Hybridization and Molecular
Orbital (MO)
Theory
Chapter 10
Historical Models
•G.N.Lewis and I. Langmuir (~1920) laid out foundations
•Ionic species were formed by electron transfer
•Covalent molecules arise from electron sharing
•Valence bond theory (VB) - a molecule arises from interaction
of complete atoms, bound together through localized overlap of
valence-shell atomic orbitals which retain their original character.
•Valence shell electron pair repulsion theory (VSEPR) – predicts
molecular shapes based on valence electrons, lewis dot structures
and electron repulsions.
•Molecular orbital theory (MO) – a molecule is formed by the
overlap of atomic orbitals to form molecular orbitals, electrons
are then distributed into MOs. A molecule is a collection of
nuclei with the orbitals delocalized over the entire molecule.
Two Theories of Bonding
• VALENCE BOND
THEORY — Linus Pauling
• valence electrons are
localized between atoms (or
are lone pairs).
• halfhalf-filled atomic orbitals
overlap to form bonds.
1
Valence Bond (VB) Theory
•
•
Covalent bonds are formed by the overlap of
atomic orbitals.
Atomic orbitals on the central atom can mix and
exchange their character with other atoms in a
molecule.
– Process is called hybridization.
hybridization
Hybrid Orbitals have the same shapes as
predicted by VSEPR.
Valence Bond (VB) Theory
Regions of High
Electron Density
Electronic
Geometry
Hybridization
2
Linear
Trigonal
planar
Tetrahedral
Trigonal
bipyramidal
Octahedral
sp
sp2
3
4
5
6
sp3
sp3d
sp3d2
Molecular Shapes and Bonding
• In the next sections we will use the following
terminology:
A = central atom
B = bonding pairs around central atom
U = lone pairs around central atom
• For example:
AB3U designates that there are 3 bonding pairs and 1
lone pair around the central atom.
2
Sigma Bond Formation by
Orbital Overlap
Two s orbitals
overlap
Sigma Bond Formation
Two s
orbitals
overlap
Two p
orbitals
overlap
Linear Electronic Geometry:AB2
Species (No Lone Pairs of
Electrons on A)
• Some examples of molecules with this
geometry are:
BeCl2, BeBr2, BeI2, HgCl2, CdCl2
• All of these examples are linear, nonpolar
molecules.
• Important exceptions occur when the two
substituents are not the same!
BeClBr or BeIBr will be linear and polar!
3
Linear Electronic Geometry:AB2
Species (No Lone Pairs of
Electrons on A)
Trigonal Planar Electronic
Geometry: AB3 Species (No
Lone Pairs of Electrons on A)
• Some examples of molecules with this geometry
are:
BF3, BCl3
• All of these examples are trigonal planar, nonpolar
molecules.
• Important exceptions occur when the three
substituents are not the same!
BF2Cl or BCI2Br will be trigonal planar and polar!
Using VB Theory
Bonding in BF3
•• ••
F ••
Boron configuration
B
••
F
••••
•••
F
•• •
↑↓
1s
↑↓
2s
↑
2p
planar triangle
angle = 120o
4
Bonding in BF3
• How to account for 3 bonds 120o apart using a
spherical s orbital and p orbitals that are 90o apart?
• Pauling said to modify VB approach with ORBITAL
HYBRIDIZATION
• — mix available orbitals to form a new set of orbitals
— HYBRID ORBITALS — that will give the
maximum overlap in the correct geometry.
Bonding in BF3
2p
2s
hydridize orbs.
2
rearrange electrons
three sp
hybrid orbitals
unused p
orbital
Bonding in BF3
•
The three hybrid orbitals are made
from 1 s orbital and 2 p orbitals → 3 sp2
hybrids.
•
Now we have 3, halfhalf-filled HYBRID orbitals
that can be used to form BB-F sigma bonds.
5
Trigonal Planar Electronic
Geometry: AB3 Species (No Lone
Pairs of Electrons on A)
BF3, Planar Trigonal
Tetrahedral Electronic Geometry:
AB4 Species (No Lone Pairs of
Electrons on A)
• Some examples of molecules with this geometry
are:
CH4, CF4, CCl4, SiH4, SiF4
• All of these examples are tetrahedral, nonpolar
molecules.
• Important exceptions occur when the four
substituents are not the same!
CF3Cl or CH2CI2 will be tetrahedral and polar!
6
Tetrahedral Electronic Geometry:
AB4 Species (No Lone Pairs of
Electrons on A)
Bonding in CH4
How do we account for 4
C—H sigma bonds 109o
apart?
o
109
109o
Need to use 4 atomic orbitals
— s, px, py, and pz — to
form 4 new hybrid orbitals
pointing in the correct
direction.
Bonding in a Tetrahedron —
Formation of Hybrid Atomic
Orbitals
4 C atom orbitals
hybridize to form
four equivalent sp33
hybrid atomic
orbitals.
orbitals.
7
Tetrahedral Electronic Geometry:
AB4 Species (No Lone Pairs of
Electrons on A)
Bonding in CH4
Figure 10.6
Tetrahedral Electronic Geometry: AB4
Species (No Lone Pairs of Electrons on
A)
8
Tetrahedral Electronic Geometry:
AB3U Species (One Lone Pair of
Electrons on A)
• Some examples of molecules with this geometry
are:
NH3, NF3, PH3, PCl3, AsH3
• These molecules are our first examples of central
atoms with lone pairs of electrons.
Thus, the electronic and molecular geometries are
different.
All three substituents are the same but molecule is polar.
polar
• NH3 and NF3 are trigonal pyramidal, polar
molecules.
Steps in predicting the hybrid orbitals used by an atom in bonding:
1. Draw the Lewis structure
2. Determine the electron pair geometry using the VSEPR model
3. Specify the hybrid orbitals needed to accommodate the electron pairs in the
geometric arrangement
NH3
1. Lewis structure
2. VSEPR indicates tetrahedral geometry
with one non-bonding pair of electrons
(structure itself will be trigonal pyramidal)
3. Tetrahedral arrangement indicates four
equivalent electron orbitals
Tetrahedral Electronic Geometry:
AB2U2 Species (Two Lone Pairs of
Electrons on A)
• Some examples of molecules with this geometry are:
H2O, OF2, H2S
• These molecules are our first examples of central
atoms with two lone pairs of electrons.
Thus, the electronic and molecular geometries are different.
Both substituents are the same but molecule is polar.
polar
• Molecules are angular, bent, or V-shaped and polar.
9
Orbital Hybridization
Figure 10.5
BONDS
SHAPE
HYBRID REMAIN
2
linear
sp
2 p’ s
3
trigonal
planar
sp2
1p
4
tetrahedral sp3
none
Compounds Containing
Double Bonds
Valence Bond Theory (Hybridization)
C atom has four electrons.
Three electrons from each C atom are in sp2
hybrids.
One electron in each C atom remains in an
unhybridized p orbital
2s 2p
three sp2 hybrids 2p
C ↑↓ ↑ ↑ ⇒
↑↑↑
↑
10
Compounds Containing
Double Bonds
• The single 2p orbital is perpendicular to the trigonal planar
sp2 lobes.
The fourth electron is in the p orbital.
Side view of sp2 hybrid
with p orbital included.
Compounds Containing
Double Bonds
• An sp2 hybridized C atom has this shape.
Remember there will be one electron in each of the three
lobes.
Top view of
an sp2 hybrid
Compounds Containing
Double Bonds
• The portion of the double bond formed from the headon overlap of the sp2 hybrids is designated as a σ bond.
11
Sometimes it is not necessary for all the valence electron orbitals to hybridize. For
example, ethylene has the following structure:
The bonds between C and H
are all sigma bonds between
sp2 hybridized C atoms and
the s-orbitals of Hydrogen.
The double bond between the
two C atoms consists of a
sigma bond (where the
electron pair is located
between the atoms) and a pi
bond (where the electron pair
occupies the space above
and below the sigma bond.
σ and π Bonding in CH2O
Compounds Containing
Triple Bonds
• Ethyne or acetylene, C2H2, is the simplest
triple bond containing organic compound.
• Compound must have a triple bond to obey
octet rule.
12
Compounds Containing
Triple Bonds
Lewis Dot Formula
H ·· C ·· ·· ·· C ·· H
or
H C C H
VSEPR Theory suggests regions of high
electron density are 180o apart.
Compounds Containing
Triple Bonds
Valence Bond Theory (Hybridization)
Carbon has 4 electrons.
Two of the electrons are in sp hybrids.
Two electrons remain in unhybridized p
orbitals.
C [He]
2s
↑↓
2p
two sp hybrids 2p
↑↑ ⇒
↑↑
↑↑
σ and π Bonding in C2H2
Figure 10.12
13
Compounds Containing
Triple Bonds
A σ bond results from the head-on overlap of
two sp hybrid orbitals.
Compounds Containing
Triple Bonds
• The unhybridized p orbitals form two π bonds.
Note that a triple bond consists of one σ and
two π bonds.
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
Some examples of molecules with this geometry
are:
PF5, AsF5, PCl5, etc.
• These molecules are examples of central atoms
with five bonding pairs of electrons.
The electronic and molecular geometries are the same.
• Molecules are trigonal bipyramidal and nonpolar
when all five substituents are the same.
If the five substituents are not the same polar molecules
can result, AsF4Cl is an example.
14
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
Valence Bond Theory (Hybridization)
4s
4p
As [Ar] 3d10 ↑↓ ↑ ↑ ↑
4d
___ ___ ___ ___ ___
⇓
five sp3 d hybrids
↑ ↑ ↑ ↑ ↑
4d
___ ___ ___ ___ ___
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2, and
AB2U3
•
•
If lone pairs are incorporated into the trigonal bipyramidal structure,
there are three possible new shapes.
1. One lone pair - Seesaw shape
2. Two lone pairs - T-shape
3. Three lone pairs – linear
The lone pairs occupy equatorial positions because they are 120o
from two bonding pairs and 90o from the other two bonding pairs.
–
Results in decreased repulsions compared to lone pair in axial
position.
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
•
AB4U molecules have:
1. trigonal bipyramid electronic geometry
2. seesaw shaped molecular geometry
3. and are polar
•
•
One example of an AB4U molecule is
SF4
Hybridization of S atom is sp3d.
15
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
Molecular Geometry
H
H C
H
H
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
• AB3U2 molecules have:
1. trigonal bipyramid electronic geometry
2. T-shaped molecular geometry
3. and are polar
• One example of an AB3U2 molecule is
IF3
• Hybridization of I atom is sp3d.
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
Molecular Geometry
H
H C
H
H
16
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
• AB2U3 molecules have:
1.trigonal bipyramid electronic geometry
2.linear molecular geometry
3.and are nonpolar
• One example of an AB3U2 molecule is
XeF2
• Hybridization of Xe atom is sp3d.
Trigonal Bipyramidal Electronic
Geometry: AB5, AB4U, AB3U2,
and AB2U3
Molecular Geometry
H
H C
H
H
Octahedral Electronic Geometry:
AB6, AB5U, and AB4U2
• AB5U molecules have:
1.octahedral electronic geometry
2.Square pyramidal molecular geometry
3.and are polar.
• One example of an AB4U molecule is
IF5
• Hybridization of I atom is sp3d2.
17
Octahedral Electronic Geometry:
AB6, AB5U, and AB4U2
Molecular Geometry
H
H C
H
H
Octahedral Electronic Geometry:
AB6, AB5U, and AB4U2
• AB4U2 molecules have:
1.octahedral electronic geometry
2.square planar molecular geometry
3.and are nonpolar.
• One example of an AB4U2 molecule is
XeF4
• Hybridization of Xe atom is sp3d2.
Octahedral Electronic Geometry:
AB6, AB5U, and AB4U2
Polarity
Molecular Geometry
H
H C
H
H
18
Summary of Electronic &
Molecular Geometries
Two Theories of Bonding
• MOLECULAR
ORBITAL THEORY —
Robert Mullikan (1896(18961986)
• valence electrons are
delocalized
• valence electrons are in
orbitals (called molecular
orbitals)
orbitals) spread over
entire molecule.
Review of Atomic Orbitals - s, p and d
19
The Need for MO
VSEPR
and VB theory are good to explain the molecular shape.
BUT they did not explain the magnetic or spectral properties of
molecules.
Molecular
orbital theory is needed.
Homonuclear Diatomic Molecules:
Molecular Orbital (MO) Theory
MOs
are derived from a linear combination (addition and
subtraction) of atomic orbitals represented as wavefunctions of
nearby atoms to form molecular orbitals.
•There are two possible combinations
•Adding two atomic orbitals forms a bonding MO.
•Subtracting two atomic orbitals forms an antibonding
MO.
•Basic Tenant –
•The number of atomic orbitals contributed equals the
number of molecular orbitals generated.
Electron Wave Functions – Wave-Particle Duality
Linear Combination of Wavefunctions – Ψ
Ψ(1) + Ψ (2)
Ψ(1) + Ψ (2)
20
If we look at H2, we see that each hydrogen atom has a 1s atomic orbital
that is half-filled. Remembering that orbitals are mathematical functions,
they can combine by adding or subtracting to give two new combinations
which we call molecular orbitals.
Homonuclear Diatomic Molecules
Molecular Orbital Theory
In Phase / Out of Phase Overlap
σ*
Ψ(1) − Ψ (2)
Ha
Hb
Ψ(1) + Ψ (2)
σ
The energy of the H2 molecule with the two electrons in the bonding
orbital is lower by 435 kJ/mole than the combined energy of the two
separate H-atoms.
On the other hand, the energy of the H2 molecule with two electrons in
the antibonding orbital is higher than two separate H-atoms. To show the
relative energies we use diagrams like this:
21
Homonuclear Diatomic Molecules:
Molecular Orbital Theory
σ label implies rotation of MO about internuclear
axis (z axis) generates no phase change
*label implies a nodal plane between the nuclei
which is orthogonal to the z axis
π label implies rotation of orbital about internuclear axis
generates a phase change
In the H2 molecule, the bonding and anti-bonding orbitals are
called sigma orbitals ( σ )
Sigma Orbital: A bonding molecular orbital with cylindrical symmetry about
an internuclear axis.
When atomic orbitals are combined to give molecular orbitals, the
number of molecular orbitals formed equals the number of atomic orbitals
used.
A molecular orbital (like an atomic orbital) can contain no more than two
electrons (Pauli Exclusion Principle), and are filled starting with the
lowest energy orbital first.
In general, the energy difference between a bonding and anti-bonding
orbital pair becomes larger as the overlap of the atomic orbitals increase.
Example: H2 molecule
Each hydrogen atom contributes one electron. These go in the bonding
molecular orbital because we fill the lowest energy orbital first.
Electrons fill MOs by standard rules - aufbau, pauli, etc.
22
Bond Order / Electron Configuration
for H2 Molecule
Ψaσ∗1s
-Bond Order (B.O.)
B.O. = 1/2 (Nb - Na)
Nb = bonding electrons
Na = antibonding electrons
σ*1s
φΗ1
φΗ1
-Molecular electron
configurations - analogous
to atomic configurations
- H2 = σ21s
σ1s
Ψbσ1s
Example: He2 molecule
Not observed because there is no energy benefit to bonding these two atoms
together.
Bond Order / Electron Configuration
for He2 Molecule
Ψaσ∗1s
-Bond Order (B.O.)
B.O. = 1/2 (Nb - Na)
Nb = bonding electrons
Na = antibonding electrons
σ*1s
φΗ1
φΗ1
-Molecular electron
configurations - analogous
to atomic configurations
- H2 = σ21s σ∗21s
σ1s
Ψbσ1s
23
MO Diagram for He2+ and H2-
σ*1s
Energy
σ*1s
σ1s
AO of
He
AO of
He+
MO of
He2+
AO of
H-
σ1s
MO of
H2 -
AO of
H
H2- bond order = ??
He2+ bond order = ??
Summary Data for First Row Homo - Diatomics
Molecule
Bonding
e-
Antibond.
e-
Bond
Order
Bond
length
(Å)
Bond
Energy
(kJ/mol)
H2+
1
0
½
1.06
269
H2
2
0
1
0.74
458
He2+
2
1
½
1.08
230
He2
2
2
0
--
--
Orbital Interaction for Li2 Molecule
Li atom - 1s22s1
σ*2s
2s
σ2s
σ*1s
Bond order for
Li2?
Molecular
electron
configuration?
Be2?
1s
σ1s
Li2+?
24
Orbital Interaction for Li2 Molecule
Li atom - 1s22s1
σ*2s
Bond order for
Li2 = ½(4-2) = 1
2s
σ2s
σ21s σ∗21sσ22s
Be2 = ½(4-4) = 0
σ*1s
σ21s σ∗21sσ22s σ∗22s
Li2+ = ½(3-2) = ½
σ21s σ∗21sσ12s
1s
σ1s
MO Diagram for He2+ and H2-
σ*1s
1s
1s
MO of
He2+
1s
1s
σ1s
σ1s
AO of
He
Energy
σ*1s
AO of
He+
He2+ bond order = 1/2
AO of
H-
MO of
H2 -
AO of
H
H2- bond order = 1/2
We can also form bonding orbitals using other atomic orbitals. For
example, we can combine two p orbitals to form a sigma bond:
25
Using p orbitals a second type of orbital called a π orbital can also be
formed. These exist above and below the internuclear axis. We see π
bonds used for the second bond of a double bond or the second and
third of a triple bond. π bonds limit rotation of the atoms in space.
Relative MO Energy Levels for Period 2
Homonuclear Diatomic Molecules
No 2s-2p repulsion
MO energy levels for
O2, F2, and Ne2
Effect of 2s-2p
repulsion
MO energy levels for
B2, C2, and N2
Homonuclear Diatomic Molecules
Molecular Orbital Theory - p Orbital Set
26
O2 molecule is an example
with sigma and pi bonds
forming between atoms. MO
theory predicts that oxygen
will be paramagnetic.
Molecular Oxygen (O2)
Using the following MO Diagram
σ21s σ∗21sσ22s σ∗22s
π42p π∗22p
BO = ½(8-4)
=2
Orbital Energies for Second Row Homodiatomics
27
Experimental Data for Homodinuclear Diatomics Li to F
Diatomic
Bond Diss.
Bond
Enthalpy
Length (Å)
(kJ/mol)
Bond
Order
Magnetic
Info
Li2
2.67
110
1
D
Be2
--
--
0
--
B2
1.59
297
1
P
C2
1.24
607
2
D
N2
1.10
945
3
D
O2
1.21
498
2
P
F2
1.41
159
1
D
Paramagnetic= > 1 unpaired electron
Diamagnetic = 0 unpaired electrons
VBT describes O2 as a double bond (O=O), however experiment
indicates the molecule is paramagnetic.
MOT describes the bonding and accounts for the paramagnetism.
The MO Diagram for HF
Energy
σ∗
Two non-bonding orbitals
are the lone pairs on F
seen in The Lewis structure
for HF
1s
Note the H1S
is less stable
than the F2P
2px 2py
2p
Note: 2s non-bonding
orbital (F) not shown
σ
MO of
HF
AO
of H
AO
of F
The MO Diagram
for NO
PARAMAGNETIC
1 unpaired e-
Energy
σ*2pz
π*2pxy
σ2pz
2p
2p
π2pxy
Note AO’s of the more
electronegative O are
More stable than those
of N
σ*2s
2s
AO’s of
N
2s
σ2s
AO’s of
O
28
Heteronuclear Diatomic Molecules - CO
Homonuclear Diatomic Molecules
Review of Bonding Types
sigma - σ
pi - π
delta - δ
29