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orbital
(full) bonding molecular orbital
1s 
atomic 
orbital
in
cr
ea
si
ng
 e
ne
rg
y
combine
out-of-phase
combine
in-phase
1s 
atomic 
orbital
helium 
atom B
bond order
(no. of electrons in bonding MOs) (no. of electrons in antibonding MOs)= −
2
bond order (H i.e. a single bond
bond order (He i.e. no bond
2
2
)
)
= − =
= − =
2 0
2
1
2 2
2
0
both MOs have rotational symmetry about the axis through the two nuc
we can rotate 
about this axis 
without changing 
the MOsσ
σ*�
Antibonding orbitals are designated
with a * e.g. σ*, or π*
What MOs result from the combina-
tion of two p orbitals? There are three
mutually perpendicular p orbitals on each
atom. As the two atoms approach each
other, these orbitals can combine in two
different ways—one p orbital from each
atom can overlap end-on, but the other
two p orbitals on each atom must com-
bine side-on.
The end-on overlap (in-phase and out-
of-phase) results in a pair of MOs that are
cylindrically symmetrical about the inter-
nuclear axis—in other words, these combinations have σ symmetry. The two molecular orbitals
resulting from the end-on combination of two 2p orbitals are labelled the 2pσ and the 2pσ* MOs.
The side-on overlap of two p orbitals forms an MO that is no longer symmetrical about the inter-
nuclear axis. If we rotate about this axis, the phase of the orbital changes. The orbital is described as
having ππsymmetry—a ππorbital is formed and the electrons in such an orbital make up a ππbond.
Since there are two mutually perpendicular pairs of p orbitals that can combine in this fashion, there
are a pair of degenerate mutually perpendicular πbonding MOs and a pair of degenerate mutually
perpendicular π* antibonding MOs.
The two sorts of molecular orbitals arising from the combinations of the p orbitals are not degen-
erate—more overlap is possible when the AOs overlap end-on than when they overlap side-on. As a
Molecular orbitals—homonuclear diatomics 99
only these two p orbitals can overlap end-on
these two pairs of p orbitals must combine side-on
two different ways that p orbitals can overlap with each other
combine
the end-on overlap of two 2p atomic orbitals to give the 2pσ* antibonding MO
2p AO 2p AO
nodal plane
2pσ* MO
combine
the end-on overlap of two 2p atomic orbitals to give the 2pσ bonding MO
symmetrical 
about this axis.
2p AO 2pσ MO2p AO
out-of-phase
 in-phase
symmetrical 
about this axis.
no symmetry 
about this axis. 
If we rotate, 
the phase changes2pπ* MO2p AO 2p AO
the side-on overlap of two 2p atomic orbitals to give the 2pπ* antibonding MO
nodal plane
combine
out-of-phase
2pπ MO2p AO 2p AO
the side-on overlap of two 2p atomic orbitals to give the 2pπ bonding MO
combine
 in-phase no symmetry 
about this axis. 
If we rotate, 
the phase changes
result, the pσ orbital is lower in energy than the pπorbital. We can now draw an energy level diagram
to show the combination of the 1s, 2s, and 2p atomic orbitals to form molecular orbitals.
Let us now look at a simple diatomic molecule—nitrogen. A nitrogen molecule is composed of
two nitrogen atoms, each containing seven electrons in total. We shall omit the 1s electrons because
they are so much lower in energy than the electrons in the 2s and 2p AOs and because it makes no
difference in terms of bonding since the electrons in the 1sσ* cancel out the bonding due to the elec-
trons in the 1sσ MO. The electrons in the 1s AOs and the 1s MOs are described as core electrons and
so, in discussing bonding, we shall consider only the electrons in the outermost shell, in this case the
2s and 2p electrons. This means each nitrogen contributes five bonding electrons and hence the mol-
ecular orbitals must contain a total of ten electrons.
The electrons in the σ and σ* MOs formed
from the 2s MOs also cancel out—these electrons
effectively sit on the atoms, two on each, and form
lone pairs—nonbonding pairs of electrons that do
not contribute to bonding. All the bonding is done
with the remaining six electrons. They fit neatly
into a σ bond from two of the p orbitals and two π
bonds from the other two pairs. Nitrogen has a
triple bonded structure.
Heteronuclear diatomics
Up to now we have only considered combining two atoms of the same element to form homonuclear
diatomic molecules. Now we shall consider what happens when the two atoms are different. First of
all, how do the atomic orbitals of different elements differ? They have the same sorts of orbitals 1s, 2s,
2p, etc. and these orbitals will be the same shapes but the orbitals will have different energies. For
100 4 . Structure of molecules
1s
2s
3 × 2p 3 × 2p
2s
1s
1sσ∗
1sσ
2sσ
2sσ∗
2pσ
2pσ∗
2 × 2pπ
2 × 2pπ∗
atomic orbitals 
on atom B
molecular orbitals resulting from the combination of atomic orbitals
in
cr
ea
si
ng
 e
ne
rg
y 
of
 o
rb
ita
ls
the 1sσ and 1sσ* MOs are much lower in energy than the other MOs
atomic orbitals 
on atom A
N N
one σ bond
two π bonds
nonbonding
lone pair
nonbonding
lone pair
�
Homonuclear and heteronuclear
refer to the nature of the atoms in
a diatomic molecule. In a
homonuclear molecule the atoms
are the same (such as H2, N2, O2,
F2) while in a heteronuclear
molecule they are different (as in
HF, CO, NO, ICl).
example, removing an electron completely from atoms of carbon, oxygen, or fluorine (that is,
ionizing the atoms) requires different amounts of energy. Fluorine requires most energy, carbon
least, even though in each case we are removing an electron from the same orbital, the 2p AO. The
energies of the 2p orbitals must be lowest in fluorine, low in oxygen, and highest in carbon.
We are talking now about electronegativity. The more electronegative an atom is, the more it
attracts electrons. This can be understood in terms of energies of the AOs. The more electronegative
an atom is, the lower in energy are its AOs and so any electrons in them are held more tightly. This is
a consequence of the increasing nuclear charge going from left to right across the periodic table. As
we go from Li across to C and on to N, O, and F, the elements steadily become more electronegative
and the AOs lower in energy.
So what happens if two atoms
whose atomic orbitals were vastly dif-
ferent in energy, such as Na and F, were
to combine? An electron transfers from
sodium to fluorine and the product is
the ionic salt, sodium fluoride, Na+F–.
The important point is that the
atomic orbitals are too far apart in
energy to combine to form new mole-
cular orbitals and no covalent bond is
formed. The ionic bonding in NaF is
due simply to the attraction between
two oppositely charged ions. When
the atomic orbitals have exactly the
same energy, they combine to form
new molecular orbitals, one with an
energy lower than the AOs, the other
with an energy higher than the AOs.
When the AOs are very different in
energy, electrons are transferred from
one atom to another and ionic bond-
ing results. When the AOs are slightly different in energy, they do combine and we need now to look
at this situation in more detail.
Heteronuclear diatomics 101
en
er
gy
2s
2px 2py 2pz
2s
2px 2py 2pz
E = 0
energy needed 
to ionize an 
oxygen atom
more 
energy needed 
to ionize a 
fluorine atom
atomic orbitals for oxygen
atomic orbitals for fluorine
2pz
2s
2px 2py
less 
energy needed 
to ionize a 
carbon atom
atomic orbitals for carbon
3s
2p
fluorine atomsodium atom
both electrons in sodium fluoride end up in the fluorine's 2p orbital
the atomic orbitals 
are too far apart to 
combine with each 
other to form a new 
molecular orbitalen
er
gy
Na FNa F
this electron
transferred
from 3s(Na)
to 2p(F)
sodium ion fluoride ion
The AOs combine to form new MOs but they do so unsymmetrically. The more electronegative
atom, perhaps O or F, contributes more to the bonding orbital and the less electronegative element
(carbon is the one we shall usually be interested in) contributes more to the antibonding orbital. This
applies both to σ