George Mason University
General Chemistry 211
Chapter 11
Theories of Covalent Bonding
Acknowledgements
Course Text: Chemistry: the Molecular Nature of Matter and
Change, 7th edition, 2011, McGraw-Hill
Martin S. Silberberg & Patricia Amateis
The Chemistry 211/212 General Chemistry courses taught at
George Mason are intended for those students enrolled in a science
/engineering oriented curricula, with particular emphasis on
chemistry, biochemistry, and biology The material on these slides is
taken primarily from the course text but the instructor has modified,
condensed, or otherwise reorganized selected material.
Additional material from other sources may also be included.
Interpretation of course material to clarify concepts and solutions to
problems is the sole responsibility of this instructor.
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1
Molecular Structure - Summary

Atomic theory

Molecular Weight (MW) – Neutrons + Protons

Mass, Atomic Mass units, Law of Definite Proportions

Moles, Chemical Equations, Stoichiometry

Gas Laws, Thermodynamics (reaction energy)

Quantum Theory – waves vs particles,
electronic structure of atoms
energy absorption, emission
electronic energy levels
quantum numbers, electron shells

Periodicity – orbital diagrams
Pauli exclusion principle
Aufbau Principle for populating subshells
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2
Molecular Structure - Summary



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Bonding – Valence electrons
Periodic table
Ionic Bonds
Covalent Bonds
Electronic Configuration
Lattice Energy, Born-Haber cycle, Bond energy
Geometry – Lewis diagrams
Resonance, Octet Rule
Formal Charge (valence electrons –
unbonded electrons –
½ bonded electrons)
Valence-Shell Electron Pair Repulsion Model (VSEPR)
Molecular Notation – AXaEb
Xa – Bonding pairs
Eb – Nonbonding pairs
sum(a + b) determines geometry (linear, tetrahedral)
if “b” > 0 molecule may form dipole (polar)
3
Bond Theories

Quantum Numbers & Electron Configuration
 In Chapters 8 & 9 an electron was defined as a
unique set of 4 quantum numbers
 The first 3 quantum numbers (n, l, ml) defined an
atomic orbital, which could contain a maximum of
2 electrons (+1/2 & -1/2 spin (ms))
 Each orbital (s, p, d) has a unique shape:
spherical (s), dumbell(p), pear shaped(d)
 All of the orbitals defined by a unique set of
n, l, ml quantum numbers, have the same
energy
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4
Bond Theories
“s” orbital
“d” orbitals
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“p” orbitals
5
Bonding Theories

Valence Bond (VB) theory is one of two basic theories,
along with Molecular Orbital (MO) theory, that were
developed to use the methods of quantum mechanics to
explain chemical bonding

Valence Bond Theory is a chemical bonding theory that
explains the bonding between two atoms caused by the
overlap of the half-filled atomic orbital from each atom

It focuses on how the atomic orbitals of the dissociated
atoms combine to give individual chemical bonds when a
molecule is formed
 The two atoms from the bonding atoms share each other's
unpaired electron to form a filled orbital to form a hybrid
orbital and bond together.
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6
Bonding Theories



Molecular Orbital (MO) theory is a method for determining
molecular structure in which electrons are not assigned to
individual bonds between atoms, but are treated as
moving under the influence of the nuclei in the whole
molecule
In this theory, each molecule has a set of molecular
orbitals, in which it is assumed that the molecular orbital
wave function, ψj ,may be written as a simple weighted
sum of the n constituent atomic orbitals
A given Atomic Orbital (s, p, d) takes the form of a subset
of “Molecular Orbitals
 bonding &  antibonding bonds and
 bonding &  antibonding bonds


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Each has its own energy
Molecular Orbital orbitals cover the whole molecule
7
Valence Bond Theory

Valence Bond Theory is an attempt to explain the
Covalent bond from a Quantum Mechanical view
 All orbitals of the same type (s, p, d, f) have the
same energy
 According to this theory, a bond forms when two
atomic orbitals (s/s s/p p/p) “overlap”
 The space formed by the overlapping orbitals has a
capacity for two electrons that have opposite spins,
+1/2 & -1/2 (exclusion principle)
Note: Each orbital forming the bond has at least
one unfilled slot to accommodate the electron
being shared from the other bonding orbital
 The bond strength depends on the attraction of the
nuclei for the shared electrons
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8
Valence Bond Theory

Valence bond theory (con’t)
 The greater the orbital overlap, the stronger
(more stable) the bond
 The extent of the overlap depends on the
shapes and directions of the orbitals
 An s orbital is spherical, but p and d orbitals
have more electron density in one direction
than in another
 Whenever possible, a bond involving p or d
electrons will be oriented in the direction that
maximizes overlap
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9
Valence Bond Theory
Hydrogen, H2
1s1
Hydrogen Fluoride, HF [He]2s22p5
To maximize overlap, half-filled H
1s and F 2p orbitals overlap along
the long axis of the 2p orbital
Fluorine, F2
[He] 2s22p5
In F2, the half-filled 2 px orbital
on one F atom points end to end
toward the half-filled 2px of the
other F to maximize overlap
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10
Hybrid Orbitals

One might expect the number of bonds formed by an
atom would equal its unpaired electrons

Chlorine, for example, generally forms one bond as it has
one unpaired electron - 1s22s22p5

Oxygen, with two unpaired electrons, usually forms two
bonds - 1s22s22p4

However, Carbon, with only two unpaired electrons,
generally forms four (4) bonds
C (1s22s22p2) [He] 2s22p2
The four bonds come from the 2 (2s) paired electrons and
the 2 (2p) unpaired electrons
For example, Methane, CH4, is well known
The uniqueness of these bonds is described next
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11
Hybrid Orbitals

Linus Pauling proposed that the valence atomic
orbitals in a molecule are different from those of
the isolated atoms forming the molecule

Quantum mechanical computations show that if
specific combinations of orbitals are mixed
mathematically, “new” atomic orbitals are
obtained

The spatial orientation of these new orbitals lead
to more “stable” bonds and are consistent with
observed molecular shapes

These new orbitals are called:
“Hybrid Orbitals”
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12
Hybrid Orbitals
Types of Hybrid Orbitals

 Each type has a unique geometric arrangement
 The hybrid type is derived from the number of s, p, d
atomic orbitals used to form the Hybrid
Hybrid Orbitals
(Hybridization)
Geometric
Arrangements
Number of
Hybrid Orbitals
Formed by
Central Atom
Example
sp
Linear
2
Be in BeF2
sp2
Trigonal
planar
3
B in BF3
sp3
Tetrahedral
4
C in CH4
sp3d
Trigonal
bipyramidal
5
P in PCl5
sp3d2
Octahedral
6
S in SF6
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13
sp Hybrid Orbitals

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SP Hybridization
 2 electron groups surround central atom
 Linear shape, 180o apart
 VB theory proposes the mixing of two
nonequivalent orbitals, one “s” and one “p”, to
form two equivalent “sp” hybrid orbitals
 Orientation of hybrid orbitals extend electron
density in the bonding direction
 Minimizes repulsions between electrons
 Both shape and orientation maximize overlap
between the atoms
14
“sp” Hybrid Orbitals
hybrid
orbitals
Ex: BeCl2
The Be-Cl bonds in BeCl2 are
neither spherical (s orbitals) nor
dumbell (p orbitals)
Beryllium Hybrid Orbital Diagram
The Be-Cl bonds have a hybrid
shape
In the Beryllium atom the 2s
orbital and one of the 2p orbitals
mix to form 2 sp hybrid orbitals
orbital box diagrams
Each Be Hybrid sp orbital overlaps
a Chlorine 3p orbital in BeCl2
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15
“sp2” Hybridization

sp2 - Trigonal Planar geometry (Central atom bonded to
three ligands)

The three bonds have equivalent hybridized shapes
The sp2 hybridized orbitals are formed from:

1 “s” orbital and 2 “p” orbitals
Note: Of the 4 orbitals available (1 s & 3 p) only the s
orbital and 2 of the p orbitals are used to form
hybrid orbitals
Note: Unlike electron configuration notation, hybrid orbital
notation uses superscripts for the number of atomic
orbitals of a given type that are mixed, NOT for the
number of electrons in the orbital, thus,
sp2 (3 orbitals), sp3 (4 orbitals), sp3d (5 orbitals)
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16
“sp2” Hybridization
BF3
Hybrid Orbital Diagram
The 3 B-F bonds are
neither spherical nor
dumbell shaped
They are all of identical
shape
In Boron, the “2s” orbital
and two of the “2p” orbitals
mix to form 3 sp2 hybrid
orbitals, each containing one
the 3 total valence electrons
Each of the Boron hybrid sp2
orbitals overlaps with a 2p
orbital of a Fluorine atom
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Boron (B) 1s22p1
Forms 3 sp2 hybrid orbitals
BF3
17
SP2 Hybridization
Total Valence electrons (e-)
4 + 3 x 6 + 2 (e-) = 24
Add C-O Bonding e3x2=6
Distribute e- to Oxygen ligands
3 x 6 = 18
Move 1 e- pair from ligand to
Central Atom to complete Octet
Determine No. Unbonded pairs
Bonding Pairs now = 4 (8e-)
24 – 16 – 8 = 0
Formal Charges
FCc 4 – ½ (8) – 0 = 0
CO1 6 – ½(2) –6 = -1 x 2
=-2
CO2 6 – ½ (4) – 4 = 0
Net Ion Charge = -2
AXaEb = AX3E0 = a + b = 3
Trigonal Planar
Hybridization – sp2 (3 orbitals)
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Carbonate Ion - CO32-
+ 2 e2p
Mix
sp2 Hybrid Orbitals
Isolated
Carbon
2s
18
sp3 Hybrid Orbitals

sp3 (4 bonds, thus, Tetrahedral geometry)

The sp3 hybridized orbitals are formed from:
1 “s” orbital and 3 “p” orbitals

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Example”
 Carbon is the basis for “Organic Chemistry”
 Carbon is in group 4 of the Periodic Chart and has 4
valence electrons – 2s22p2
 The hybridization of these 4 electrons is critical in the
formation of the many millions of organic compounds
and as the basis of life as we know it
 The following slides show 3 different forms of the
electronic structure and explains why the hybridized
form reflects the observed structure of organic
compounds
19
sp3 Hybrid Orbitals
2p
Energy
2s
2s
This structure implies
different shapes and
energies for the “s” and “p”
bonds in carbon
compounds.
Observations indicate that
all fours bonds are
equivalent
1s
C atom (ground state)
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2p
1s
C atom (promoted)
20
sp3 Hybrid Orbitals

One bond on Carbon would form using the 2s
orbital while the other three bonds would use 3
2p orbitals

This does not explain the fact that the four bonds
in CH4 appear to be identical

Valence bond theory assumes that the four
available atomic orbitals (2s22p2) in carbon
combine to make four equivalent “hybrid”
orbitals
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21
Hybrid Orbitals

Hybrid orbitals are orbitals used to describe bonding
that is obtained by taking combinations of atomic orbitals
of an isolated atom
 In the case of Carbon, one “s” orbital and three “p”
orbitals, are combined to form 4 sp3 hybrid orbitals
 The carbon atom in a typical sp3 hybrid structure has 4
bonded pairs and zero unshared electrons, therefore,
Tetrahedral structure
AXaEb (a + b) 4 + 0 = AX4
 The four sp3 hybrid orbitals take the shape of a
tetrahedron
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22
Hybridization of Carbon in CH4
4 sp3 orbitals formed
sp3
2p
sp3
Energy
C-H bonds
2s
1s
C atom
(ground state)
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1s
C atom
(hybridized state)
1s
C atom
(in CH4)
23
Spatial Arrangement of
sp3 Hybrid Orbitals
Shape of sp3 hybrid orbital
different than either s or p
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24
sp3d Hybrid Orbitals

sp3d (5 molecules, thus, Trigonal Bypyramidal geometry)

Molecules with central atoms from Period 3 or higher, can
utilize “d” orbitals in the formation of hybrid orbitals

The sp3d hybridized orbitals are formed from:
1 “s” orbital, 3 “p” orbitals, 1 “d” orbital
:
F:
F:
:
:
:
F
P
: :
:F
: :
AX5E0
:F:
:
AXaEb
:
PCl5
hybrid orbitals – 5 (sp3d)
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25
sp3d Hybrid Orbitals
Hybridized Orbital Diagram for
PCl5

5 equivalent (hybrid) orbitals are required

The one 3s orbital, the 3 3p orbitals and one of the unused 3d orbitals of
the Phosphorus atom mix to form the 5 sp3d hybrid orbitals

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The remaining 4 empty 3d orbitals (unhybridized) are not used
26
Diagrams of Hybrid Orbitals Showing their
Spatial Arrangements
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27
Hybrid Orbitals

To obtain the bonding description of any atom in a
molecule, you proceed as follows:
 Write the Lewis electron-dot formula for the
molecule
 From the Lewis formula, use the VSEPR theory to
determine the arrangement of electron pairs
around the central atom, i.e., the geometry
 From the geometric arrangement (AXaEb) of the
electron pairs, obtain the hybridization type
 Assign valence electrons to the hybrid orbitals of this
atom one at a time, pairing only when necessary
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 Form bonds to the central atom by overlapping singly
occupied orbitals of other atoms with the singly
occupied hybrid orbitals of the central atom
28
Oxygen Atom Bonding in H2O
4 sp3 Hybridized Orbitals
2p


Energy
2s
a+b
2+2=4
Tetrahedral
AX2E2
bent
1s
O
Central Atom
(ground state)
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sp3
sp3
H O H
Tetrahedral
1s
O atom
(hybridized state)
lone
pairs
O-H
bonds
1s
O atom
(in H2O)
29
Practice Problem
What hybrid orbitals of Sulfur are involved in the bonding in
Sulfur Trioxide (SO3)?
a. sp
A
b. sp2
c.
d.
sp3
sp2d
e. sp3d2
Ans: b
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


O




O
S
B



O

fcS = +3






O

O
S
C



O

fcS = +2





O


O
S
D






O
fcS = +1
O


O 
S

O

fcS = 6-0-1/2(12)
fcS = 0
(preferred form)
Total Valence e- - 3 x 6 + 6 = 24
Bonded Pairs
3 x2= 6
Distribute e- about O atoms =
3 x 6 = 18
Unshared e- about S atom = 24 - 6 -18 = 0
Move e- pairs from O to S to form alternative forms of SO3
Compute formal charge on S; select form with least formal charge (D)
AXaEb = 3 + 0 = 3 = AX3 (trigonal Planar)
3 O-S hybridized orbitals are required:
one “s” orbital blended with 2 “p” orbitals (sp2)
30
Sulfur Trioxide – Hybrid Orbitals
3p
3p
3p
VSEPR – AX3
Trigonal Planar
3s
3 sp2 orbitals required
sp2
S atom
(ground state)
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S atom
(hybridized state)
sp2
S atom
(in SO3)
31
Nitrogen Atom Bonding in NH3
4 sp3 orbitals required
2p
H
Energy
2s

N
H
H
a+b
3+1=4
Tetrahedral
AX3E1
trigonal
pyramidal
1s
N atom
(ground state)
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sp3
Tetrahedral
1s
N atom
(hybridized state)
sp3
lone
pair
N-H
bonds
1s
N atom
(in NH3)
32
Multiple Bonds

Types of Covalent Bond & Orbital Overlap
 Orbitals can overlap two ways
Side to Side or End to End
 Two types of Covalent Bonds:
Sigma Bonds (C-C)
pi () Bonds (C=C)
 Multiple Bonds
Ethane
Tetrahedral
(both carbons)
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Ethylene
Trigonal planar
(both carbons)
Acetylene
Linear
(both carbons)
180o
109.5o
120o
sp3
sp2
sp
double bond
acts as single
electron group
triple bond
acts as single
electron group
33
Multiple Bonds

End-to-End overlap & Sigma Bonds
 The C – C bond in Ethane (C2H6) involves overlap of 1
sp3 orbital from each carbon
 Each of the six (6) C – H bonds involves the overlap of
a Carbon sp3 and a Hydrogen 1 s orbital
 All bonds involve overlap of one end of orbital with the
end of the other orbital
 The bond formed from end-to-end overlap is called a
“sigma bond” (symbol - )
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34
Multiple Bonding

According to Valence Bond theory, one hybrid orbital is
needed for each bond (whether a single or multiple) and
for each lone pair
– For example, consider the molecule:
Ethene (or Ethylene)
H
H
C C
H
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H
35
Multiple Bonding (Ethene)

Each Carbon atom is bonded to three other atoms and no
lone pairs, which indicates the need for three hybrid
orbitals
 This implies AX3E0 (Trigonal) sp2 hybridization
1 2s
&
2 2p orbitals
 The third 2p orbital is left unhybridized and lies
perpendicular to the plane of the trigonal sp2 hybrids
 The following slide represents the sp2 hybridization of
the Carbon atoms in Ethene
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36
Multiple Bonding (Ethene)
(unhybridized)
2p
2p
sp2
Energy
2s
1s
C atom (ground state)
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1s
C atom (hybridized)
37
Multiple Bonding

Each carbon atom is sp2 hybridized

Each of the carbon atom’s 4 valence electrons fill ½ its 3
sp2 orbitals and its unhybridized 2p orbital, which lies
perpendicular to sp2 plane




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Two sp2 orbitals of each carbon form C – H sigma ()
bonds by overlapping the 1 s orbitals of the two H atoms
The 3rd sp2 orbital of one carbon forms a C – C () bond
with the sp2 orbital of the other carbon with end-to-end
overlap
A pi () bond is formed when the two unhybridized 2p
orbitals (one from each carbon) overlap side-to-side,
forming two regions of electron density, one above and
one below the -bond axis
A double bond always consists of:
one -bond and one
 bond
38
Multiple Bonding
 Two of the sp2 hybrid orbitals of each carbon overlap endto-end with the 1s orbitals of the 2 hydrogen atoms
forming a sigma bond
 The remaining sp2 hybrid orbital, one on each carbon,
overlap end-to-end to form a sigma bond
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39
Multiple Bonding

The remaining “unhybridized” 2p orbitals, one on each of the
carbon atoms, overlap side-to-side, one on top of the sigma
bond and one on the bottom of the sigma bond, forming a 
bond
The carbon-carbon double bond is described as
one s bond and one  bond
The two electron pairs in a double bond act as a “single”
electron group
The electron pairs do not repulse each other because each
electron pair occupies a distinct orbital, a specific region of
electron density, thus repulsions are reduced
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40
Practice Problem
Use valence bond theory to describe the bonding in CO2
Ans:
1. Draw Lewis structure
2. Determine hybridization
3. Draw diagram of hybrid atomic orbitals
4. Pair electrons (O) with hybrid C orbitals
forming sigma bonds
5. Pair electrons (O) with unpaired p electrons
in C atom to form pi () bonds
Con’t
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41
Practice Problem (Con’t)
Use valence bond theory to describe the bonding in CO2
O C O




O C O




O C O
Unshared pair
of electrons
2 pair from
each oxygen
2 bonding pairs
0 non-bonding pairs
AXaEb = a + b = 2 + 0 = 2 (Linear)
Hybridization – sp (2 hybrid orbitals required
2p
2s
1s
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p
C-O p ()
(unhybridized)
2s
sp
Carbon atom
2s22p2
Hybridized
Carbon
2p
C-O sp ()
Oxygen atom
2s22p4
42
Molecular Orbital (MO) Theory

Molecular Orbital (MO) theory is a theory of the electronic
structure of molecules in terms of molecular orbitals,
which may spread over several atoms or the entire
molecule
 MO theory explains the observed and computed energy
differences among orbitals, which Valence Bond theory
does not

As atoms approach each other and their atomic orbitals
overlap, molecular orbitals (MO) are formed
 Note: Only outer (valence) Atomic orbitals (AO)
interact enough to form Molecular Orbitals (MO)

Electron motions are complex making solutions to the
Schroedinger equation approximations

Mathematically, the combination of atomic orbitals to form
molecular orbitals involves adding or subtracting atomic
wave functions
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43
Molecular Orbital (MO) Theory

Adding Wave Functions
 Forms a “Bonding” () molecular orbital (MO)
● Region of high electron density between
nuclei
● Electron charge between nuclei is dispersed
over a larger area than in atomic orbitals
(AO)
● MO orbital energy is lower than in the AO
because of the reduction in electron repulsion
● Bonding MO is more stable than AO
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44
Molecular Orbital (MO) Theory
Subtracting Wave Functions
 Forms a “Nonbonding” (*) molecular orbital
● The node between the nuclei has most of the
electron density outside the node with very
little density (zero) between the nuclei
● Thus, the electrons do not shield one nuclei
from the other resulting in increased nucleusnucleus repulsion
● Therefore, the antibonding MO has a higher
energy than the corresponding atom orbitals
(AO)
● When the antibonding orbital is occupied, the
molecule is less stable than when the orbital
is not occupied
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45

Molecular Orbital Theory

Example: The bonding of two Hydrogen atoms
 1s
(bonding) molecular orbital is formed
 1s * (antibonding) molecular orbital is formed

The following slide illustrates the relative energies
of the molecular orbitals (MO) compared to the
original atomic orbitals (AO)

Because the energy of the two electrons in the
bonding orbital is lower than the energy of the
individual atoms, the molecule is stable
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46
Molecular Orbital Theory
Atomic orbital
H atom
Molecular Orbital
Atomic orbital
H2 molecule
H atom
1s*
1s
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1s
1s
More Stable
47
Bonding and Antibonding Orbitals from 1s
Hydrogen Atom Orbitals
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48
Bond Order

The term bond order refers to the number of
electron pairs shared between two atoms
 The bond order of a diatomic molecule is
defined as one-half the difference between the
number of electrons in bonding orbitals, nb, and
the number of electrons in antibonding orbitals,
na
Bond
Order
=
1
(nb - na )
2
For example, try H2 and He2. Determine bond orders
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49
Bond Order
H2
Atom
Molecule
Atom
H – 1s1
Bond Order
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Energy
BO = ½[(2) – (0)]
= ½[2]
=1
1s*
1s
1s
1s
50
Bond Order
He2
Atom
Molecule
Atom
He – 1s2
BO = ½[(2) – (2)]
= ½[0]
=0
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Energy
Bond Order
1s*
1s
1s
1s
51
Diatomic Homonuclear
Substances in 2p period

The 2p orbitals can overlap in two ways
 End-to-End gives 2p and *2p molecular
orbitals (MO)
 Side-to-Side gives a pair of 2p and *2p MOs
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52
Diatomic Homonuclear
Substances in 2p period

The order of MO energy levels, whether bonding
or nonbonding, is based on the AO (atomic
orbital) energy levels and on the mode of the p
orbital combination
 MOs formed from 2s orbitals are lower in
energy than 2p orbitals because 2s AOs are
lower in energy than 2p AOs
 Bonding MOs are lower in energy than
antibonding MOs
● 2p is lower in energy than *2p
● 2p is lower in energy than *2p
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Diatomic Homonuclear
Substances in 2p period
 Atomic p orbitals (AO) can interact more
extensively End-to-End than Side-to-Side
 Thus, 2p MO is lower in energy than 2p
 The destabilizing effect of the *2p MO is
greater than that of the *2p MO
 The energy order for MOs derived from 2p
orbitals is:
2p < 2p < *2p < *2p
Most Stable
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Least Stable
54
Diatomic Homonuclear
Substances in 2p period

Several factors are involved in the relative
energies of the various molecular orbitals (MO)
 Bond length
 Bond energy
 Bond order
 Magnetic properties
 Electron valence shell configuration
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Diatomic Homonuclear
Substances in 2p period

Factors that affect the MO energy level order
 There are three (3) mutually perpendicular 2p
orbitals in each atom of a diatomic molecule
(2px 2py 2pz)
 When the 6 p orbitals (3 from each element)
combine, only one orbital from each element
can interact end-to-end forming a  (bond)
and a * (antibonding) Molecular Orbital (MO)
 The other two pairs of orbitals interact side to
side to form two  MOs and two * MOs of
the same energy giving the expected MO
diagrams for the p-block Period 2 homonuclear
diatomic molecules
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Diatomic Homonuclear
Substances in 2p period
End to end
Side to side
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Diatomic Homonuclear
Substances in 2p period

Other factors influence the MO energy level order
 “s" and “p” AOs can be similar in energy or
differ considerably in energy, which determines
whether the orbitals mix or don’t mix
 O, F, Ne atoms are relatively small and
electron repulsions raise the energy of 2p
orbitals high enough above 2s orbitals to
minimize orbital mixing
 Atoms, such as B, C, N, are larger in size and
the “s” and “p” AOs have less electron repulsion
and the energy difference between 2s & 2p is
less, resulting in mixing of the “s” & “p” orbitals
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Diatomic Homonuclear
Substances in 2p period
 This smaller difference in energy of the 2p & 2s
orbitals in the P, C, N atoms permits some
mixing of the orbitals between the 2s orbital of
one atom and the end–on of the 2p orbital of
the other atom
 This orbital mixing:
 lowers the energy of the 2s and *2s MOs
and
 raises the energy of the 2p and *2p MOs
 The  MOs are not affected
 The effect of the mixing is the reversal of the
2s and 2p MOs
2p < 2p < *2p < *2p
 The next slide illustrates these differences
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Diatomic Homonuclear
Substances in 2p period
Without
2s -2p
mixing
Effect of
Mixing
MO
energy levels
O2, F2, Ne2
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
The  MOs
are not
affected

Reversal of
the 2s and
2p MOs
With
2s -2p
mixing
MO
energy levels
B2, C2, N2
60
Diatomic Homonuclear
Substances in 2p period
MO occupancy and
molecular properties for
B2 through Ne2
Bond energy and bond
order are inversely
related to bond length
Orbitals with unpaired
electrons are:
paramagnetic
and are attracted to an
external magnetic field
Note reversal of
2p & 2p energy levels
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Diatomic Homonuclear
Substances in 2p period
The arrows show the
occupation of molecular
orbitals by the valence
electrons in N2
Bond Order
BO = ½(Nb - Na)
BO = ½[(2+4+2) - (2)]
= ½[8-2]
=3
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Sample Problem
Which of the following species has a bond order of 2.5?
O2
O 2–
O22–
O 2+
NO
2p*
2p*
2p
Ans: d or e
for
Energy
a.
b.
c.
d.
e.
2p
2p
Nitrogen
1s22s22p3
2p
Oxygen
1s22s22p4
NO
2s*
BO = ½[(2+4+2)-(2+1)]
= ½(8-3)
= 2.5
2s
2s
2s
Con’t
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Sample Problem
Which of the following species has a bond order of 2.5?
a. O2
b. O2–
c. O22–
d. O2+
e. NO
for O2+
BO = ½[(2+4+2)-(2+1)]
= ½(8-3)
2p*
2p
Energy
Ans: d or e
2p*
2p
2p
Oxygen
1s22s22p4
2p
Oxygen+
1s22s22p3
2s*
2s
2s
2s
= 2.5
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Diatomic Heteronuclear
Substances in 2p period

Heteronuclear diatomic molecules are composed
of two different atoms – HF NO , etc.

Heteronuclear molecules have “Asymmetric” MO
diagrams

Atoms with greater effective nuclear charge (Zeff )
draw their electrons closer to the nucleus, thus,
they have higher electronegativity
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Diatomic Heteronuclear
Substances in 2p period
Example: Hydrogen Fluoride(HF)
 Higher effective nuclear charge
of Fluorine nucleus holds
electrons more tightly than H
(proton nucleus)
Hydrogen
Fluorine
 All occupied atomic orbitals of
F have lower energy than the
1s orbital of Hydrogen
 The Hydrogen 1s orbital reacts
with the F 2p orbitals
 Only one of the 3 F 2p orbitals,
2pz leads to “end-to-end
overlap with Hydrogen 1s
orbital producing a  MO
 The other two p orbitals (2px &
2py) are not involved in the
bonding and are called
“nonbonding” MOs)
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Diatomic Heteronuclear
Substances in 2p period

Example
 Bonding in Heteronuclear Nitrogen Monoxide, NO
 Highly reactive compound because it has a lone electron
 Two possible Lewis Structures
Formal charge 
I
II
 Formal charge
 Not clear where lone electron resides (N or O)
 Lower Formal charge on N suggests structure I
 MO theory predicts electron resides closer to the
Nitrogen atom
 Measured bond energy suggests bond order
higher than 2
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Diatomic Heteronuclear
Substances in 2p period
Example: Nitrogen Monoxide
 The 11 valence electrons of NO fill MOs
in order of increasing energy, leaving the
lone electron in one of the *2p orbitals
 Atomic orbitals of O have lower energy
than those of N – Oxygen is more
electronegative than Nitrogen
 The 8 bonding electrons and the 3 nonbonding electrons give a bond order of
½(8-3) = 2.5
 The bonding electrons lie in MOs closer
in energy to the AOs of the Oxygen atom
 The lone unshared electron occupies an
anti-bonding orbital (*2p)
 Because this orbital receives a greater
contribution from the 2p orbitals of the N
atom, it resides closer to the Nitrogen
atom
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Nitrogen
Oxygen
68
Molecular Orbital Template
Homonuclear Diatomic Molecules
(without 2s – 2p mixing)
Atom
(AO)
Molecule
(MO)
Atom
(AO)
Energy
2p*
2p*
2p
2p
2p
2p
2s*
2s
2s
2s
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Molecular Orbital Template
Homonuclear Diatomic Molecules
(with 2s – 2p mixing)
Atom
(AO)
Molecule
(MO)
Atom
(AO)
2p*
Energy
2p*
2p
2p
2p
2p
2s*
2s
2s
2s
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Molecular Orbital Template
Heteronuclear Diatomic Molecules
(without 2s – 2p mixing)
Atom
(AO)
Molecule
(MO)
Atom
(AO)
2p*
2p*
Energy
2p
2p
2p
2p
2s
2s*
2s
2s
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Molecular Orbital Template
Heteronuclear Diatomic Molecules
(with 2s – 2p mixing)
Atom
(AO)
Molecule
(MO)
Atom
(AO)
2p*
2p*
Energy
2p
2p
2p
2p
2s
2s*
2s
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Hybrid Orbital Diagram
Mix
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Equation Summary
1
(n - n )
a
2 b
n - number of electrons in bonding orbitals
b
n - number of electrons in anti - bonding orbitals
a
Bond
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Order
=
74
Equation Summary

VESPR Model Molecular Notation:
AXaEb
A – The Central Atom (Least Electronegative atom)
X – The Ligands (Bonding Pairs)
a – The Number of Ligands
E – Non-Bonding Electron Pairs
b – The Number of Non-Bonding Electron Pairs
 Double & Triple Bonds count as a “single” electron pair
 The Geometric arrangement is determined by:
sum (a + b)
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