goal of molecular orbital theory is to describe molecules in a similar
way to how we describe atoms, that is, in terms of orbitals, orbital
diagrams, and electron configurations. For example, to give you a
glimpse at where we are headed, the following are orbital diagrams for O2
line in the molecular orbital diagram represents a molecular orbital,
which is the volume within which a high percentage of the negative
charge generated by the electron is found. The molecular orbital volume
encompasses the whole molecule. We assume that the electrons would fill
the molecular orbitals of molecules like electrons fill atomic orbitals
|The molecular orbitals are filled in a
way that yields the lowest potential energy for the molecule.|
|The maximum number of electrons in each
molecular orbital is two. (We follow the Pauli exclusion principle.)|
|Orbitals of equal energy are half
filled with parallel spin before they begin to pair up. (We follow
we continue with a description of a model used to generate molecular
orbital diagrams, letís get a review of light and electron waves and
how two waves can interact. The wave description of light describes the
effect that the light has on the space around it. This effect is to
generate an oscillating electric and magnetic fields. These fields can
vary in intensity, which is reflected in varying brightness of
wave description of the electron describes the variation in the
intensity of negative charge generated by the electron.
Light waves can
interact in-phase, which leads to an increase in the intensity of the
light (brighter) and out-of-phase, which leads to a decrease in the
intensity of the light (less bright). Electron waves can also interact
in-phase and out-of-phase. In-phase interaction leads to an increase in
the intensity of the negative charge. Out-of-phase interaction leads to
a decrease in the intensity of the negative charge.
common approximation that allows us to generate molecular orbital
diagrams for some small diatomic molecules is called the Linear
Combination of Atomic Orbitals (LCAO) approach. The following
assumptions lie at the core of this model.
|Molecular orbitals are formed from the
overlap of atomic orbitals.|
|Only atomic orbitals of about the same
energy interact to a significant degree.|
|When two atomic orbitals overlap, they
interact in two extreme ways to form two molecular orbitals, a
bonding molecular orbital and an antibonding molecular orbital.|
example, our model assumes that two 1s atomic orbitals can overlap in
two extreme ways to form two molecular orbitals. One of the ways the
atomic orbitals interact is in-phase, which leads to wave
enhancement similar to the enhancement of two in-phase light waves.
Where the atomic orbitals overlap, the in-phase interaction leads to an
increase in the intensity of the negative charge in the region where
they overlap. This creates an increase in negative charge between the
nuclei and an increase in the plus-minus attraction between the electron
charge and the nuclei for the atoms in the bond. The greater attraction
leads to lower potential energy. Because electrons in the molecular
orbital are lower potential energy than in separate atomic orbitals,
energy would be required to shift the electrons back into the 1s
orbitals of separate atoms. This keeps the atoms together in the
molecule, so we call this orbital a bonding molecular orbital. The
molecular orbital formed is symmetrical about the axis of the bond.
Symmetrical molecular orbitals are called sigma, s,
molecular orbitals. The symbol s1s
is used to describe the bonding molecular orbital formed from two 1s
second way that two atomic orbitals interact is out-of-phase. Where the
atomic orbitals overlap, the out-of-phase interaction leads to a decrease
in the intensity of the negative charge. This creates a decrease in
negative charge between the nuclei and a decrease in the plus-minus
attraction between the electron charge and the nuclei for the atoms in
the bond. The lesser attraction leads to higher potential energy. The
electrons are more stable in the 1s atomic orbitals of separate atoms,
so electrons in this type of molecular orbital destabilize the bond
between atoms. We call molecular orbitals of this type antibonding molecular orbitals.
The molecular orbital formed is symmetrical about the axis of the bond,
so it is a sigma molecular orbital with a symbol of s*1s. The asterisk indicates an antibonding molecular orbital.
following diagram shows the bonding and antibonding molecular orbitals
formed from the interaction of two 1s atomic orbitals.
two larger atoms atoms combine to form a diatomic molecule (like O2,
F2, or Ne2), more
atomic orbitals interact. The LCAO approximation assumes that only the
atomic orbitals of about the same energy interact. For O2,
F2, or Ne2, the orbital energies are different enough
so only orbitals
of the same energy interact to a significant degree.
Like for hydrogen, the 1s from one
atom overlaps the 1s from the other atom to form a s1s bonding
molecular orbital and a s*1s
antibonding molecular orbital. The shapes would be similar to those
formed from the 1s orbitals for hydrogen. The
2s atomic orbital from one atom overlaps the 2s from the other atom to form a s2s
bonding molecular orbital and a s*2s
antibonding molecular orbital. The shapes of these molecular orbitals
would be similar to those for the s1s
molecular orbitals. Both s2s
and s*2s molecular orbitals are higher energy and larger than the s1s
and s*1s molecular orbitals.
p atomic orbitals of the two atoms can interact in two different ways, parallel or
end-on. The molecular orbitals are different for each type of
interaction. The end-on interaction between two 2px atomic orbitals
yields sigma molecular orbitals, which are symmetrical about the axis of
two 2py atomic orbitals overlap in parallel and form two pi molecular
orbitals. Pi molecular orbitals are asymmetrical about the axis of the
2pz-2pz overlap generates another pair of p2p
and p*2p molecular orbitals. The
2pz-2pz overlap is similar to the The 2py-2py
overlap. To visualize this overlap, picture all of the orbitals in the
image above rotated 90 degrees so the axes that run through the atomic
and molecular orbitals are perpendicular to the screen (paper). The
molecular orbitals formed have the same potential energies as the
molecular orbitals formed from the 2py-2py
is less overlap for the parallel atomic orbitals. When the interaction
is in-phase, less overlap leads to less electron charge enhancement
between the nuclei. This leads to less electron charge between the
nuclei for the pi bonding molecular orbital than for the sigma bonding
molecular orbital. Less electron character between the nuclei means less
plus-minus attraction, less stabilization, and higher potential energy
for the pi bonding molecular orbital compared to the sigma bonding
the interaction is out-of-phase, less overlap leads to less shift of
electron charge from between the nuclei. This leads to more electron
charge between the nuclei for the pi antibonding molecular orbital than
for the sigma antibonding molecular orbital. More electron charge
between the nuclei means more plus-minus attraction and lower potential
energy for the pi antibonding molecular orbital compared to the sigma
antibonding molecular orbital.
expected molecular orbital diagram from the overlap of 1s, 2s and 2p
atomic orbitals is as follows. We will use this diagram to describe O2,
F2, Ne2, CO, and NO.
use the following procedure when drawing molecular orbital diagrams.
We describe the
stability of the molecule with bond order.
bond order = 1/2 (#e- in
bonding MO's - #e- in antibonding MO's)
use bond orders to predict the stability of molecules.
|If the bond order for a molecule is
equal to zero, the molecule is unstable.|
|A bond order of greater than zero
suggests a stable molecule.|
|The higher the bond order is, the more
stable the bond.|
can use the molecular orbital diagram to predict whether the molecule is
paramagnetic or diamagnetic. If all the electrons are paired, the
molecule is diamagnetic. If one or more electrons are unpaired, the
molecule is paramagnetic.
1. The molecular orbital diagram for a diatomic hydrogen molecule, H2,
|The bond order is 1.
Bond Order = 1/2(2 - 0) = 1|
|The bond order above zero suggests that
H2 is stable.|
|Because there are no unpaired
electrons, H2 is diamagnetic.|
The molecular orbital diagram for a diatomic helium molecule, He2,
shows the following.
|The bond order is 0 for He2.
Bond Order = 1/2(2 - 2) =
|The zero bond order for He2
suggests that He2 is unstable.|
|If He2 did form, it would be
The molecular orbital diagram for a diatomic oxygen molecule, O2,
|O2 has a bond order of 2.
Bond Order = 1/2(10 - 6) = 2|
|The bond order of two suggests that
the oxygen molecule is stable.|
|The two unpaired electrons show that O2 is
The molecular orbital diagram for a diatomic fluorine molecule, F2,
|F2 has a bond order of 1.
Bond Order = 1/2(10 - 8) = 1|
|The bond order of one suggests that
the fluorine molecule is stable.|
|Because all of the electrons are paired, F2
The molecular orbital diagram for a diatomic neon molecule, Ne2,
|Ne2 has a bond order of 0.
Bond Order = 1/2(10 - 10) = 0|
|The zero bond order for Ne2
suggests that Ne2 is unstable.|
|If Ne2 did form, it would be
can describe diatomic molecules composed of atoms of different elements in a similar way. The
bond between the carbon and oxygen in carbon monoxide is very strong
despite what looks like a strange and perhaps unstable Lewis Structure.
The plus formal charge on the more electronegative oxygen
and the minus formal charge on the less electronegative carbon would
suggest instability. The molecular orbital diagram predicts CO to be
very stable with a bond order of three.
We predict the nitrogen
monoxide molecule to be unstable according to the Lewis approach to
unpaired electron and the lack of an octet of electrons around nitrogen
would suggest an unstable molecule. NO is actually quite stable. The
molecular orbital diagram predicts this by showing the molecule to have
a bond order of 2.5.