Covalent Bonding Theory #2 –
Valence Bond Theory
Introducing Orbital Hybridization
Chapter 9
Recall that…
• The Localized Electron (LE) model views a
molecule as a collection of atoms bound together
by sharing electrons between their orbitals
▫ Arrangement of valence electrons is represented
by the Lewis structure
▫ The molecular geometry can be predicted from the
VSEPR model
Problems with LE Model
• Let’s consider methane, CH4
▫ In general, we assume that bonding involves only
the valence orbitals
▫ This means that the hydrogen atoms in methane use
1s orbitals to bond
▫ The carbon atoms will use 2s and 2p orbitals to bond
• In thinking about how carbon can use these
orbitals to bond to the hydrogen atoms, two
related problems emerge…
Problems with the LE Model
Continued…
• Problem #1
▫ Using the 2p and 2s atomic orbitals will lead to 2
different types of C-H bonds:
 Those from the overlap of a 2p orbital of carbon and
a 1s orbital of hydrogen
 There will be 3 of these bonds
 Those from the overlap of a 2s orbital of carbon and
a 1s orbital of hydrogen
 There will be 1 of these bonds
▫ The problem is that methane is experimentally
known to have four identical C-H bonds
Problems with the LE Model
Continued…
• Problem #2
▫ Since the carbon 2p orbitals are mutually
perpendicular, we might expect the three C-H
bonds formed with these orbitals to be oriented at
90° angles
 The methane molecule is known by experiment to be
tetrahedral with bond angles of 109.5°
So, One Must Conclude Based on the
Evidence…
• The LE electron model is wrong
or
• Carbon adopts a set of orbitals other than its
“native” 2s and 2p orbitals to bond to the
hydrogen atoms when forming the methane
molecule
▫ This conclusion is more reasonable
Hybridization
• So, carbon “mixes” its native atomic orbitals to
form special orbitals for bonding
▫ It does so by promoting one 2s valence electron to
the open 2p orbital
 This creates one sp3 hybrid orbital
 sp3 because they are formed from one 2s and three 2p
orbitals (s1p3)
• This process is called hybridization
• There is an energy pay-off with forming hybrid
orbitals, or else this wouldn’t occur!
Carbon Forming Hybrid Orbitals in
Methane – Energy Diagram
Orbitals in a free C atom
Orbitals in C in the CH4 molecule
The Hybrid Orbitals in Methane
Putting it All Together –
A New Look at Methane’s Molecular
Geometry
In General…
• Whenever a set of equivalent tetrahedral atomic
orbitals is required by an atom, the atom adopts
a set of sp3 orbitals
Another Hybridization Example Ethylene
• The Lewis Dot structure for ethylene is
shown to the right
• In ethylene (C2H4), each carbon atom
employs 3 effective electron pairs
▫ Double bond acts as one effective electron
pair
• This requires a trigonal planar
arrangement of valence electrons with
bond angles of 120 degrees
▫ Since the 2s and 2p valence orbitals of
carbon do not have the required
arrangement, a set of hybrid orbitals is
needed!
The Hybridization of C in Ethylene
• The sp3 orbitals we have just considered will not
work because they are at angles of 109.5° rather
than the required 120°
• A set of 3 orbitals arranged at 120° angles in the
same plane can be obtained by combining one sorbital and two p-orbitals
▫ Since one 2s and two 2p orbitals are used to form
these hybrid orbitals, this is called sp2
hybridization
Carbon Forming Hybrid Orbitals in
Ethylene – Energy Diagram
Orbitals in an free C atom
Carbon orbitals in ethylene
The Hybrid Orbitals in Ethylene
The Hybridization of C in Ethylene
• Notice that in forming
sp2 orbitals, one 2p
orbital on carbon has
not been used
▫ This remaining p orbital
is oriented perpendicular
to the plane of sp2
orbitals
Ethylene and Sigma Bonds
• The three sp2 orbitals can be used to share electron
pairs with the other carbon and hydrogens
▫ In each of these bonds, the electron pair is shared in an
area centered on a line running between the atoms
 This type of covalent bond is called a sigma (σ) bonds
• In the ethylene molecule, the sigma bonds are formed
using the sp2 orbitals on each carbon atom and the 1s
orbital on each hydrogen atom
Ethylene and its Double Bond
• In the sigma bond, the electron pair occupies the space
between the carbon atoms
• The second bond must therefore result from sharing an
electron pair in the space above and below the sigma bond
▫ This type of bond can be formed using the 2p orbital
perpendicular to sp2 hybrid orbitals on each carbon atom
▫ Called a pi (π) bond
• Therefore, a double bond always consists of:
▫ One σ bond where the electron pair is located directly between
the atoms
▫ One π bond where the shared pair occupies the space above and
below the σ bond
The σ and π Bonds in Ethylene
In General…
• Whenever an atom is surrounded by three
effective pairs, a set of sp2 hybrid orbitals is
required
Another Hybridization ExampleCarbon Dioxide
• In the CO2 molecule, the C atom has two effective pairs
that will be arranged at an angle of 180 degrees
▫ We therefore need a pair of atomic orbitals oriented at 180°
• To obtain two hybrid orbitals with this arrangement
requires sp hybridization
▫ Formed when one s-orbital and one p-orbital are hybridized
Carbon Forming Hybrid Orbitals in
Carbon Dioxide – Energy Diagram
Orbitals in a free C atom
Orbitals in the sp hybridized C
in CO2
Carbon Forming Hybrid Orbitals in
Carbon Dioxide
• Note that two 2p orbitals
remain unchanged on the sp
hybridized carbon
▫ These are used to form the pi
bonds with the oxygen atoms
What About the Oxygen Atoms?
• Oxygen has 3 effective electron
pairs around it
▫ Trigonal planar electron
arrangement
 sp2 hybridization
▫ One p-orbital on each oxygen
is unchanged
 Used for pi bond with
carbon atom
• sp hybrid orbitals on carbon
and sp2 hybrid orbitals on the
two oxygen atoms are used to
form sigma bonds
▫ Remaining sp2 orbitals on
oxygen atoms hold lone pairs
In General…
• Whenever an atom is surrounded by two
effective pairs, a set of sp hybrid orbitals is
required
Another Hybridization ExamplePhosphorus Pentachloride
• PCl5 is surrounded by five
effective electron pairs
▫ Requires trigonal
bipyramidal arrangment
• Such a set of orbitals is formed
from one d-orbital, one sorbital, and three p-orbitals
▫ dsp3 hybridization
• The dsp3 hybridized
phosphorus atom in the PCl5
molecule uses its five dsp3
orbitals to share electrons with
the 5 chlorine atoms
Phosphorus Forming Hybrid Orbitals in
PCl5– Energy Diagram
What About the Chlorine Atoms?
• Each chlorine in PCl5 is
surrounded by four effective
electron pairs (3 lone pairs,
1 bonding pair)
▫ Tetrahedral electron
arrangement
▫ sp3 hybrid orbitals
• 5 P-Cl sigma bonds are
formed by sharing electrons
between a dsp3 orbital on P
and an sp3 orbital on Cl
▫ Other sp3 orbitals on Cl hold
lone pairs
In General…
• Whenever an atom is surrounded by five
effective pairs, a set of dsp3 hybrid orbitals is
required to achieve the trigonal bipyramidal
arrangement
Another Hybridization ExampleSulfur Hexafluoride
• SF6 is surrounded by
six effective electron
pairs
▫ Requires octahedral
arrangement
• Such a set of orbitals
is formed from two
d-orbitals, one sorbital, and 3 porbitals
▫ d2sp3 hybridization
Sulfur Forming Hybrid Orbitals in SF6–
Energy Diagram
What About the Fluorine Atoms?
• Each fluorine in SF6 is
surrounded by four effective
electron pairs (3 lone pairs,
1 bonding pair)
▫ Tetrahedral electron
arrangement
▫ sp3 hybrid orbitals
• 6 S-F sigma bonds are
formed by sharing electrons
between a d2sp3 orbital on S
and an sp3 orbital on F
▫ Other sp3 orbitals on F hold
lone pairs
In General…
• Whenever an atom is surrounded by six effective
electron pairs, a d2sp3 hybridization of that atom is
needed to achieve an octahedral arrangement
Summary of Number/Types of Atomic
Orbitals Mixed to Obtain Hybrids
Linear
Atomic
Orbitals
Mixed
Hybrid
Orbitals
Formed
Unhybridized
Orbitals
Remaining
Trigonal
Planar
Tetrahedral
Trigonal
Bipyramidal
Octahedral
Hybrid Orbital Formation
Hybridization
Summary Table
Linear
Trigonal
Planar
Tetrahedral
Trigonal
Bipyramidal
Octahedral
Atomic
Orbitals Mixed
One s
One p
One s
Two p
One s
Three p
One s
Three p
One d
One s
Three p
Two d
Hybrid
Orbitals
Formed
Two sp
Three sp2
Four sp3
Five sp3d
Six sp3d2
Unhybridized
Orbitals
Remaining
Two p
One p
None
Four d
Three d
Summary of Orbital Hybridization
Another Orbital Hybridization
Summary with Examples
Molecular Orbital (MO) Model
• Will not be covered on the AP Exam
• If interested, read section 9.2 in your book!
• This model is useful because:
▫ Electrons are not always localized as in the VSEPR theory
 Therefore, resonance must be added and explained as best as
possible
▫ Molecules containing unpaired electrons are not easily
dealt with using the LE model
▫ Magnetism is easily described using the MO model
 Oxygen is paramagnetic and this is NOT explained by the LE
model
▫ Bond energies are not easily related using the LE model