REVISION.
Covalent bonding involves atoms sharing electron pairs.
The number of electron pairs shared (i.e. the number of
covalent bonds formed) by a particular atom is determined
by the Noble Gas law – atoms share electrons in such a
way as to attain the electron configuration of the nearest
Noble Gas.
Atomic orbitals interact to form new orbitals which
surround both nuclei and hence are called molecular
orbitals.
Electrons in molecular orbitals interact with both nuclei of
the atoms involved in covalent bonding and, in that sense,
are ‘shared’ between them.
Combination of any two atomic orbitals produces two
molecular orbitals (MOs) one of which is bonding and the
other antibonding.
a + b
+
a
b
1s
bonding
1s*
anti-bonding
a - b
The bonding MO corresponds to the sum of the atomic
wave functions. Electron density in the BMO is
concentrated between the nuclei. This shields the +ve
nuclei from repelling each other and the two +ve nuclei are
held together by attraction for the –ve electron density
between them.
The anti-bonding MO corresponds to the difference of
the atomic wave functions. Here there is zero electron
density between the nuclei. Hence electrons in an ABMO
do not hold the nuclei together – and in fact tend to drive
the nuclei apart.
The BMO has lower energy (i.e. is more stable) than the
two isolated atomic orbitals.
The ABMO has higher energy (i.e. is less stable) than the
two isolated atomic orbitals.
A  (sigma) MO (also called a  bond) is characterised by
having electron density concentrated along the bond axis,
the imaginary line joining the two nuclei.
Combination of:
two s AO’s
or
end-on combination of one s AO + one p AO
or
end-on combination of two p AOs
generates one  (sigma) and one * (sigma star) MO.
 bond
s-s
s-p
p-p
A  MO (also called a bond) is characterised by electron
density concentrated above and below the bond axis.
Sideways-on combination of two p AOs produces a  (pi,
bonding) and a * (pi star, anti-bonding) MO.
 bond
 bonds are found
in double bonds and
triple bonds.
The Aufbau Principle, Pauli Principle and Hund’s Rule
apply to the filling of MOs as they do to the filling of
atomic orbitals.
Bond Order (BO) is a measure of the degree of bonding
between two atoms. Bond order of one signifies a single
bond, bond order of two a double bond and bond order of
three a triple bond.
Bond Order (BO) is calculated by the relationship:
BO =
(No. of Bonding Electrons) - (No. of Anti-Bonding Electrons)
2
MO energy diagram for the H2 molecule:
E = 458 kJ mol-1
Energy
+ E
H 1s 1
- E
H 1s 1
H2
Distance
H2 (1s)2 (*1s)0
2-0
BOH2 = 2 = 1 i.e. a single bond.
Energy
Consider a possible He2 molecule:
He 1s2
He 1s2
He2
Distance
He2 (1s)2 (*1s)2
2-2
BOHe2 = 2 = 0 i.e. there is no bond, the molecule
cannot exist
Energy
Consider a possible [H2]+, i.e. a hydrogen molecule cation:
H 1s 1
[H 1s0]+
[H2]+
Distance
[H2]+ (1s)1 (*1s)0
BO[H2]+ =
1-0
2 = 0.5 i.e. there is H-H bonding, but with
only half the strength of a normal single bond, i.e. the
species is capable of existence but will be much less stable
than H2.
Energy
Consider a possible Li2, i.e. a di-Lithium molecule:
Li 1s 2 2s1
Li (K) 2s 1
Li 1s 2 2s1
Li (K) 2s 1
Li2
Distance
Li2 KK (2s)2 (*2s)1
Core electrons (here 1s2 – or a filled K shell - on each Li)
do not take part in bonding. Hence the two K shells are
written unchanged in the electronic formulation of the
molecule.
BOLi2 =
2-0
2 = 1 i.e. there is a single bond in Li2. The
bond is weaker than that in H2 because of repulsion
between the two filled K shells.
MULTIPLE BONDS – THE NITROGEN MOLECULE
The valence shell of N is 2s2 2px1, 2py1, 2pz1. In the nitrogen
molecule, NN, the two nitrogen atoms are held together by
three electron pairs, i.e. a triple bond.
A triple bond consists of a sigma () bond and two pi ()
bonds.
In a simplified picture we can regard the triple bond as
being built up from interactions of the three p orbitals on the
two nitrogen atoms:
z
z
x
x
y
y
When two nitrogen atoms come together, as illustrated
above, the 2px orbitals will overlap in a head-on fashion to
give a  bonding orbital, while the 2py and 2pz orbitals
overlap sideways-on to form two  bonding orbitals.
z
x
 2px
y
z
x
 2pz
y
z
x
y
 2p y
Note that each interaction of two orbitals also generates a
corresponding antibonding orbital which is not shown
here.