Symmetry and Molecular
Orbitals (I)
Simple Bonding Model
http://chiuserv.ac.nctu.edu.tw/~htchiu/Chemistry/Fall-2005/Chemical-Bonds.htm
Lewis Structures
Octet Rule
Resonance
Formal Charge
Oxidation Number
Hypervalence
Resonance and Formal Charge
A0
A+1
VSEPR Some Molecules
VSEPR Some Molecules
VSEPR Model
Less Repulsion
More Repulsion
Bond Length
Bond Strength
Why Sharing Electron Forms
Covalent Bond?
Without Electrons, Internuclei Repulsion Forces Pushes
Nuclei Apart.
Sharing Electrons (in some area around the nuclei)
Generates Attractive Force to Bind Nucleus Together.
Why Sharing Electron Forms AntiBond?
In Some Area, Sharing Electrons Generates Repulsive
Force.
Bonding and Antibonding
Region Around The Nuclei has Binding (bonding) and
Antibinding (antibonding) Zones.
Spherical Boundary Surface of s and p
Orbitals
Spherical Boundary
Surface of d
Orbitals
Spherical Boundary Surface of f
Orbitals
Valence Bond Theory
• VB Theory is a quantum mechanical model
describes the distribution of electrons in bonds.
Developed from Lewis theory and the VSEPR model.
• Usually provides bonding picture with localized view.
• Simple VB theory cannot explain bonding in
polyatomic molecules. The concept of Hybridization
is developed to explain different geometry variations.
Describes molecular geometry easier.
• Using Delocalization and Resonance to explain
extended distribution of electrons over many atoms in
a substance.
Valence Bond Theory
N2

p
s

p
p
Square of a Wavefunction is
Probability Density
Constructive and Destructive
Interference
Hybridization
• Linear Combination of Atomic Orbitals of an Atom
forms a new set of orbitals.
• Hybridization divides the electron density distribution
of an atom into new areas.
• (sp)A
=
(1/2)1/2((s) + (p))
• (sp)B
=
(1/2)1/2((s) - (p))
• (sp2)A
=
(1/3)1/2(s) + (2/3)1/2(px)
• (sp2)B
=
(1/3)1/2(s) - (1/6)1/2(px) + (1/2)1/2(py)
• (sp2)C
=
(1/3)1/2(s) - (1/6)1/2(px) - (1/2)1/2(py)
• (sp3)A
=
(1/2)((s) + (px) + (py) + (pz))
• (sp3)B
=
(1/2)((s) + (px) - (py) - (pz))
• (sp3)C
=
(1/2)((s) - (px) + (py) - (pz))
• (sp3)D
=
(1/2)((s) - (px) - (py) + (pz))
Hybridization sp
Hybridization sp
+
-
Hybridization sp2
Hybridization sp2
Hybridization sp2 + p
Hybridization sp3
Hybridization sp3
Hybridization H2O Bonds
Hybridization C2H2 Bonds
Molecular Orbital Theory
• Electrons occupy orbitals that spread through the entire
molecule.
• Providing bonding pictures with non-localized view.
• Deals with entire area surrounding a molecule.
• Hyperchem Lite
http://www.hyper.com/sales/electronic/electronic-lite.htm
• CACAO98 (Beta Version)
http://www.chembio.uoguelph.ca/oakley/310/cacao/cacao.htm
Rules of Molecular Orbitals
Rules for forming bonding and antibonding MOs
number of total molecular orbitals = number of total atomic orbitals
atomic orbitals have the right symmetry
atomic orbitals overlap well
atomic orbitals have similar energy
Rules for filling electrons are the same for MOs and AOs.
start filling from the lowest energy orbital
follows Pauli exclusion principle and Hund's rule
Provides molecular energy information
Explains magnetic behavior
Can provide molecular structural explanation, but more
difficult to comprehend than VB theory
Bonding Molecular Orbitals
Bonding Molecular Orbitals
Constructive Interference
Symmetric: i
Antibonding Molecular
Orbitals
Antibonding Molecular Orbitals
Destructive Interference
Anti-symmetric: i
Molecular Orbital Energy Level Diagram
•Better Overlap => Higher E
•Bond Order = ½(# of B.O. e - - # of A.O. e -)
•Diamagnetic: all e- paired
•Paramagnetic: with e- unpaired
B.O.
E
E
H2+ ½
Magnetic
Property
P
H2
1
D
H2-
½
P
He2 0
-
Overlap of MOs
+
+
+
Wrong symmetry
+
Right symmetry
+
+
Bad Overlap
Good Overlap
+
+
Wrong symmetry
+
+
-
MO Symmetry
bond: no nodal plane passing through internuclear axis
bond: 1 nodal plane passing through internuclear axis
bond: 2 nodal planes passing through internuclear axis
+
+
+
+
+ +
+
-
-
-
+ +

+
-
-

+

P Orbitals
P Orbitals
MO Symmetry
g: gerade
u: ungerade
+
+
+
-
+
+
-
-
-
+
+
-
B.MO
A.MO
MO Energies of Period 2 M2 Molecules
Energy Levels of
Many Electron
Atoms in Periodic
Table
M2 MO Energy Level Diagrams
O2 –F2
1g
Li2 –N2
1g
1u
1u
1g
Higher Zeff
2s 2p more separated
2s e- closer to nuclei
2s MOs more like 2s AOs
s-s overlap not effective
1g
2s and 2pz in same space
between nuclei
Greater 1 u –2 g repulsion
2s 2pz MOs same symmetry
More mixing
MO of Period 2 M2 Molecules
LUMO
Lowest
Unoccupied
Molecular
Orbital
HOMO
Highest
Occupied
Molecular
Orbital
B.O.
1
0
1
2
3
2
1
Magnet.
D
D
P
D
D
P
D
Photoelectron
Spectroscopy
•Ek = h–I
measured known
calculated E(MO)
UV photoelectron Spectrum of N2
Heteronuclear Diatomic Molecules
• A more electronegative
• B less electronegative
+
-
+
+
+
+
CO MO Energy Level Diagram
2
1g
1u
3
1
1g
2
CO MO Energy Level Diagram
2
3
1
2
CO MO Energy Level Diagram
2
3
1
2
ICl MO Energy Level Diagram
1g
1u
1g
HF MO Energy Level Diagram
H+ F-
AMO
: :
H :F:
NBMO
BMO
Bond Order, Strength and Length
Bond Strength and Length
C-C
N-N
C-N,C-O
O-O