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Lecture 11 Bonding Theories
Text: Chapter 3, Sections 4 and following
Covalent Bonding and Orbital Overlap
valence-bond theory
orbital overlap
H
H
H
Cl
Cl
Cl
1s
3p
3p
3p
Sigma bonds form the skeleton of the molecule. For diatomic molecules, one
atomic orbital from each atom combine to form a -bond between the atoms.
Chapter 9 Molecular Geometry 1
Pi bonds form the extra double or triple bonds in a bond region.
Hybrid Orbitals (Used for molecules with 3 or more atoms)
The mathematical combinations of wave functions on the same atom to form a new
set of equivalent wave functions are called hybrid atomic functions. On an atom,
there is one hybrid orbital per Electron Domain. They point in the same directions
as the lone pairs and bond regions.
Chapter 9 Molecular Geometry 2
Chapter 9 Molecular Geometry 3
1s
2s
2p
1s
sp
2p
1s
2s
2p
1s
sp2
2p
1s
2s
2p
1s
sp3
Geometry
Bond Angles
Hybridization
Linear
180°
2 sp orbitals
Trigonal
120°
3 sp2 orbitals
Tetrahedral
109.5°
4 sp3 orbitals
Trigonal bipyramidal
2 x 90°, 3 x 120°
5 sp3d orbitals
Octahedral
90°
6 sp3d2 orbitals
Chapter 9 Molecular Geometry 4
Multiple Bonds
internuclear axis
sigma () bonds
electron density along internuclear axis.
pi (p) bonds overlap of two p orbitals oriented perpendicularly to the internuclear
axis.
Overlap is above and below internuclear axis, no probability of finding electron on
the internuclear axis.
H
C
C
H
H
H
=
H
H
H
C
C
All single bonds are sigma bonds.
All multiple bonds contain one sigma bond.
Delocalized bonding
Chapter 9 Molecular Geometry 5
H
Molecular Orbitals
A molecular orbital is a mathematical function that describes the wave-like
behavior of an electron in a molecule.
Whenever two atomic orbitals overlap, two molecular orbitals form.
Chapter 9 Molecular Geometry 6
y = exp(-x)
y = exp(-abs(x))
y = exp(-|x-1|)
y = exp(-|x+1|)
Chapter 9 Molecular Geometry 7
y = exp(-|x-1|) + exp(-|x+1|)
y = exp(-|x-1|) - exp(-|x+1|)
Chapter 9 Molecular Geometry 8
energy-level diagram (molecular orbital diagram)
bonding molecular orbital ()
antibonding molecular orbital (*)
Procedure for Using Molecular Orbital Energy Diagrams
1) Sum up electrons from two atoms and possible charge
2) Fill in the boxes on appropriate MO diagram according to Hund’s rule.
Chapter 9 Molecular Geometry 9
Bond Order =
1
2
Bond Order =
# bonding electrons - # antibonding electrons
1
single bond
2
double bond
3
triple bond
Bond orders can be 1/2, 3/2, 5/2 with radicals
Chapter 9 Molecular Geometry 10
Second-Row Diatomic Molecules
1. The number of molecular orbitals formed equals the number of atomic orbitals
combined.
2. Atomic orbitals combine most efficiently with other atomic orbitals of similar
energy.
3. As the overlap increases the bonding MO lowers in energy.
4. Each molecular orbital can accommodate, at most, two electrons, with their
spins paired (Pauli exclusion principle).
5. When MOs have the same energy, one electron enters each orbital (with the
same spin) before spin pairing occurs (Hund’s rule).
Molecular Orbitals from 2p Atomic Orbitals
paramagnetism – some electrons unpaired
diamagnetism – all electrons paired
NO, NO+, NO–
Chapter 9 Molecular Geometry 11
Chapter 9 Molecular Geometry 12