Chapter 9
Covalent Bonding: Orbitals
Hybridization
• The mixing of atomic orbitals to form
special orbitals for bonding.
• The atoms are responding as needed to
give the minimum energy for the
molecule.
The Valence Orbitals on a Free
Carbon Atom: 2s, 2px, 2py, and 2pz
The Formation of sp3 Hybrid Orbitals
An Energy-Level Diagram Showing
the Formation of Four sp3 Orbitals
Tetrahedral Set of Four sp3 Orbitals
The Nitrogen Atom in Ammonia is sp3 Hybridized
sp3 Hybridization
The experimentally known structure of CH4 molecule
can be explained if we assume that the carbon atom
adopts a special set of atomic orbitals. These new orbital
are obtained by combining the 2s and the three 2p
orbitals of the carbon atom to produce four identically
shaped orbital that are oriented toward the corners of a
tetrahedron and are used to bond to the hydrogen atoms.
Whenever a set of equivalent tetrahedral atomic orbitals
is required by an atom, this model assumes that the atom
adopts a set of sp3 orbitals; the atom becomes sp3
hybridized.
The Hybridization of the s, px, and py Atomic Orbitals
An Orbital Energy-Level Diagram for sp2 Hybridization
• A sigma () bond centers along the
internuclear axis.
• A pi () bond occupies the space above
and below the internuclear axis.
H

H
C C
H
H
An sp2 Hybridized C Atom
The  Bonds in Ethylene
Sigma and Pi Bonding
The Orbitals for C2H4
When One s Orbital and One p Orbital are Hybridized, a
Set of Two sp Orbitals Oriented at 180 Degrees Results
The Hybrid Orbitals in the CO2 Molecule
The Orbital Energy-Level Diagram for the
Formation of sp Hybrid Orbitals on Carbon
The Orbitals of an sp Hybridized Carbon Atom
The Orbital Arrangement for an
sp2 Hybridized Oxygen Atom
The Orbitals for CO2
The Orbitals for N2
A Set of dsp3 Hybrid Orbitals on a Phosphorus Atom
An Octahedral Set of d2sp3 Orbitals on a Sulfur Atom
The Relationship of the Number of Effective Pairs, Their
Spatial Arrangement, and the Hybrid Orbital Set Required
The Localized Electron Model

Three Steps:
Draw the Lewis structure(s)

Determine the arrangement of electron
pairs (VSEPR model).

Specify the necessary hybrid orbitals.
Molecular Orbitals (MO)
• Analagous to atomic orbitals for atoms, MOs
are the quantum mechanical solutions to the
organization of valence electrons in molecules.
• Molecular orbitals have many of the same
characteristics as atomic orbitals, such as they
can hold two electrons with opposite spins and
the square of the molecular orbital wave
function indicates electron probability.
The Combination of Hydrogen 1s Atomic
Orbitals to Form Molecular Orbitals
The Molecular Orbitals for H2
Types of MOs
• bonding: lower in energy than the atomic
orbitals from which it is composed. Electrons in
this type of orbital will favor the molecule.
• antibonding: higher in energy than the atomic
orbitals from which it is composed. Electrons in
this type of orbital will favor the separated
atoms.
Bonding and Antibonding Molecular Orbitals (MOs)
The Molecular Orbital Energy-Level
Diagram for the H2 Molecule
The Molecular Orbital Energy-Level Diagram for the H2- Ion
Bond Order (BO)
• Difference between the number of bonding
electrons and number of antibonding
electrons divided by two.
# bonding electrons  # antibonding electons
BO =
2
• Bonds order is an indication of bond
strength. Large bond order means greater
bond strength.
The Molecular Orbital Energy-Level Diagram for the He2 Molecule
Bonding in Homonuclear
Diatomic Molecules
In order to participate in MOs, atomic
orbitals must overlap in space.
(Therefore, only valence orbitals of
atoms contribute significantly to MOs.)
The Relative Sizes of the Lithium 1s and 2s Atomic Orbitals
The Molecular Orbital Energy-Level Diagram for the Li2 Molecule
The Molecular Orbitals from p Atomic Orbitals
The Expected Molecular Orbital Energy-Level Diagram Resulting
from the Combination of the 2p Orbitals on Two Boron Atoms
The Expected Molecular Orbital Energy-Level
Diagram for the B2 Molecule
Paramagnetism

unpaired electrons

attracted to induced magnetic field

much stronger than diamagnetism
Diamagnetism

paired electrons

repelled from induced magnetic field

much weaker than paramagnetism
Diagram of the Kind of Apparatus Used to
Measure the Paramagnetism of a Sample
The Correct Molecular Orbital Energy-Level
Diagram for the B2 Molecule
Molecular Orbital Summary of Second Row Diatomics
Outcomes of MO Model
1. As bond order increases, bond energy
increases and bond length decreases.
2. Bond order is not absolutely associated with
a particular bond energy.
3. N2 has a triple bond, and a correspondingly
high bond energy.
4. O2 is paramagnetic. This is predicted by the
MO model, not by the LE model, which
predicts diamagnetism.
Combining LE and MO Models
  bonds can be described as being
localized.
  bonding must be treated as being
delocalized.
The Resonance Structures for O3 and NO3-
A Benzene Ring
The Sigma System for Benzene
The Pi System for Benzene
The NO3- Ion