Molecular Orbital Theory Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology
Dec 22, 2015
Molecular Orbital TheoryEdward A. Mottel
Department of Chemistry
Rose-Hulman Institute of Technology
A Little Review
What is an orbital?
What is the maximum number of electronsthat can be in one orbital?
What is the name of the mathematical functionthat determines the shape of an orbital?
Give an example of an atomic 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 forms1s atomic
orbital1s atomic
orbitals
b molecularorbital
sigma s bonding molecular orbital
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Molecular Orbitals
Orbital wave functionscan add & subtract to givenew wave functions andcorrespondingmolecular orbitals (mo).
Atoms bondtogether when
the wave functionsconstructively overlap.
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SIGMA BOND ()
A bond between two atoms in which the electrondensity of the molecular orbital is between the
two nuclei is called a sigma bond.
(sb)2 molecular
orbital
nuclei
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Molecular Orbital Theory
Atomic orbitals can mix togetherto give a new set of molecular orbitals.
Similarities of atomic & molecular orbitals2 electrons max/orbital
occupy specific regions of space
One molecular orbital is formed for each atomic orbital used
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Orbitals Are Wave Functions
Wave functions contain mathematical termsthat can have positive and negative values.
An s orbital value can either beless than zero or greater than zero.
The two lobes of a p orbital are separated bya node and have opposite signs.
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z
Sigma Antibond Formation
pz- pz Orbital Overlap
(z*)
Resulting AntibondingMolecular Orbital
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Sigma Bonds indicates themost probable
electron positionis on the
internuclearaxis
(zb)
(z*)
b indicates a bondingmolecular orbital
z indicates themolecular orbital involves
two pz atomic orbitals
* indicates an antibondingmolecular orbital
Electrons in this orbitalwill weaken the bondsbetween these atoms.
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Sigma Bonds
z
s indicates the molecular orbital involvesat least one s atomic orbital.
(sb)
(s*)
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Pi Bond Formation
z
y
py- py Orbital Overlap
A pi bond () occurswhen two lobes of eachatomic orbital overlap.
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Pi Bond Formation
z
y
z
y
py- py Orbital Overlap Resulting BondingMolecular Orbital
yThe molecular orbital
does not lie directly onthe internuclear axis.
Antibond Formation
What is the symbol of a antibond?
What does a antibond look like?
How is a antibond formed?
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Pi Antibond Formation
z
y
py- py Antibond Orbital Overlap
Resulting AntibondingMolecular Orbital
z
y
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Pi Bonds
yb
yb bonding orbital
has two lobes andholds a maximumof two electrons.
y*
y* bonding orbitalhas four lobes andholds a maximumof two electrons.
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Pi Bonding Involving Px Orbitals
xx
px- px Orbital OverlapResulting BondingMolecular Orbital
xb
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Pi Bonding Involving Px Orbitals
px- px AntibondingOrbital Overlap
Resulting AntibondingMolecular Orbital
xx x*
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Pi Bonding Involving p Orbitals
2ppx-px overlap gives x
b and x*
py-py overlap gives yb and y*
From the mo diagram,how can you determine that
xb and y
b
are equally stable?x
z
yy
Why are xb and y
b equally stable?
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Molecular Orbital DiagramsInvolving s and p Orbitals
ener
gy2s
1s
2p
overlap
direction
energy
The molecular orbitalsformed depend onthe atomic orbitals’
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Molecular Orbital DiagramsInvolving s and p Orbitals
2s
1s
2p
Bonding molecularorbitals
Antibonding molecularorbitals
Nonbonding molecularorbitals
Sigma bonds and antibonds
Pi bonds and antibonds
Identify the orbitalsthat represent the
following
Weak pz-s mo interaction Homonuclear examples:
O2, F2
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Diatomic Molecular Orbital DiagramStrong pz-s interaction
ener
gy
2s
1s
2pHomonuclearExamples:
Li2, B2, C2, N2
HeteronuclearExamples:
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
ener
gy
2s
1s
2p
sn
sb
s*
x,yb
zb
x,y*z*
(sn) (s
b) (s*) (x,yb) (z
b) (x,y*) (z*)
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Complete the mo diagram for Li2, Be2, B2, C2 or N2
Dilithium (6 total e–) Bond Order and Magnetic Properties?
Diberyllium (8 total e–) Bond Order and Magnetic Properties?
Diboron (10 total e–) Bond Order and Magnetic Properties?
Dicarbon (12 total e–)Bond Order and Magnetic Properties?
Dinitrogen (14 total e–)
ener
gy
2s
1s
2p
sn
sb
s*
x,yb
zb
x,y*z*
Bond Order and Magnetic Properties?
First,fill in thevalence
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 O2
2–
ener
gy
2s
1s
2p
sn
sb
s*
x,yb
x,y*z*
zb
O2O2+O2–O22–
1.207 Åproperties?1.123 Å
properties?1.26 Å
properties?1.49 Å
properties?
Dioxygen
What are the advantages and disadvantagesof this description of dioxygen?
OO ••
••• •
•• ••• •
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Compare the physical properties predicted for Dioxygen by the Lewis Dot Diagram and MO Theory
Bond Order Magnetic Properties
Lewis DotStructure
MolecularOrbitalTheory
2 ? (diamagnetic)
2paramagnetic
2 unpaired electrons
OO ••
••• •
•• ••• •
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
BondLength
BondOrder
O2+
O2
O2–
O22–
1.123 Å
1.207
1.26
1.49
2.5
2
1.5
1
MagneticProperties
paramagnetic (1)
paramagnetic (2)
paramagnetic (1)
diamagnetic
Oxygen-Oxygen Bonds
Which oxygen-oxygen bond is easier to break?
OO
••• •
••
• • HOH O
• • • •
• • • •
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Difluorine (18 total e–)Bond Order and Magnetic Properties?
Dineon (20 total e–)
ener
gy
2s
1s
2p
sn
sb
s*
x,yb
x,y*z*
zb
Bond Order and Magnetic Properties?
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Homodiatomic MoleculesElectronic Configuration
H2
He2
Li2
Be2
B2 (sn)4 (s
b)2 (s*)2 (xb)1 (y
b)1
(sn)4 (s
b)2 (s*)2
(sn)4 (s
b)2
(sb)2 (s*)2
(sb)2
bondlength
(Å)
magneticproperties
0.74
2.67
1.59
diamagnetic
diamagnetic
paramagnetic
bondorder
1
0
1
0
1
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Homodiatomic Molecules
C2
N2
O2
F2
Ne2
bondlength (Å)
magneticproperties
1.31
1.207
diamagnetic
diamagnetic
paramagnetic
bondorder
2
3
2
1
0
diamagnetic1.10
1.42
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Skeleton Diagram FailuresCarbon Monoxide
C O C Oor
How would the hybridization of theatoms in carbon monoxide be described?
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Carbon Monoxide
Sigma orbital overlaps of CO.
+
- + -+
+
+ + + +
+
- + - +
-
+ + - -
-
- + + -
-
- + + -
-
- + + -
+
- + - +
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Beryllium Hydride
Draw the orbital overlaps of BeH2.
Rank the orbitals in terms of energy.
++ +
++ - -
-+ +
-+ + -
Draw a molecular orbital diagram of BeH2.
(draw the nodes in each diagram)
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energ
y
BeH2Be 2 H
Sigma () bonds form
orbitals are conserved
two bonds are formed
all e- are paired
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Draw the molecular orbital diagram forthe 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- orbitalsgoing to split?
How many nonbonding orbitals are expected?
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Nitrate Ion
N••••
• •• •O
O ••••
•• ••
O
••
••••
••
N••••
• •• •O
O ••••
••••
O
••
••••
••
N••••
• •• •O
O ••••
••
O ••••
••••••
The double bond is delocalized overthe three nitrogen-oxygen bonds.
Bond order = 1.33
+ + +
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Nitrate Ion
The nitrogen-oxygen bond length is intermediate between N-O and N=O.
typical N-O bond length: 1.40 Å
typical N=O bond length: 1.21 Å
-
NOO
O1.22 Å
What is thehybridizationof nitrogen?
How do the orbitals of the atomsin nitrate overlap?
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Nitrate Ion
Top down view(xz plane)
The nitrogen atomin nitrate ion
is sp2 hybridizedand overlaps a
pz orbital oneach oxygen.
three N - Osigma bonds
N••••
• •• •O
O ••••
•• ••
O
••
••••
••
+
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Nitrate Ion
Top down view(xz plane)
If you don’tbelieve in
hybridization.
three N - Osigma bonds
N••••
• •• •O
O ••••
•• ••
O
••
••••
••
+
How doesthe doublebond form?
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Nitrate Ion
Edge on view
N••••
• •• •O
O ••••
•• ••
O
••
••••
••
pi overlap involvesthe nitrogen py orbitalwith all three oxygen
py orbitals toform one pi bond
the oxygen orbitalswith single electrons
change from oneoxygen atom to another
+y
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Nitrate Ion
Edge on view
one N - O pi bonddelocalized over
three oxygen atomsthis hybridizationrequires that the
nitrate ion isplanar
What would the py-orbitalslook like if all four atoms
in this ion were not planar?
y
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Nitrate Ion
Edge on view
one N - O pi bonddelocalized over
three oxygen atomsifnitrate ion
wasn’tplanar
What would the py-orbitalslook like if all four atoms
in this ion were not planar?
y