Molecular Orbital Theory
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Transcript of Molecular Orbital Theory
General Chemistry
Molecular Orbital Theory
Dr. S. K. Tan
Topics to be Covered in this Lecture
Concepts of Molecular Orbitals
Correlation Energy Diagram
Prediction of Reactivity of Molecules
Bonding Theories
We have already been introduced to one of the main bonding theories -
The Valence Bond Theory(VB)
* Pairs of electrons repel each other, therefore orient themselvesPairs of electrons repel each other, therefore orient themselvesin a in a
way that minimizes these repulsions. way that minimizes these repulsions.
* Covalent bonds are formed by overlapping of atomic Covalent bonds are formed by overlapping of atomic orbitalsorbitals..
* The electrons that form a bond between two atoms are localized The electrons that form a bond between two atoms are localized
between the atoms.between the atoms.
There is however another contender to the throne for bonding theory
- and this is called The Molecular Orbital Theory (MO )
* Atomic Atomic orbitalsorbitalsare combined into new are combined into new orbitalsorbitals, called molecular , called molecular
orbitalsorbitals(MOs). (MOs).
* MOs need not be localized between two atoms. MOs need not be localized between two atoms.
* The number of MOs formed is equal to the sum of atomic The number of MOs formed is equal to the sum of atomic orbitalsorbitalsin in
all the atoms comprising the molecule.all the atoms comprising the molecule.
* When atomic When atomic orbitalsorbitalscombine to form bonding MOs, the resulting combine to form bonding MOs, the resulting
MO is lower in energy. MO is lower in energy.
* AntibondingAntibondingMOs are less stable than the MOs are less stable than the AOsAOs..
Bonding Theories
Molecular Orbital Theory
Here, if we have two nuclei that are close to each other, when we
include the electrons into consideration, the electrons will move into
molecular orbitals.
This is analogous to the electrons occupying atomic orbitals in the case
of the atoms.
For the atomic orbitals, there are s, p, d, f,... orbitals.
In the case of molecular orbitals, there are σ, π, δ, ...; where the
orbitals are determined by quantum numbers.
Molecular Orbital Theory (2)
To obtain the molecular orbital, the Schrödinger equation must be
solved, and here lies the problem.
The equation cannot be solved exactly and therefore certain
approximations must be made.
One of them involves the BornBorn--Oppenheimer ApproximationOppenheimer Approximation,
which assumes that nuclei moves much more slowly than electrons(also known as the Clamped-Nuclei Approximation).
This separates the situation into two problems - an electronic and a
nuclear motion problem.
Molecular Orbital Theory (3)
The electronic problem solves for the wave function of the electrons
while the nuclear motion solves for the motion of the nuclei.
Another approximation that is made is that the molecular orbitals may
be approximated by taking the Linear Combination of Atomic Linear Combination of Atomic
OrbitalsOrbitals ((LCAOLCAO ).).
The rationale is that most of the time the electrons are close to nuclei
and will most probably be ‘controlled’ by one of the two nuclei.
Hence, the molecular orbital will most probably be a combination of
the atomic orbitals.
Molecular Orbital Theory (4)
So, if we have two atomic orbitals, ΨA
and ΨB, we can combine them
to obtain two molecular orbitals.
Ψb= Ψ
A+ Ψ
B; and Ψ
a= Ψ
A- Ψ
B, where Ψ
bis a bonding molecular
orbital and is an Ψaanti-bonding molecular orbital.
The electron distribution is then calculated by taking the square of
that function.
Hence, Ψb
2 = ΨA
2 + 2ΨAΨ
B+ Ψ
B
2 , while the corresponding electron
distribution for the anti-bonding molecular orbital is Ψa
2 = ΨA
2 - 2ΨA
ΨB
+ ΨB
2 .
Molecular Orbital Theory (5)
The two orbitals Ψb
and Ψa
differ from
each other.
In the bonding molecular orbital, the
wave functions for the component atoms
reinforce each other in the region
between the nuclei.
Ψb2 is the electron distribution in the
hydrogen molecule, also known as the
probability function.
ΨA
and ΨB
Ψb = Ψ
A+ Ψ
B
Ψb
2
Molecular Orbital Theory (6)
Note that in the bonding situation, the
electrons are in between two nuclei.
In the anti-bonding orbital , the wave
functions cancel, forming a node between
the nuclei.
In this situation, the electrons are not in
between the two nuclei.
ΨA
and ΨB
Ψa = Ψ
A- Ψ
B
Ψa
2
Correlation Energy Diagrams (1)
The diagram in the opposite panel shows
the energy correlation diagramenergy correlation diagram of the
molecular orbitals and the atomic
orbitals.
The atomic orbitals are both on the
right and the left of the diagram.
The energy levels in the centre are those
of the corresponding bonding (1sσ) and
anti-bonding (1sσ*
) molecular orbitals.
1sA 1s
B
1sσ
1sσ*
↑ ↑
Energy
Notice that the bonding orbitals have a lower energy level compared to the atomic orbitals - one of the reasons for bonding is to achieve lower energy levels
Correlation Energy Diagrams (2)
In H2, each atom provides 1 electron to
the molecular orbital.
This results in the two electrons pairing
up in the 1sσ
bonding orbital (Hund’s
rule, Pauli Exclusion principle).
This results in a stable bonding between
H-H atoms, and this is exemplified
experimentally.
1sA
1sB
1sσ
1sσ*
↑ ↑
Energy
↑↓
Correlation Energy Diagrams (3)
How about H2+?
In this case, the dihydrogen cation has
only one electron and therefore has only
one electron in the bonding molecular
orbital of 1sσ.
Although only one electron exists, this
provides an energy stabilisation of ∆E
compared to the atomic orbitals.
In the case of H2, it has a total energy
stabilisation of 2∆E.
1sA 1s
B
1sσ
1sσ*
↑
Energy
↑∆E
Correlation Energy Diagrams (4)
How about H2-?
For the dihydrogen anion, there are three electrons to distribute to the molecular orbitals, and the third electron populates the 1sσ* orbital.
This is an anti-bonding orbital and will result in the electron gaining destabilisation energy of ∆E’ .
Assuming ∆E = ∆E’ , the bond energy for H2
- is then 2∆E – ∆E’ = ∆E (similar to that of H2
+).
1sA 1s
B
1sσ
1sσ*
↑↓ ↑
Energy
↑↓
↑
∆E
∆E’
Energy Correlation Diagrams (5)
How about He2?
In He2, we have a total of four electrons to populate into the molecular orbitals.
The third and fourth electron goes into the 1sσ* orbital, and since it is an anti-bonding orbital, the net stabilisation obtained from the bonding orbital is lost as it is cancelled by the anti-bonding orbitals.
As a result, He2 is predicted to be unstable.
1sA 1s
B
1sσ
1sσ*
↑↓ ↑↓
Energy
↑↓
↑↓
Considerations for Molecular Orbital formation
In order to determine which atomic orbitals interact to form molecular
orbitals, we have to consider the factors that impact on the interaction
between atomic orbitals.
They are:
* The energy differencebetween the interacting orbitals must be small,
* The overlap between the orbitals must be large.
This means that the 2s orbitals will only interact with other 2s orbitals
and not with the 1s or 2p orbitals.
Molecules with Electrons in the 2s Orbitals (1)
When we include the 2s atomic orbitals
into the formation of molecular orbitals, we
combine them in the same fashion as we
did for the 1s atomic orbitals.
The 2sσ
results from 2sA
+ 2sB, while 2s
σ*
results from 2sA
- 2sB.
The molecular orbital diagram appears as
in the panel.
2sA 2s
B
2sσ
2sσ*
1sA 1s
B
1sσ
1sσ*
Molecules with Electrons in the 2s Orbitals (2)
In the case of Li2, there are a total of 3
electrons for an atomic configuration of
1s2 2s1.
These will combine as shown in the panel
- only a single bond results.
Note that the 1s orbitals do not form
bonds (as we expect) from the MO theory
as it is cancelled out by the anti-bonding
orbitals.
The electronic configuration of Li2
is then
(1sσ)2 (1s
σ*)2 (2s
σ)2.
2sA 2s
B
2sσ
2sσ*
1sA 1s
B
1sσ
1sσ*
↑
↑↓ ↑↓
↑↓
↑↓
↑↓
↑
Molecules with Electrons in the 2s Orbitals (3)
For Be2, there are four electrons for each
Be atom thus giving an electronic configuration of 1s2 2s2.
The MO for Be2
is as shown in the opposite panel.
The electrons populating the 2s molecular orbitals gives use an electronic configuration of(1s
σ)2(1s
σ*)2(2s
σ)2 (2s
σ*)2.
Be2
is not expected to be stable, and thus will not exist.
2sA 2s
B
2sσ
2sσ*
1sA 1s
B
1sσ
1sσ*
↑↓
↑↓ ↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
Molecules with Electrons in the 2p Orbitals (1)
There are three 2p orbitals, each of these orbitals are in the x, y and z directions of the Cartesian coordinates.
Elements such as B, C, N, O, F, ... have electronic configurations that utilise the p-orbitals.
Here, if the p-orbital is lying along the internuclear axis, then it can undergo symmetric combination to give a bonding orbital.
Alternatively, it can undergo anti-symmetric combination to give an anti-bonding orbital .
Symmetric
Anti-symmetric
Molecules with Electrons in the 2p Orbitals (2)
The σ2p
molecular orbital has bulk of the electron density between the nuclei, thus contributes towards the bonding.
The σ*2p
molecular orbital has the electron density mainly outwith the internuclear area, thus does not contribute towards the bonding.
Molecules with Electrons in the 2p Orbitals (3)
The remaining p-orbitals (px and py) do not overlap, but they lie
perpendicular to the internuclear axis.
They can undergo either plus or minus combination to give 2pπ orbitals
and are called doubly degenerate as the orbitals formed are equal in
energy and size but differ in direction.
MO Theory in Bonding of O2 (1)
O has eight electrons; O2
has 16 electrons.It has the following electronic configuration
(1sσ)2 (1s
σ*)2 (2s
σ)2 (2s
σ*)2 (2p
σ)2 (2p
π)4 (2p
π*)2
There are 4 nett bonding electrons.
2pσ
2pσ*
1s 1s
1sσ
1sσ*
↑↓
↑↓↑↓
↑↓
2s 2s
2sσ
2sσ*
↑↓
↑↓↑↓
↑↓
↑↓ 2pπ
2pπ*
2p
↑↓↑↓
↑ ↑
↑↓ ↑↑ ↑↓ ↑↑2p
MO Theory in Bonding of O2
(2)
4 (2pπ) + 2 (2p
σ) - 2 (2p
π*)
Hence there are 4/2 = 2 bondspresent (O=O). There are also 2 anti-bonding unpaired electrons.
This explains the paramagnetic behavior of dioxygen.
2pσ
2pσ*
1s 1s
1sσ
1sσ*↑↓
↑↓↑↓
↑↓
2s 2s
2sσ
2sσ*
↑↓
↑↓↑↓
↑↓
↑↓ 2pπ
2pπ*
2p↑↓↑↓
↑ ↑↑↓ ↑↑ ↑↓ ↑↑
2p
MO Theory in Bonding of F2
(1)F has 9 electrons while F
2has 18 electrons.
It has the following electronic configuration
(1sσ)2 (1s
σ*)2 (2s
σ)2 (2s
σ*)2 (2p
σ)2 (2p
π)4 (2p
π*)4
There are 2 nett bonding electrons and a single bond(F-F).
There are four anti-bonding electrons, thus F2
is highly reactive species.
2pσ
2pσ*
1s 1s
1sσ
1sσ*↑↓
↑↓↑↓
↑↓
2s 2s
2sσ
2sσ*↑↓
↑↓↑↓
↑↓
↑↓ 2pπ
2pπ*
2p↑↓
↑↓
↑↓ ↑ ↑↓ ↑
2p
↑↓ ↑↓
↑↓↑↓
2sσ*
↑↓
MO Theory in Bonding of N2
N2
has a different energy level compared to those of O2
and F2.
N2
has the following electronic structure
(1sσ)2 (1s
σ*)2 (2s
σ)2 (2s
σ*)2 (2p
π)4 (2p
σ)2
There are 6 nett bonding electrons, giving 3 bonds.
N2
is therefore very stable and unreactive as there are no anti-bonding electrons.
2pσ
2pσ*
1s 1s
1sσ
1sσ*↑↓
↑↓↑↓
↑↓
2s 2s
2sσ
↑↓
↑↓↑↓
↑↓
↑↓2p
π
2pπ*
2p↑↓
↑ ↑2p
↑↑↑↑
MO Theory in Bonding of Ne2
Ne has 10 electrons and Ne2 has 20 electrons.It has the following electronic structure
(1sσ)2 (1s
σ*)2 (2s
σ)2 (2s
σ*)2 (2p
σ)2 (2p
π)4 (2p
π*)4 (2p
σ*)2
This means that there are no nett bonding electrons and Ne2 will not exist.
2pσ
2pσ*
1s 1s
1sσ
1sσ*
↑↓
↑↓↑↓
↑↓
2s 2s
2sσ
2sσ*
↑↓
↑↓↑↓
↑↓
↑↓ 2pπ
2pπ*
2p
↑↓↑↓
↑↓ ↑↓
2p
↑↓ ↑↓
↑↓↑↓
↑↓ ↑↓
↑↓
Topics Covered in this Lecture
Concepts of Molecular OrbitalsCorrelation Energy DiagramPrediction of Reactivity of Molecules