we form the valence bonds we first construct
a new set of equivalent orbitals, called hybrid orbitals (in this case sp
hybrid orbitals).
We can envision the process taking place as indicated below.
While the process of forming hybrid orbitals raises the energy of the
electrons in Be, this is more than made up for when the two Be - H bonds
are formed.
Formation of sp Hybrid Orbitals
The sp hybrid orbitals are formed from combinations of the s and
px atomic orbitals. Since we begin with two atomic orbitals, we end up
with two hybrid orbitals.
Use of sp Hybrid Orbitals For Bonding (BeH2)
The two sp hybrid orbitals formed in Be can now be used to form
the two Be - H valence bonds.
sp3 Hybrid Orbitals
In methane (CH4) we need the central carbon atom to have four
equivalent hybrid orbitals to form the four C - H bonds. This is done
using sp3 hybridization.
CH4.
C: 1s2 2s2 2p2
As before, we start by “unpairing” the electrons in the carbon atom by
promoting one electron from a 2s to a 2p orbital
__
__ __ __
2s
2p
promote
__
__ __ __
2s
2p
sp3 Hybrid Orbitals (Continued)
Now that we have one electron in our 2s atomic orbital, and in
each of the three 2p atomic orbitals, we combine the four orbitals to form
our set of four sp3 hybrid orbitals.
Since we began with four atomic orbitals, we end up with four
hybrid orbitals.
These sp3 hybrid orbitals can now be used to form valence bonds
or to hold lone pairs of electrons.
Naming and Use of Hybrid Orbitals
We name hybrid orbitals by listing the type of atomic orbitals
used to construct the hybrid orbitals (s, p, or d). If we use more than one
of a particular type of orbital, we indicate the number of orbitals used by
a superscript to the right of the symbol for the orbital.
There is a simple relationship between the number of electron
containing regions around a central atom and the type of hybrid orbitals
that are required.
Number of regions
2
Hybrid orbitals
sp
Electron geometry
linear
3
sp2
trigonal planar
4
sp3
tetrahedral
5*
sp3d
trigonal bipyramid
6*
sp3d2
octahedral
* Not possible for atoms from 2nd row of periodic table
Why PF5 Exists and NF5 Does Not
We can now return to an observation we made in the last chapter,
that in looking at molecules made from a group 5 nonmetal and fluorine
the molecule PF5 exists, but NF5 does not. We can see why this is the
case by looking at the hybridization required for the central atom in these
two molecules.
N [He] 2s2 2p3
P [Ne] 3s2 3p3 3d0
promote
__
__ __ __ __ __ __ __ __
__ __ __ __ __ __ __ __ __
3s
3p
3d
Hybridize to get 5 sp3d hybrid orbitals. This is not possible for nitrogen
because there are no 2d orbitals, and so hybrid orbitals requiring use of
one or more d orbitals cannot be formed.
Appearance of Hybrid Orbitals
Each particular type of hybrid orbital has its own geometry,
which in all cases corresponds to the geometries predicted using VSEPR
theory.
Also notice that in all cases the number of atomic orbitals we begin with
is equal to the number of hybrid orbitals we end up with.
Sigma () and Pi () Bonds
The above description works well for single bonds between
atoms. However, when we have a multiple bond (double or triple bond),
the bonds can be divided into two types:
sigma bond - Formed from the overlap of atomic or hybrid
orbitals; places electrons directly between the bonded atoms.
pi bond - Formed from the overlap of p type atomic orbitals;
places electrons above and below the region between the bonded atoms.
In general, a single bond will always be a sigma bond. For a
multiple bond, one of the bonds will be a sigma bond and the other bonds
will be pi bonds.
Example: C2H4 (ethene) (C atoms are sp2 hybridization)
Summary
Total number
bonds
Number of
sigma bonds
Number of
pi bonds
1
1
0
2
1
1
3
1
2
So the first bond is always a sigma bond, while any additional
bonds are pi bonds.
Example
How many sigma bonds and how many pi bonds are present in
the molecule shown below?
How many sigma bonds and how many pi bonds are present in
the molecule shown below?
There are seven sigma bonds.
There are two pi bonds.
Pi Bonds and Free Rotation
Because pi bonds are formed from the overlap of p orbitals,
molecules that contain pi bonds (molecules with double or triple bonds)
cannot rotate freely around those bonds, since to do so would mean
breaking one or more pi bond.
In ethane (C2H6) rotation around the C - C bond does not affect the bond
and so is allowed. In ethene (C2H4) rotation around the C = C bond
breaks the pi bond, and so will not occur (except at high energy).
Molecular Orbital Theory
In molecular orbital theory we solve the Schrodinger equation to
find information about molecules (energies, geometries, electron
distribution, and so forth). Just as we find atomic orbitals for atoms, we
find molecular orbitals for molecules or ions. This is a very
mathematical theory, and so we will only discuss simple cases in a
nonmathematical way.
The usual way people do MO theory is called the LCAO-MO
method. In this method, linear combinations of atomic orbitals are used
to construct molecular orbitals. We also focus on the valence electrons,
and generally ignore core electrons.
Molecular Orbital Theory for H2
For H2, we begin with the two 1s atomic orbitals on the two H
atoms. There are two ways in which these can be combined, corresponding to two molecular orbitals. One molecular orbital lowers the
energy and therefore corresponds to a  bonding orbital, while the other
molecular orbital raises the energy and therefore corresponds to a *
antibonding orbital (note we use a * to indicate an antibonding orbital).
We often also indicate the starting atomic orbitals.
1s atomic orbitals
1s MO
*1s MO
MO Diagram
In a molecular orbital diagram we indicate the starting atomic
orbitals and the molecular orbitals made from them with the correct
relative energies.
The above diagram represents the MO picture for the H2 molecule. As is
the case for atoms, we can give an electron configuration for molecules
as well. For the above we have H2: (1s)2
Rules for Adding Electrons
The rules for filling molecular orbitals are the same as filling
atomic orbitals. They are:
Pauli principle.
Aufbau principle
Hund’s rule
Just as for atoms, we can write electron configurations for
molecules by listing the occupied orbitals in order of energy, and
indicating the number of electrons in an orbital by a superscript to the
right of the orbital name. We usually place each orbital in parentheses.
Example
H2 molecule
So
H2- ion
H2
(1s)2
H2-
(1s)2 (1s*)1
He2
(1s)2 (1s*)2
He2 “molecule”
Bond Order
We may define the bond order (BO) as follows
BO = (# bonding e-) - (# antibonding e-)
2
The higher the bond order the stronger the bond. Note that fractional
bond orders are possible.
H2
(1s)2
BO = 1
H2-
(1s)2 (1s*)1
BO = 1/2
He2
(1s)2 (1s*)2
BO = 0
If the bond order is zero, then we don’t expect the molecule or ion to be
stable.
Period 2 Homonuclear Diatomics
We may apply the above procedure to the period 2 homonuclear
diatomic molecules and ions. Note that we only look at he molecular
orbitals involving atomic orbitals in the valence shell.
The 2s atomic orbitals present in the valence shell of second row
atoms can be used to form a bonding and an antibonding sigma orbital,
as was the case with the 1s atomic orbitals.
*2s
2s
2s
2s
AO
MO
AO
Molecular Orbitals From 2p
Atomic Orbitals
The 2p atomic orbitals present in second row atoms can be used
to form two types of molecular orbitals - sigma orbitals (bonding and
antibonding) and pi orbitals (bonding and antibonding).
*2p
*2p
2p
2p
2p
2p
AO
MO
AO
Formation of  Molecular Orbitals
From px Atomic Orbitals
Formation of  Molecular Orbitals
From py and pz Atomic Orbitals
Period 2 Homonuclear Diatomics
The molecular orbitals formed from the 2s and 2p atomic orbitals
of second period atoms are shown below. The order of these orbitals in
terms of energy depends on the particular type of homonuclear diatomic
species being discussed.
Order for Li2 to N2
Order for O2, F2
Example: Give the electron configuration and bond order for C2, C2+,
and C2-.
C2 (8 e-)
(2s)2 (2s*)2 (2p)4
BO = (6-2)/2 = 2
C2+ (7 e-)
(2s)2 (2s*)2 (2p)3
BO = (5-2)/2 = 1 1/2
C2- (9 e-)
(2s)2 (2s*)2 (2p)4 (2p)1
BO = (7-2)/2 = 2 1/2
MOs For Period 2 Homonuclear Diatomics
Summary of Bonding Theories
Lewis theory - Simple to use, useful in making qualitative
predictions about bond lengths and bond strengths. Not directly useful
for three dimensional structure of molecules, sometimes makes incorrect
predictions concerning bond order, unpaired electron spins. Difficulties
in use for some molecules (requiring resonance structures).
VSEPR- Based on Lewis theory, and allows predictions of
molecular geometries. However, some of the same weaknesses of Lewis
theory.
Valence Bond theory (with hybridization) - Explains the
formation of covalent bonds in more detail than Lewis theory, and also
why atoms in the third row and below can violate the octet rule. Fails in
the prediction of some properties of molecules, such as paramagnetism in
O2.
Molecular Orbital theory - Most rigorous theory for molecules,
but also the most complicated and mathematical theory. Difficult to
apply in a simple way for large molecules.
Multicenter Pi Bonding
We may combine valence bond theory and MO theory to account
for resonance structures in terms of multicenter pi bonds, that is, pi
bonds among more than two atoms.
NO2- 24 valence electrons (and so 4 covalent bonds)
When there are resonance structures that is usually evidence that
the bonding needs to be described in terms of multicentered pi bonds. A
correct description of bonding in this case requires use of both valence
bond theory and molecular orbital theory.
Formation of Sigma Bonds
The N atom and three O atoms can
each form sp2 hybrid orbitals. These form
the N - O sigma bonds, and also contain
two sets of lone pair electrons for each
oxygen atom.
Formation of Multicenter Pi Bonds
The remaining p orbitals on each
atom that are perpendicular to the plane of
the molecule can be used to form a final,
multicentered pi bond, along with two other
multicentered molecular orbitals (not
shown) for the additional two sets of lone
pair electrons.
antibonding MO
4 pz
lone pair MOs
bonding MOs (multicentered
pi bond)
Benzene
Benzene (C6H6) is an important example of a molecule that gains
stability due to the presence of multicentered pi bonds.
End of Chapter 9
“Physicists are notoriously scornful of scientists from other
fields. When the wife of the great Austrian physicist Wolfgang Pauli left
him for a chemist, he was staggered with disbelief. ‘Had she taken a
bullfighter I would have understood,’ he remarked in wonder to a friend.
‘But a chemist…’” Bill Bryson, A Short History of Nearly Everything
“The physicist's greatest tool is his wastebasket.”
- Albert Einstein
“Hofstadter's law: It always takes longer than you expect, even
when you take into account Hofstadter's law.” - Douglas Hofstadter
“Love hides in molecular structures.” - Jim Morrison