CHAPTER 4: MOLECULAR ORBITAL THEORY
It is clear that hybridized valence bond theory does not explain much of the
observed phenomena for small molecules such as paramagnetism or UV
absorption and a better theory needs to be introduced to rationalize these
experimental observations.
In molecular orbital (MO) theory, electrons occupy orbitals each of which
spans the entire molecule.
Molecular orbitals each hold up to two electrons and obey Hund’s rule, just like
atomic orbitals.
Ground-rule of MO theory: number of MOs that can be formed must equal the
number of atomic orbitals of the constituent atoms.
Each MO has an associated energy and to derive the electronic ground state of
a molecule, the available electrons are placed in MOs according to the aufbau
principle, beginning with the lowest energy.
CHEM210/Chapter 4/2014/01
BONDING IN HYDROGEN
An approximate description of the MOs in hydrogen can be obtained by
considering them a linear combinations of atomic orbitals (LCAOs).
Each of the H atoms has 1s atomic orbital with associated wave functions, Ψ1
and Ψ2 and the signs of the wavefunction associated with the 1s orbital may
be either + or -.
The possible combinations of the two 1s orbitals are given by equations:
ΨMO (in-phase) = ΨMO = N[Ψ1 + Ψ2]
ΨMO (out-of-phase) = Ψ*MO = N*[Ψ1 - Ψ2]
where N and N*are the normalization factors, ΨMO is an in-phase (bonding)
interaction and Ψ*MO is an out-of-phase (antibonding) interaction
1sA + 1sB = MO1
constructive interference
1sA – 1sB = MO2
destructive interference
CHEM210/Chapter 4/2014/02
The label for a molecular orbital tells us three things:
• its shape.
• the parent atomic orbitals from which it was formed.
• its stability (bonding or anti-bonding): antibonding character is designated
with an asterisk (*)
The interaction between
the H 1s AOs on forming
H2 may be represented by
the MO diagram shown
below.
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CHEM210/Chapter 4/2014/04
The ground state electronic configuration of H2 may be written as using the
notation; σg (1s2).
The orbital interaction diagram can be used to predict several properties of
the H2 molecule:
• H2 molecule is diamagnetic.
• Bond order = 1.
Bond order = ½[(number of bonding electrons) – ( number of antibonding electrons)]
CHEM210/Chapter 4/2014/05
HELIUM (He2)
σg (1s2) σu* (1s2)
The bonding effect of the σg (1s2) is
cancelled by the antibonding effect
of σu* (1s2)
Electrons in the anti-bonding MO
(1sA-1sB) offset the energy gained by
placing electrons in the bonding
orbitals.
The He2 molecule is not a stable
species
CHEM210/Chapter 4/2014/06
Bond order = 0
A high bond order indicates high bond energy and short bond length.
Consider H2+, H2, He2+, He2: first row diatomic molecules and ions
H2
H 2+
He2+
↑↓
↑↓
σg (1s2)
He2
σu* (1s2)
↑↓
↑
↑
↑↓
Magnetism
Dia-
Para-
Para-
-
Bond order
1
½
½
0
Bond energy
(kJ/mol)
436
225
251
-
Bond length
(pm)
74
106
108
-
E
CHEM210/Chapter 4/2014/07
LITHIUM (Li2)
Remember Li: 1s22s1
Both the 1s and 2s overlap to
produce s bonding and antibonding orbitals
σg (1s2) σu* (1s2) σg (2s2)
BO = ½(nb - na) = ½(4 - 2) = 1
= a single bond
CHEM210/Chapter 4/2014/08
BERYLLIUM (Be2)
Remember Be: 1s22s2
σg (2s2) σu* (2s2)
BO = ½(nb - na) = ½(4 - 4) = 0 No bond! The molecule is not stable!
What about p orbitals?
If the overlap lies along the major bond axis then must constitute a σ bond.
If they overlap perpendicular to the axis they will form π bonds.
FLUORINE (F2) AND OXYGEN (O2)
The valence shell of a fluorine atom contains 2s and 2p AOs and the
formation of the F2 molecule involves 2s – 2s and 2p – 2p interactions.
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CHEM210/Chapter 4/2014/10
For F: 1s22s22p5
We expect F to use 2p orbitals this time (valence electrons).
subtraction
addition
subtraction
addition
CHEM210/Chapter 4/2014/01
F2 - It has 14 valence
electrons
O2 – has the same MO
configuration but has
two electrons less.
This makes O2
paramagnetic as you
will have unpaired
electrons
Determine the bond
orders
CHEM210/Chapter 4/2014/12
Fluorine and oxygen follow the simple logic of LCAO as they are both very
electronegative and the energy difference between the 2s and 2p is large.
With boron, carbon and nitrogen a slightly different story emerges: for these
elements, a degree of “s and p orbital interaction” occurs, whereby a change
in the energy of the relative molecular orbitals occurs
This leads to another arrangement of the molecular orbitals.
σ2p*
π2p* π2p*
E
σ2p
2p
π2p
2p
π2p
CHEM210/Chapter 4/2014/13
HETERONUCLEAR DIATOMICS
Even when the atoms in a diatomic molecule are different, we use the
homonuclear diatomic diagram with the s-p interaction as an approximation.
NITRIC OXIDE (NO)
Valence electrons = 5 + 6 = 11
σ2p*
π2p*
↑
Molecule is stable and paramagnetic –
agrees with experimental data.
↑↓
σ2p
π2p
Bond order = 2.5
↑↓
↑↓
σ2s*
↑↓
σ2s
↑↓
CHEM210/Chapter 4/2014/14
NO+: Number of valence electrons: 5 + 6 - 1 = 10
CN–: Number of valence electrons: 4 + 5 + 1 = 10
These structures are isoelectronic
σ2p*
π2p*
↑↓
σ2p
π2p
↑↓
Bond order = 3.0
↑↓
σ2s*
↑↓
σ2s
↑↓
CHEM210/Chapter 4/2014/15
Question: Can NeO exist?
Number of valence electrons: 8 + 6 = 14
σ2p*
π2p*
↑↓
↑↓
σ2p
π2p
↑↓
↑↓
Bond order = 1.0
↑↓
σ2s*
↑↓
σ2s
↑↓
What about NeO2-?
CHEM210/Chapter 4/2014/16