Molecular Orbital Theory

1
Molecular Orbital Theory

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

2
Bonding Theories

• Ionic Model
• Skeleton Diagrams
• Lewis Dot Diagrams
• Formal Charge, Resonance
• Molecular Orbital Theory
• Extends atomic orbitals concepts to molecules

3
Bonding in Diatomic Molecules
Diatomic molecule contains two atoms
large difference in electronegativity
small difference in electronegativity
Give an example of a compound with ionic bonding.
4
Homodiatomic Molecules
The best example of covalent bonding involves
homodiatomic molecules.
Contains two of the same type of atom.
e.g., H2, O2, F2, N2
Why are these molecules the best examples of
covalent bonding?
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Homodiatomic Molecules
The best example of covalent bonding involves
homodiatomic molecules.
Contains two of the same type of atom.
e.g., H2, O2, F2, N2
Why are these molecules the best examples of
covalent bonding?
Bonding electrons are exactly shared because both
atoms have the same electronegativity.
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Heterodiatomic Molecules
HF, BN and CO are heterodiatomic molecules.
Contain two different atoms.
H - F
These molecules are polar covalent.
What factors might help predict the positive and
negative ends of the molecule?
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A Little Review
What is an orbital?
Give an example of an atomic orbital?
What is the name of the mathematical
function that determines the shape of an orbital?
What is the maximum number of electrons that can
be in one orbital?
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Molecular Orbitals
When two atoms come close to each other, what
happens to the orbitals of each atom?
a bond forms
ssb molecular orbital
sigma s bonding molecular orbital
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Molecular Orbitals
Orbital wave functions can add subtract to
give new wave functions and corresponding molecula
r orbitals (mo).
Atoms bond together when the wave
functions constructively overlap.
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SIGMA BOND (s)
A bond between two atoms in which the
electron density of the molecular orbital is
between the two nuclei is called a sigma bond.
(ssb)2 molecular orbital
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Molecular Orbitals (mo)

• Obey many of the same rules as atomic orbitals
  (ao).

• two electrons per molecular orbital.
• specific regions of space.
• one molecular orbital formed for each atomic
  orbital used.

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Wave Functions
The amplitude (height) of each wavefunction can
either be positive or negative.
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WavefunctionsBonding Antibonding Orbitals
sb
Constructively interfere in certain regions of
space.
s
Destructively interfere in certain regions of
space.
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Bonding Antibonding Orbitals
When a bonding molecular orbital forms, an
antibonding molecular orbital also forms.
Bonds form where orbitals overlap and electrons
are.
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Atomic and Molecular Orbitals
Atomic orbitals include
3dz2
2py
1s
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Atomic and Molecular Orbitals
Molecular orbitals include
z
ssb
sz
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Atomic and Molecular Orbitals
This represents an orbital
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Atomic and Molecular Orbitals
carbon 1s2 2s2 2p2
An orbital can be empty or can contain 1 or 2
electrons.
Orbitals can have different energies
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Molecular Orbital Diagrams

• Examples
• dihydrogen
• dihelium
• dihelium(I) ion

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Dihydrogen, H2
ss
ssb
The branch lines indicate which atomic orbitals
are involved in generating the molecular orbitals.
Two 1s1 hydrogen orbitals overlap to form a ssb
bonding molecular orbital
1s1 hydrogen orbital of two hydrogen atoms
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Dihydrogen, H2
What advantage can an orbital gain in forming a
molecular orbital from an atomic orbital?
Why is dihydrogen diamagnetic?
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Dihelium, He2
Two electrons occupy the highest molecular
orbital forming a ss
ss
Each helium atom has the electronic configuration
1s2 (each contributes 2 electrons to the
helium molecular orbitals)
Two electrons occupy the lowest molecular
orbital forming a ssb
ssb
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Dihelium, He2
Why doesnt He2 exist as a stable molecule?
The electronic configuration of the dihelium
molecule is (ssb)2 (ss)2
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Dihelium, He2
Why doesnt He2 exist as a stable molecule?
The electronic configuration of the dihelium
molecule is (ssb)2 (ss)2
Antibonding implies there is a negative bond 1
bond 1 antibond zero net bonds
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Dihelium(I) Ion, He2
ss
ssb
How many valence electrons must be considered in
the dihelium(I) ion?
Complete the molecular orbital diagram using the
available electrons.
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Dihelium(I) Ion, He2
These represent the atomic orbitals.
ss
ssb
Shaded means 2 electrons
Lined means 1
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Dihelium(I) Ion, He2
ss
ssb
Draw an outline of the molecular orbitals.
Fill-in the molecular orbitals, shaded for 2
electrons, lined for 1.
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Dihelium(I) Ion, He2
The sigma bonding orbital contains two
electrons, the sigma antibonding orbital contains
one electron.
What is the electronic configuration of
the dihelium(I) ion?
(ssb)2 (ss)1
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Dihelium(I) Ion, He2
What physical properties are predicted for
the dihelium(I) ion?
(magnetic and bond order)
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Dihelium(I) Ion, He2
What physical properties are predicted for
the dihelium(I) ion?
(magnetic and bond order)
Dihelium(I) ion is paramagnetic (one unpaired
electron) and has a bond order of 1/2.
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Orbitals Are Wave Functions

• Wave functions contain mathematical terms that
  can have positive and negative values.
• An s orbital value can either be less than zero
  or greater than zero.
• The two lobes of a p orbital are separated by a
  node and have opposite signs.

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Orbitals Are Wave Functions
Different colors represent opposite mathematical
signs.
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Pi Bond Formation
y
A pi bond (p) occurs when two lobes of
each atomic orbital overlap.
z
py- py Orbital Overlap
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Pi Bond Formation
The molecular orbital does not lie directly
on the internuclear axis.
y
y
z
Resulting Bonding Molecular Orbital
py- py Orbital Overlap
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p Antibond Formation

• What is the symbol of a p antibond?
• How is a p antibond formed?
• What does a p antibond look like?

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Pi Antibond Formation
y
z
py- py Antibond Orbital Overlap
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Pi Bonds
py bonding orbital has four lobes and holds a
maximum of two electrons.
pyb bonding orbital has two lobes and holds a
maximum of two electrons.
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Pi Bonding Involving Px Orbitals
x
pxb
Resulting Bonding Molecular Orbital
px- px Orbital Overlap
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Pi Bonding Involving Px Orbitals
px
Resulting Antibonding Molecular Orbital
px- px Antibonding Orbital Overlap
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Pi Bonding Involving p Orbitals
px-px overlap gives pxb and px
py-py overlap gives pyb and py
From the mo diagram, how can you determine
that pxb and pyb are equally stable?
Why are pxb and pyb equally stable?
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Molecular Orbital DiagramsInvolving s and p
Orbitals
The molecular orbitals formed depend on the
atomic orbitals
overlap
direction
energy
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Molecular Orbital DiagramsInvolving s and p
Orbitals
Identify the orbitals that represent the following
Bonding molecular orbitals
Antibonding molecular orbitals
Nonbonding molecular orbitals
Pi bonds and antibonds
Sigma bonds and antibonds
Weak pz-s mo interaction Homonuclear
examples O2, F2
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Diatomic Molecular Orbital DiagramStrong pz-s
interaction
Homonuclear Examples Li2, B2, C2, N2
Heteronuclear Examples NO, BO, BO, CO, CO, CN,
CN
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Homonuclear Diatomic Molecules

• Determine is the sequence of molecular orbitals
  based on the strong pz-s interaction diagram.

• Determine the bond order and magnetic properties
  for homodiatomic molecules of the first nine
  elements.
• Show the bond lengths are consistent with these
  diagrams.

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Orbital Sequence
(ssn)
(ssb)
(ss)
(px,yb)
(szb)
(px,y)
(sz)
sz
px,y
szb
px,yb
ss
ssb
ssn
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Dinitrogen (14 total e)
Dilithium (6 total e)
Diberyllium (8 total e)
Diboron (10 total e)
Dicarbon (12 total e)
Complete the mo diagram for Li2, Be2, B2, C2 or N2
Bond Order and Magnetic Properties?
Bond Order and Magnetic Properties?
Bond Order and Magnetic Properties?
Bond Order and Magnetic Properties?
Bond Order and Magnetic Properties?
First, fill in the valence electrons.
Then, fill in the mo diagram
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Compare the bond order, bond length and magnetic
properties of O2, O2 , O2 and O22
O2
O2
O2
O22
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Dioxygen
What are the advantages and disadvantages of this
description of dioxygen?
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Compare the physical properties predicted for
Dioxygen by the Lewis Dot Diagram and MO Theory
Bond Order
Magnetic Properties
2
? (diamagnetic)
2
Liquid dioxygen will cling to the pole of a
magnet.
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Compare the physical properties for the
Dioxygenyl(I) Ion, Dioxygen, Superoxide Ion and
Peroxide Ion
Bond
Length
O2
paramagnetic (1)
1.123 Å
2.5
O2
paramagnetic (2)
1.207
2
O2
paramagnetic (1)
1.26
1.5
O22
diamagnetic
1.49
1
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Oxygen-Oxygen Bonds
Which oxygen-oxygen bond is easier to break?
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Difluorine (18 total e)
Dineon (20 total e)
Bond Order and Magnetic Properties?
Bond Order and Magnetic Properties?
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Homodiatomic Molecules
bond length (Å)
magnetic properties
bond order
Electronic Configuration
H2
(ssb)2
0.74
He2
(ssb)2 (ss)2
Li2
(s1sn)4 (ssb)2
2.67
Be2
(s1sn)4 (ssb)2 (ss)2
B2
(s1sn)4 (ssb)2 (ss)2 (pxb)1 (pyb)1
1.59
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Homodiatomic Molecules
Electronic Configuration
(s1sn)4 (ssb)2 (ss)2 (px,yb)4
C2
N2
(s1sn)4 (ssb)2 (ss)2 (px,yb)4 (szb)2
O2
(s1sn)4 (ssb)2 (ss)2 (px,yb)4 (szb)2 (px)1
(py)1
F2
(s1sn)4 (ssb)2 (ss)2 (px,yb)4 (szb)2 (px,y)4
Ne2
(s1sn)4 (ssb)2 (ss)2 (px,yb)4 (szb)2 (px,y)4
(sz)2
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Homodiatomic Molecules
bond length (Å)
bond order
magnetic properties
C2
1.31
diamagnetic
N2
1.10
diamagnetic
O2
1.207
paramagnetic
F2
1.42
diamagnetic
Ne2
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