In our discussion of valence bond theory, we saw
that chemical bonds are formed when two nuclei share a pair of
electrons between them. The sharing lowers the potential energy of
both electrons by exposing them to increased nuclear attractions. The
decrease in potential energy is greatest when the two electrons are
confined to a region between the two nuclei. This type of bond is
described as a localized bond. For example, in methane,
CH4, each pair of electrons is considered to be confined
to the region between the carbon nucleus and a hydrogen nucleus. One
of the limitations of valence bond theory is that it assumes all
bonds are localized bonds. As we will see, this is not a valid
Another limitation of valence bond theory is that is sometimes
makes incorrect predictions. The case of dioxygen provides a good
example. Consider the two Lewis structures for dioxygen shown in
Exercise 1 Which of the
alternatives in Figure 1 best represents the structure of dioxygen
according to valence bond theory?
Since structure 2 implies that all of the electrons are
paired, you should expect dioxygen to be diamagnetic. It is not.
Several lines of experimental evidence indicate that dioxygen is
paramagnetic, i.e. it contains at least one unpaired electron.
Whenever a theory makes incorrect predictions or is shown to be
inconsistent with experimental fact, chemists have two choices:
We will see how chemists have modified valence bond theory to deal
the limitations of localized bonds when we discuss resonance theory.
But first we will consider molecular orbital (MO) theory as an
alternative to valence bond theory.
Chemists view molecules as combinations of atoms. They consider
molecular orbitals as combinations of atomic orbitals, specifically
as linear combinations of atomic
orbitals. Don't let this term put you off. It simply means
that molecular orbitals are formed by adding and subtracting atomic
orbitals. Remember, electrons behave like waves, and their wavelike
behavior may be described by mathematical functions similar to the
sine or cosine function. These mathematical functions are what we
call orbitals. The addition of atomic wave functions is analogous to
constructive interference that occurs with sound waves. The
subtraction corresponds to destructive interference.
Consider the simplest molecule, dihydrogen. In our discussion of
Lewis structures, we imagined a process in
which two hydrogen atoms came together to form a molecule of
dihydrogen. That process represents a linear combination of the two
hydrogen atoms' 1s atomic wave functions. Mathematically molecular
orbital theorists describe the process by the equation y =
1sA + 1sB, where y (psi) stands for the molecular orbital, while
1sA and 1sB represent the
atomic orbitals for HA and HB, respectively.
y is the
molecular orbital equivalent of a s bond in
valence bond theory.
A fundamental rule of molecular orbital theory is that the number
of molecular orbitals must be equal to the number of atomic orbitals.
For two hydrogen atoms, there are two atomic orbitals, which means
that there must be two molecular orbitals for dihydrogen. The second
molecular orbital is described by the equation y* =
1sA - 1sB. There is no valence bond equivalent
Figure 2 illustrates the energy changes that accompany these
linear combinations of atomic orbitals. The molecular orbital y corresponds to the minimum of the potential
energy diagram we considered during our introductory discussion of
valence bond theory.
Figure 3 offers an alternative description of the information
shown in Figure 2. The colored spheres and elipses represent regions
of electron density about the nuclei, which are shown as dots at the
centers of the two 1s atomic orbitals.
There are several features of Figure 3 that deserve comment:
Before we turn our attention to the MO diagram of dioxygen, there
is one additional aspect of Figures 1 and 2 that you should know. The
MOs y and y*are called the Highest Occupied Molecular Orbital (HOMO) and
the Lowest Unoccupied Molecular Orbital
(LUMO), respectively. These terms will be useful when we discuss
chemical reactivity and spectroscopy. Chemical reactions involve the
transfer of electron density from the HOMO of one reactant to the
LUMO of another. Spectroscopy is the interaction of light with
matter, an interaction which alters the populations of different
Don't worry about the details of this MO diagram. The important
feature of the figure is that there are two HOMOs that have the same
energy. Each one contains a single electron. According to Hund' Rule the energy of the system will be
lower if the spins of these two electrons are unpaired than if they
are paired. In other words, the most stable form of dioxygen should
be paramagnetic, not diagmagnetic.