Unit 9: Orbitals and Theories of Chemical Bonding
Overview:
 Valence bond theory and orbital overlap
 Hybridization
 Multiple bonding and delocalized systems
 Molecular orbital theory
 Bond order
 Molecular orbital diagrams for simple diatomic molecules
 Application of molecular orbital theory to unsaturated and aromatic systems
Learning Outcomes:
 Understand
o the concept of valence bond theory and orbital overlap model
o the concept of hybridization to accommodate varying bond angles
o application of valence bond theory to multiple bonding
o application of valence bond theory to benzene and other delocalized systems
o the three principles of molecular orbital theory – note one should add a fourth
namely the extent of bonding depends crucially on the extent to which the orbitals
can overlap.
o The concept of bond order and be able to calculate bond order for chemical bonds
in simple molecules
o the reason for the non-existence of certain diatomic molecules such as Be2
because of their zero bond order
 Be able to construct molecular orbital diagrams for simple diatomic molecules
 Understand
o application of molecular orbital theory to simple heteronuclear diatomic
molecules
o application of molecular orbital theory to resonance structures and delocalized
orbitals noting that from n atomic orbitals we generate n molecular orbitals
o application of molecular orbital theory to benzene
Readings: Sections 9.1 – 9.3
Assignment: From Chapter 9: # 2, 4, 8, 18, 20, 22, 42
Introduction:
To this point, you have learned some very practical theories of bonding that allow you to
predict many properties of molecules. Recall that theories are modified or new theories are
developed to address observations not explained by earlier theories. With this in mind, we will
look at two more theories of chemical bonding: valence bond (VB) theory and molecular orbital
(MO) theory. These are a little more complicated than VSEPR theory, but we use them because
we need them. For many types of bonding addressed at the first-year level, VSEPR theory works
very well, so there is no reason for you to discard it.
By now, you are comfortable with the idea of orbitals on atoms. The main idea behind
valence bond theory is overlap of these atomic orbitals. As orbitals overlap, electrons are shared
between the two atoms, and the bonded atoms that result are lower in energy than the two
independent atoms that formed the diatomic molecule. This concept is easy to understand, but
hybridization is somewhat more complex. For example, if you consider the p atomic orbitals on
carbon, px, py and pz, they are orthogonal to each other. If these simple atomic orbitals were used
to explain the bonding of carbon, the bond angles at carbon would be 90º. This does not fit
experimental data so the concept of hybridization is introduced. Here, the s and p orbitals are
mixed together. This is the hybridization. The resulting hybrid orbitals (sp, sp2 and sp3) are
neither pure s nor p, but have intermediate character (just as a mule is neither a donkey nor a
horse, but a hybrid of the two). After hybridization new sets of orbitals result in bond angles of
180º, 120º and 109.5º which support the experimental data.
When orbitals overlap in an end-on fashion, a sigma (σ) bond results where electron
density lies along the internuclear axis joining the two atoms. Atoms that are sp or sp2
hybridized also contain unhybridized p orbitals. If the atoms are small enough, the half-filled p
orbitals can overlap in a side-on fashion resulting in a pi (π) bond. The π bond forms in addition
to the σ bond. If you look at some models you will see that the electron density of the π bond
lies around, not along, the internuclear axis. This has the effect of restricting rotation of the
groups connected by the bonds. Note that the methyl groups of ethane can freely rotate with
respect to each other, but the methylene groups of ethene can not.
Molecular orbital theory allows us to more accurately describe the bonding in molecules.
Using valence bond theory we said that the electrons were localized between the two atoms that
were connected by the bond. According to MO theory, atomic orbitals combine to form
molecular orbitals, and the electrons are delocalized over the molecule. Also the total number of
atomic orbitals that combine must equal the total number of molecular orbitals that form. These
new molecular orbitals are categorized as bonding orbitals and anti-bonding orbitals. Electrons
in bonding orbitals serve to stabilize the molecule so bonding orbitals are lower in energy than
the atomic orbitals from which they were formed. Electrons in antibonding orbitals serve to
destabilize the molecule, and these orbitals are higher in energy than the atomic orbitals from
which they were formed. If the energies of the combining atomic orbitals are similar, the orbital
overlap is better and a stronger bond is formed. As the difference in energies of the atomic
orbitals increases, the weaker the bond. Notice that MO theory accurately predicts that He2 does
not form, but He2+ is stable. Extending MO theory to the second-row diatomic molecules and
their ions shows how useful this theory is. If you consider the electronic structure of O2 using
the valence bond approach, you would say that there is a π bond and all electrons are paired up.
Since all electrons are paired, the molecule should be diamagnetic. It turns out that O2 is
paramagnetic, and this is demonstrated using an MO diagram. Create the MO diagram of O2 and
fill the molecular orbitals with electrons. Just as you followed the Pauli Exclusion Principle and
Hund's rule when deriving the electronic configurations of atoms, do the same when filling
molecular orbitals starting with the lowest energy orbitals first. As you add the last two electrons
to the MO diagram of O2 you will notice that each of these electrons goes into an anti-bonding pi
(π*) orbital. Since the electrons are not paired, MO theory correctly predicts the magnetism of
O2. As predicted by valence bond theory and supported by experimental evidence, the bond
order of O2 is two. This is consistent with the MO diagram too; subtract the number antibonding electrons from bonding electrons and divide the result by two. This will give the correct
bond order.
Concluding Remarks:
The material presented in this chapter is abstract, but it provides more sophisticated
theories to explain bonding. To appreciate the difference in VB and MO theories, attempt to
explain how these theories differ, what aspects of bonding each address and the strengths of each
theory. After doing this exercise, you will have a better idea of which theory to use when
addressing a specific question about bonding. Molecular orbital theory is commonly
encountered in advanced courses in spectroscopy and organic and inorganic chemistry.