Orbital Theory (Incomplete)
Orbital Theory or MO Theory utilizes concepts of atomic orbitals to
rationalize general behaviour of chemicals. MO Theory is based on the
“mixing” or combining of orbitals. As two atoms form a successful
covalent bond, their valence electrons become shared. In the case of
atomic orbitals, only major interactions between the nucleus and
electrons are considered; no electron-electron interactions are
considered. However, when electrons on shared, their behaviour changes
wavefunctions that defined electron motion with respect to one nucleus
is no longer applicable. The complications that arise from the
interactions of a second nucleus are very complex, and difficult to
accurately model. The resulting mathematical equations are very complex.
MO Theory takes a more general approach. Instead of combining the
wavefunctions and adding various correction factors, only the visible
representations are combined. The resulting linear combinations of the
atomic orbitals give rise to a variety of molecular orbitals.
In order for
orbitals to mix, they need to be of comparable energy. If the energy
levels are two high or low, they have no net interaction with one
another. Each suitable pairing has a bonding orbital and an anti-bonding
combination. The bonding and antibonding orbitals between two s-orbitals
is denoted denoted σ and σ* respectively. Bonding and antibonding
between a s-orbital and p-orbital or two p orbitals is denoted by π and
π* respectively. This notation will be left off the MO diagrams produced
due to space restrictions.
When drawing up
the angular portions of the orbitals, different colours were used to
denote the various phases. While there exist no real differences between
the two phases, there are theoretical considerations. When two phases of
the same type align, they generate a mutual or constructive field that
leads to bonding. When two phases of the opposite type align, they
generate a “destructive” field that leads to anti-bonding.
There will be
two examples presented: Hydrogen Fluoride and Carbon Monoxide.
Fluoride (HF) is an excellent example to introduce the primary concepts
of MO Theory.
only one single valence electron in an s-orbital. It has an electron
configuration of 1s1. The 1s refers to the
valence shell. The regular “1” refers to its general energy level (1st
row element), and the s denotes its shape type (a spherical shape). The
superscript “1” means that it has one electron in this shell.
seven valence electrons available for bonding. It has an electron
configuration of [He]2s22p5. The [He] symbol means
that it has base electron configuration that is the same as helium
(1s2). The square bracket notation is used for both convenience and
clarity. Any electrons that are included in base element (in this case
He) are considered non-reactive. The two electrons in the 1s shell do
not participate in bonding. The 2s22p5
means that there are seven electrons available for bonding: two reside
in a 2s orbital, and five are in a 2p orbital. This following is a
picture of their relative energies.
In total, the
combination of the single electron of hydrogen and seven of fluorine
means that there are eight electrons available for bonding. We begin by
drawing the orbitals that are available for bonding, and their relative
energies (top left). The first thing to note is that the 2s orbital of
the F atom is too low to participate in bonding with the 1s of the H
(top center). This means that we draw a line of the same energy level as
the 2s orbital in the middle. While it does not participate in
bonding it still carries electrons. Also, there are two
orbitals that have unfavorable geometry. When the axis of the angular
elements is perpendicular to the H atom, successful overlap cannot occur
Of all the
bonding possibilties, the 1s of the H can mix with a p orbital that lies
on the same axis. This generates one bonding (low energy) and one
anti-bonding pair high energy (bottom left). A pair of dashed lines are
used to draw together the mixing orbitals (bottom center). Now will fill
up the diagram with the either electrons available, starting from the
bottom up (bottom right). .This completes the diagram for Hydrogen
(CO) will build upon the general principles that the hydrogen fluoride
example introduced, but will be slightly more involved.
Carbon has an
electron configuration of [He]2s22p2, so it has
four valence electrons available for bonding. Oxygen has six valence
electrons from its electronic configuration of [He]2s22p4.
This is a total of 10 electrons.
Unlike in the
case of hydrogen fluoride, both atoms have s and p orbitals that are
available for bonding. As a result, there
are more possible interactions. Start with the
relative energy levels of all the orbitals (top left). The s-Orbital of
oxygen is far to low to participate in bonding, and is drawn into the
middle. If the s-orbital of carbon, and one of the p-orbitals from
carbon align (such that the angular element of the p-orbital is on an
axis that runs through the s-orbital), there can be some successful
overlap (top right). Another pair with
bonding character lie on the axis that runs through both atoms. Imagine
a pair of p-orbitals from both atoms that have the same axis of
symmetry. One lobe of the p from each of the atoms can mix together and
overlap. This creates a moderate bonding orbital (top right).
In the case of
the last four orbitals, orbital overlap is a possibility, but it
requires that the two atoms be very close together, and the overlap is
very minimal. The axis of these orbitals are parallel, and overlap is
due mainly to the width of the lobes of the orbitals. As such, the
energy reduction from the orbital mixing is minimal. However, the
resulting anti-bonding combination is only slightly higher in energy.
(bottom right). The bottom right diagram shows filling of the ten
Introduction to Quantum Chemistry