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Chemical Bonding II
Valence Bond &
Molecular Orbital
Theory
Valence Bond Theory
Orbital Overlap in Chemical Bonds
Bonding Theories Hybridization
The Valence Shell Electron Pair Repulsion
approach works very well for many covalent
compounds. It can be used to predict molecular
shape, bond angles and molecular polarity.
Several bonding theories have been
developed to explain how the central atom
rearranges its orbitals to minimize electronic
repulsion.
Bonding Theories Hybridization
One of the simpler approaches involves
hybridization, or the mixing of the atomic orbitals
on the central atom.
When orbitals hybridize, the properties of
the resulting hybridized orbitals are a mixture of
the properties of the original orbitals that were
mixed together.
Hybridization
Bonding Theories Hybridization
The compounds of carbon will be used for
illustration.
Methane, CH4, has four equivalent bonds
which point towards the corners of a
tetrahedron. Theorists have shown that the
mixing of the 2s, 2px, 2py, and 2pz orbitals on
carbon will produce four equivalent hybrid
orbitals that are 109.5o apart.
Bonding Theories Hybridization
Since the hybrid orbitals result from mixing
an s orbital with three p orbitals ( the 2px, 2py
and 2pz ), the hybrid orbitals that result are
called sp3 hybrid orbitals.
Bonding Theories Hybridization
When orbitals are mixed, a hybrid orbital is
formed for each atomic orbital that is
hybridized. In methane, a total of four atomic
orbitals on carbon (2s, 2px, 2py and 2pz)
produces four equivalent sp3 hybrid orbitals.
Bonding Theories Hybridization
Bonding Theories Hybridization
Four equivalent
bonds are formed
with hydrogen to
form a tetrahedral
molecule.
Hybridization of Methane
Hybridization of Methane
The hybridization of the orbitals on carbon
accounts for the bond angles of the bonds in
methane. However, atomic carbon has only two
unpaired electrons, and would not be expected
to make four bonds.
↓ 2p   _
C: 1s2, 2s2, 2p2 =[He] 2s_
Hybridization of Methane
Scientists
proposed
that an
electron
from the 2s
level is
promoted
up to the
2p level.
Hybridization of Methane
The carbon
atom can
now make
four bonds
instead of
two.
Hybridization of Methane
Hybridization of
the 2s and 2p
orbitals produces
four equivalent
hybrid orbitals.
Hybridization of Methane
Although the
promotion of an
electron and the
mixing of orbitals
requires energy,
there is a net release
of energy since four
bonds are made,
and repulsions are
minimized.
Sigma Bonds
The bonds between carbon and hydrogen in
methane puts electron density on the line
connecting the nuclei of the atoms. This type of
bond is called a σ (sigma) bond.
All covalent molecules contain σ bonds.
3
sp
Hybridization
Molecules such as
water or ammonia
are also sp3
hybridized, with
hybrid orbitals used
for the bonds and
any lone pairs of
electrons.
Hybridization
Trigonal planar geometry results when an s
orbital is mixed with two p orbitals. If the
molecule is in the xy plane, the px and py orbitals
are mixed with an s orbital to form three sp2
hybrid orbitals. The pz orbital remains
unchanged, and can be used for making multiple
bonds.
Hybridization
Hybridization
Hybridization
The energy level diagram shows the mixing of
orbitals, with the pz orbital remaining
unchanged.
↑ ↑ ↑
↑
↑
↑
↑ ↑
Hybridization
The orbitals on
the central atom
show trigonal
planar geometry,
with the pz orbital
perpendicular to
the molecular
plane.
z
xy plane
Hybridization
In ethylene, H2C=CH2, the sp2 orbitals are
used to make one of the bonds between the
carbon atoms and the bonds between carbon
and hydrogen.
These bonds have electron density along the
internuclear (bond) axis. This type of bond is
called a σ (sigma) bond.
The σ Bonds of Ethylene
Hybridization
There are
unhybridized pz
orbitals on each of
the carbon atoms,
and they each contain
an electron. A
second bond forms
between the carbon
atoms.
pz orbitals
The  Bond of Ethylene
Bonds resulting from
side-by-side overlap
are called π (pi)
bonds. The electrons
in the π bond are
found above and
below the line
connecting the two
carbon nuclei.
The  Bond of Ethylene
Even though there
are two overlapping
lobes (one above the
molecular plane and
one below it), this is
only one π bond, as it
involves the sharing
of only one pair of
electrons.
σ and π Bonding
Hybridization
The Bonding of Ethylene
sp Hybridization
Molecules in which the central atom has two
atoms attached to it (and no lone pairs of
electrons) undergo sp hybridization.
Acetylene, HCCH, has a triple bond between
the carbon atoms.
H-C=C-H
sp Hybridization
The shape of the molecule is linear around
each carbon atom. The σ bonds between the
carbons and between carbon and hydrogen
result from the mixing of an s and p orbital on
carbon.
The result is two sp hybrid orbitals on each
carbon.
sp Hybridization
If the molecule lies along the x axis, the px
orbital on each carbon atom will be used in
hybridization. This leaves the py and pz orbitals
available for π bonding.
sp Hybridization
sp Hybridization
z
x
x
y
sp Hybridization
The σ bond between
the carbon atoms
arises from overlap of
the sp orbitals. The
bonds with the
hydrogen atoms use
the other sp hybrid
orbital on each
carbon atom.
sp Hybridization
There are two p orbitals (the py and pz) on each
carbon atom. These are used to make two π
bonds between the carbons.
↑ ↑
↑
↑
↑
↑
↑
↑
The Bonding in Acetylene
The result is a σ bond along the C-C bond
axis, and two π bonds which are perpendicular
to each other.
pz orbitals
py orbitals
The Bonding in Acetylene
The result is a σ bond along the C-C bond
axis, and two π bonds which are perpendicular
to each other.
sp Hybridization
The end result is a carbon-carbon triple bond.
H
C
C
H
The σ bonds are shown in yellow, and the π
bonds are shown in red.
3
dsp
Hybridization
Central atoms with a total of 5 atoms and lone
pairs form trigonal bipyramidal structures.
3
dsp
Hybridization
The central atom must be in the third period or
below, since d orbitals are used to make five
dsp3 or (sp3d) hybrid orbitals.
2
3
d sp
Central atoms
with a total of 6
atoms and
electron pairs
form octahedral
shapes.
Hybridization
2
3
d sp
The hybridization
is d2sp3 (or sp3d2),
producing six
hybrid orbitals
that point toward
the corners of an
octahedron.
Hybridization
Molecular Orbital
Theory
Molecular Orbital Theory
Valence Bond theory fails to fully explain the
bonding in fairly simple molecules. These
include molecules or ions with resonance. It
also fails to fully explain the bonding of oxygen.
Bonding of Oxygen
Oxygen had a double bond which is
predicted by the valence bond approach.
: :
: :
O=O
However, O2 is paramagnetic, and contains 2
unpaired electrons. The valence bond approach
cannot explain the paramagnetism of oxygen.
Molecular Orbital Theory
Molecular orbital theory views bonds as
resulting from the interaction of the wave
functions on individual atoms. The waves can
interact constructively or destructively.
The resulting molecular orbitals belong to
the entire molecule, and are not viewed as
localized electron pairs.
Molecular Orbital Theory
The bonding orbital
results in increased
electron density
between the two nuclei,
and is of lower energy
than the two separate
atomic orbitals.
Molecular Orbital Theory
The antibonding
orbital results in a node
between the two nuclei,
and is of greater energy
than the two separate
atomic orbitals.
Molecular Orbital Theory
Molecular Orbital Theory
+
-
+
+
-
+
The signs on the molecular orbitals indicate the
sign of the wave function, not ionic charge.
Molecular Orbital Theory
For hydrogen, the
result is an energy level
diagram with the
bonding orbital
occupied by a pair of
electrons. The filling
of the lower molecular
orbital indicates that
the molecule is stable
compared to the two
individual atoms.
Rules for Combining Atomic
Orbitals
1.
2.
The number of molecular orbitals = the
number of atomic orbitals combined.
The strength of the bond depends upon the
degree of orbital overlap.
Orbital Overlap
In order to overlap and form molecular
orbitals, the atomic orbitals must have:
1. Proper symmetry to overlap
2. Comparable energies: The closer the two
orbitals are in energy, the lower the energy of
the bonding orbital, and the higher in energy the
antibonding orbital.
Period 2 Diatomic Molecules
For the second period, assume that, due to a
better energy match, s orbitals combine with s
orbitals, and p orbitals combine with p orbitals.
The symmetry of p orbitals permits end-onend overlap along the bond axis, or side-by-side
overlap around, but not along, the internuclear
axis.
MOs using p orbitals
+ -
-
-
+
+
-
With the x axis as the bond axis, the px
orbitals may combine constructively or
destructively. The result is a σ bonding orbital
and a σ anti-bonding orbital.
MOs using p orbitals
+ -
+
-
+ -
-
The designation σ indicates symmetric
electron density around the internuclear (x) axis.
The + and – signs indicate the sign of the wave
function, and not electrical charges.
π Molecular Orbitals
+
-
+
+
side-by-side
overlap
-
p orbitals can also overlap side-by-side.
Symmetry requires that the py orbital on one atom
combines with the py orbital on the other atom.
Similar overlap occurs between pz orbitals.
π Molecular Orbitals
+
-
+
+
side-by-side
overlap
-
The orbital overlap side-by-side is less than
that of overlap along the bond axis (end-on-end).
As a result, the π bonding orbital will be higher in
energy than the σ bond formed by the px orbitals.
π Molecular Orbitals
+
-
+
+
side-by-side
overlap
-
π orbitals have electron density surrounding
the bond axis, with a node along the internuclear
axis.
Molecular Orbital Diagram
This is a molecular
orbital energy level
diagram for the p
orbitals. Note that the
σ bonding orbital is
lowest in energy due to
the greater overlap
end-on-end.
2p
2p
Molecular Orbital Diagrams
1.
2.
3.
4.
Electrons preferentially occupy molecular
orbitals that are lower in energy.
Molecular orbitals may be empty, or contain
one or two electrons.
If two electrons occupy the same molecular
orbital, they must be spin paired.
When occupying degenerate molecular
orbitals, electrons occupy separate orbitals
with parallel spins before pairing.
Molecular Orbital Diagrams
Although molecular orbitals also result from
the inner (core) electrons as well as valence
electrons, many molecular orbital diagrams
include only the valence level.
Molecular Orbital Diagrams
For O2, there
will be a total of
12 valence
electrons that
must be placed in
the diagram.
Molecular Orbital Diagrams
2p
2s
2p
2s
For O2, there
will be a total of
12 valence
electrons that
must be placed in
the diagram.
Molecular Orbital Diagrams
2p
2s
2p
2s
The molecular
orbital diagram for
oxygen shows two
unpaired electrons,
consistent with
experimental data.
Bond Order
Bond order is an indicator of the bond
strength and length. A bond order of 1 is
equivalent to a single bond. Fractional bond
orders are possible.
The bond order of the molecule =
(# e- in bonding orbtls) - (# e- in anti-bonding orbtls)
2
2
Molecular Orbital Diagrams
2p
2s
2p
2s
The bond order of
O2 is:
8-4 = 2
2
This is consistent
with a double
bond.
Molecular Orbital Diagrams
This energy level
diagram works well
for atoms in which
the 2s and 2p levels
are fairly far apart.
These are the
elements at the right
of the table: O, F and
Ne.
MO diagram for Li through N
The elements on the left side of period 2
have a fairly small energy gap between the 2s
and 2p orbitals. As a result, interaction between
s and p orbitals is possible. This can be viewed
in different ways.
MO diagram for Li through N
In some approaches, the s orbital on one atom
interacts with the p orbital on another. The interaction
can be constructive or destructive.
MO diagram for Li through N
In another approach, the s and p orbitals on
the same atom interact in what is called orbital
mixing.
Either approach yields the same result. The
σ bonding and anti-bonding orbitals are raised in
energy due to the interaction with a p orbital.
MO diagram for Li through N
MO diagram for N2
N2 has 10
valence
electrons.
Resonance
The bonding in molecules with resonance aren’t
accurately described using Lewis structures. An
example is ozone, O3, which has two resonance
structures:
: :
:
: :
: :
:
: :
:O-O=O ↔ O=O-O:
Resonance
Either resonance structure provides the same
molecular shape- bent with an angle of
approximately 120o.
However, both bonds are identical in length
and strength. The bonds are intermediate
between single bonds and double bonds.
Resonance
Resonance
A more accurate
description of the
bonding can be
obtained by
considering the π
bonding to be
delocalized, or spread
out over all three
oxygen atoms.
Valence Bond & Molecular
Orbital Theory
The delocalized or extended pi system is
consistent with the lowest energy bonding orbitals
obtained using molecular orbital theory.
Extended  Bonding
Extended  Bonding
Extended  Bonding
Extended π Bonding – Nitrate
Bonding in Metals
A simple model of the bonding of metals is
called the electron sea model. The structure if
viewed as metal ions sitting in a sea of valence
electrons. Since the electrons are not associated
with a particular nucleus or atom, they are free to
move and conduct an electrical current.
Bonding in Metals
Metals are malleable (can be pounded into
thin sheets) and ductile (can be drawn into wires).
These properties suggest that there are no
localized bonds between the metal atoms, so the
structure can be easily deformed without breaking.
Band Theory
A more sophisiticated description of the
bonding in metallic solids is called band theory. This
approach applies molecular orbital theory (the
constructive and destructive interaction of atomic
orbitals) to create orbitals that are delocalized over
the entire solid crystal.
Band Theory
The greater number of atoms in the crystal
results in molecular orbitals that are very close in
energy, resulting in a continuous band of energies.
Band Theory
Semiconductors
In a conductor, there is no energy gap
between the valence band and the conduction
band.
In a semiconductor, there is a small energy
gap, and electrons can be promoted into the
conduction band.
In insulators, the gap is too large for
electrons to enter the conduction band.
Semiconductors