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
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3. Bonding in Diatomic Molecules
Diatomic: molecule contains two atoms • B A+
Ionic bonding
Covalent bonding • D C
large difference in
electronegativity
small difference in
electronegativity
Give an example of a compound with ionic bonding.
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4. Homodiatomic Molecules
The best example of covalent bonding
involves homodiatomic molecules.
Contains two of the same type of atom. • A
e.g., H2, O2, F2, N2
Why are these molecules the best examples
of covalent bonding?
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5. Homodiatomic Molecules
The best example of covalent bonding
involves homodiatomic molecules.
Contains two of the same type of atom. • A
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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6. Heterodiatomic Molecules
HF, BN and CO are heterodiatomic molecules.
Contain two different atoms.
H - F
positive end
negative end
These molecules are polar covalent.
What factors might help predict the positive
and negative ends of the molecule?
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7. 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?

8. Molecular Orbitals a bond forms
When two atoms come close to each other,
what happens to the orbitals of each atom?
a bond forms
1s atomic
orbital
ssb molecular
orbital
sigma s bonding molecular orbital
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9. Molecular Orbitals Orbital wave functions can add & subtract to give
new wave functions and
corresponding
molecular orbitals (mo).
Atoms bond
together when
the wave functions
constructively overlap.
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10. 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.
nuclei
(ssb)2 molecular
orbital
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11. 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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12. Wave Functions The amplitude (height) of each wavefunction
can either be positive or negative.
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13. Wavefunctions Bonding & Antibonding Orbitals
Constructively interfere in certain regions of space. s*
Destructively interfere in certain regions of space.
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14. Bonding & Antibonding OrbitalsH
ssb
When a bonding
molecular orbital forms,
an antibonding
molecular orbital
also forms.
ss*
Bonds form where orbitals overlap and electrons are.
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15. Atomic and Molecular Orbitals
Atomic orbitals include x y z
3dz2 1s
2py
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16. Atomic and Molecular Orbitals
Molecular orbitals include z
px* x y
ssb
sz*
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17. Atomic and Molecular Orbitals
This represents an orbital
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18. Atomic and Molecular Orbitals
carbon: 1s2 2s2 2p2
energy
Orbitals
can have
different energies
An orbital can be empty
or can contain
1 or 2 electrons.
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19. Molecular Orbital Diagrams
Examples
dihydrogen
dihelium
dihelium(I) ion
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20. Dihydrogen, H2 H energy H 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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21. Dihydrogen is diamagnetic (one pair of bonding electrons).
Dihydrogen, H2
What advantage can
an orbital gain in forming
a molecular orbital from
an atomic orbital? ao mo
ssb
energy
ss*
Dihydrogen is diamagnetic
and contains one bond
(one pair of bonding electrons). H
electronic configuration
of the hydrogen molecule.
(ssb)2
Why is dihydrogen
diamagnetic?
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22. 2 electrons to the helium
Dihelium, He2
Two electrons occupy
the highest molecular orbital
forming a ss*
ss*
energy
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
atomic orbital
of one He atom
atomic orbital
of the other
He atom
ssb
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23. Dihelium, He2 energy Why doesn’t He2 exist ss* as a stable molecule?
ssb
ss*
Why doesn’t He2 exist
as a stable molecule?
The electronic configuration
of the dihelium molecule is
(ssb)2 (ss*)2
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24. Dihelium, He2 energy Why doesn’t He2 exist ss* as a stable molecule?
ssb
ss*
Why doesn’t 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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25. Complete the molecular orbital diagram using the available electrons.
Dihelium(I) Ion, He2+ He
ss*
energy He
He+
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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26. Dihelium(I) Ion, He2+ energy He He+ These represent
the atomic orbitals.
ss*
energy He
He+
ssb
Shaded means
2 electrons
Lined
means 1
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27. Dihelium(I) Ion, He2+ energy He He+ 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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28. Dihelium(I) Ion, He2+ energy ss* ssb
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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29. What physical properties
Dihelium(I) Ion, He2+
energy
ssb
ss*
What physical properties
are predicted for the
dihelium(I) ion?
(magnetic and bond order)
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30. Dihelium(I) Ion, He2+ energy What physical properties ss*
ssb
ss*
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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31. 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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32. Orbitals Are Wave Functions
Different colors represent
opposite mathematical signs.
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33. atomic orbital overlap.
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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34. does not lie directly on
Pi Bond Formation
The molecular orbital
does not lie directly on
the internuclear axis. z y y y z
Resulting Bonding
Molecular Orbital
py- py Orbital Overlap
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35. p Antibond Formation What is the symbol of a p antibond?
How is a p antibond formed?
What does a p antibond look like?

36. Resulting Antibonding
Pi Antibond Formation y
Resulting Antibonding
Molecular Orbital z y z
py- py Antibond
Orbital Overlap
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37. Pi Bonds py* pyb py* bonding orbital pyb 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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38. Pi Bonding Involving Px Orbitals
pxb
Resulting Bonding
Molecular Orbital
px- px Orbital Overlap
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39. Pi Bonding Involving Px Orbitals
px- px Antibonding
Orbital Overlap
Resulting Antibonding
Molecular Orbital
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40. Pi Bonding Involving p Orbitals
px-px overlap gives pxb and px* z y
py-py overlap gives pyb and py* x
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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41. Molecular Orbital Diagrams Involving s and p Orbitals
energy 2s 1s 2p
The molecular orbitals
formed depend on
the atomic orbitals’
overlap
direction
energy
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42. Molecular Orbital Diagrams Involving s and p Orbitals
Identify the orbitals
that represent the
following
Sigma bonds and antibonds
Nonbonding molecular
orbitals
Antibonding molecular
orbitals
Pi bonds and antibonds
Bonding molecular
orbitals
Weak pz-s mo interaction
Homonuclear examples:
O2, F2
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43. Diatomic Molecular Orbital Diagram Strong pz-s interaction
energy 2s 1s 2p
Homonuclear
Examples:
Li2, B2, C2, N2
Heteronuclear
Examples:
NO, BO, BO+,
CO, CO+,
CN, CN–
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44. 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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45. Orbital Sequence (ssn) (ssb) (ss*) (px,yb) (szb) (px,y*) (sz*) sz*
energy 2s 1s 2p
px,y*
szb
px,yb
ss*
ssb
ssn
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46. Diberyllium (8 total e–)
Diboron (10 total e–)
Dinitrogen (14 total e–)
Dicarbon (12 total e–)
Diberyllium (8 total e–)
Dilithium (6 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?
energy 2s 1s 2p
ssn
ssb
ss*
px,yb
szb
px,y*
sz*
First,
fill in the
valence
electrons.
Then,
fill in the
mo diagram
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47. Compare the bond order, bond length and magnetic properties of O2, O2+ , O2– and O22–
energy 2s 1s 2p
ssn
ssb
ss*
px,yb
px,y*
sz*
szb
O22–
O2+
O2– O2
1.49 Å
properties?
1.26 Å
properties?
1.207 Å
properties?
1.123 Å
properties?
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48. Dioxygen O What are the advantages and disadvantages•
What are the advantages and disadvantages
of this description of dioxygen?

49. Liquid dioxygen will cling to the pole of a magnet.
Compare the physical properties predicted for Dioxygen by the Lewis Dot Diagram and MO Theory O •
Bond Order
Magnetic Properties
Lewis Dot
Structure 2
? (diamagnetic)
Molecular
Orbital
Theory
paramagnetic
2 unpaired electrons 2
Liquid dioxygen will cling to the pole of a magnet.
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50. Compare the physical properties for the Dioxygenyl(I) Ion, Dioxygen, Superoxide Ion and Peroxide Ion
Bond
Bond
Order
Magnetic
Properties
Length
O2+
1.123 Å
2.5
paramagnetic (1) O2
1.207 2
paramagnetic (2)
O2–
1.26
1.5
paramagnetic (1)
O22–
1.49 1
diamagnetic
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51. Which oxygen-oxygen bond is easier to break?
Oxygen-Oxygen Bonds O • H O •
Which oxygen-oxygen bond is easier to break?

52. Dineon (20 total e–) Difluorine (18 total e–) energy 2s 1s 2p ssn ssb
Bond Order and Magnetic Properties?
Bond Order and Magnetic Properties?
energy 2s 1s 2p
ssn
ssb
ss*
px,yb
px,y*
sz*
szb
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53. Homodiatomic Molecules
bond
length
(Å)
bond
order
magnetic
properties
Electronic Configuration H2
(ssb)2 1
0.74
diamagnetic
paramagnetic
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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54. Homodiatomic Molecules
Electronic Configuration C2
(s1sn)4 (ssb)2 (ss*)2 (px,yb)4 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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55. Homodiatomic Molecules
bond
length (Å)
bond
order
magnetic
properties C2 2 3 1
1.31
diamagnetic N2
1.10
diamagnetic O2
1.207
paramagnetic F2
1.42
diamagnetic
Ne2
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