Molecular Orbital Theory

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Molecular Orbital Theory

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

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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 Orbital Theory
Atomic orbitals can mix together to give a new
set of molecular orbitals.
One molecular orbital is formed for each atomic
orbital used
Similarities of atomic molecular orbitals
2 electrons max/orbital occupy specific regions
of space
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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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Sigma Bond Formation
z
pz- pz Orbital Overlap
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Sigma Bonds
pz- pz Orbital Overlap
Resulting Molecular Orbital
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Sigma Antibond Formation
z
pz- pz Orbital Overlap
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Sigma Antibond Formation
z
(sz)
pz- pz Orbital Overlap
Resulting Antibonding Molecular Orbital
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Sigma Bonds
s indicates the most probable electron
position is on the internuclear axis
b indicates a bonding molecular orbital
indicates an antibonding molecular orbital
z indicates the molecular orbital involves two pz
atomic orbitals
Electrons in this orbital will weaken the
bonds between these atoms.
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Sigma Bonds
s indicates the molecular orbital involves at
least one s atomic orbital.
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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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Skeleton Diagram FailuresCarbon Monoxide
How would the hybridization of the atoms in
carbon monoxide be described?
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energy
O
CO
C
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Carbon Monoxide
Sigma orbital overlaps of CO.




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Is the HOMO of carbon monoxide bonding,
nonbonding or antibonding?
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Where on carbon monoxide is the HOMO located?
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Species containing three or more atoms
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Beryllium Hydride
Draw the orbital overlaps of BeH2.
Rank the orbitals in terms of energy.
(draw the nodes in each diagram)
Draw a molecular orbital diagram of BeH2.
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orbitals are conserved
two bonds are formed
all e- are paired
energy
Sigma (?) bonds form
2 H
BeH2
Be
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Draw the molecular orbital diagram for the
nitrate ion.
What is the hybridization of nitrogen?
How many atomic orbitals are there?
How many p-? orbitals are there?
How are the energies of the p-? orbitals going to
split?
How many nonbonding orbitals are expected?
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Nitrate Ion



The double bond is delocalized over the three
nitrogen-oxygen bonds.
Bond order 1.33
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Nitrate Ion
What is the hybridization of nitrogen?
The nitrogen-oxygen bond length is intermediate
between N-O and NO.
How do the orbitals of the atoms in nitrate
overlap?
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Nitrate Ion
The nitrogen atom in nitrate ion is sp2
hybridized and overlaps a pz orbital on each
oxygen.

Top down view (xz plane)
three N - O sigma bonds
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Nitrate Ion
If you dont believe in hybridization.

Top down view (xz plane)
How does the double bond form?
three N - O sigma bonds
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Nitrate Ion
pi overlap involves the nitrogen py orbital with
all three oxygen py orbitals to form one pi bond

the oxygen orbitals with single electrons change
from one oxygen atom to another
Edge on view
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Nitrate Ion
one N - O pi bond delocalized over three oxygen
atoms
this hybridization requires that the nitrate ion
is planar
What would the py-orbitals look like if all four
atoms in this ion were not planar?
Edge on view
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Nitrate Ion
one N - O pi bond delocalized over three oxygen
atoms
if nitrate ion wasnt planar
What would the py-orbitals look like if all four
atoms in this ion were not planar?
Edge on view
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energy
3 O
N
NO3-
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Sigma Bonding Patterns Nitrogen s, px and py
orbitals overlap with oxygen.
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energy
3 O
N
NO3-
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How are the energies of the p-? orbitals going to
split?
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energy
3 O
N
NO3-
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energy
O
CO
C
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energy
O
O
O
N
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