MOLECULAR ORBITAL THEORY
Hybridization
• Definitions
– Hybridization is defined as mixing of two atomic orbitals
with the same energy levels to give a degenerated new
type of orbitals.
– Atomic orbitals (AOs) are mathematical functions that
describe the location and wave-like behavior of an
electron in an atom
• Shows the physical region or space where the electron can be
calculated to be present
– Molecular orbitals (MOs) are formed when atomic
orbitals combine together and form bonds such as sigma
(σ) and pi (π) bonds.
• Atomic orbital and Molecular orbitals are approximate solution
to the Schrödinger equation
Electrons in an atom
• Electrons in Atomic Orbitals (AOs) and Molecular Orbitals
(MOs) are described by four quantum numbers
– Principal quantum number (n)
– Azimuthal quantum number (ℓ)
– Magnetic quantum number (mℓ)
– Spin quantum number (s)
Principal quantum number (n)
• The principal quantum
number describes the
energy level or electron
shell of an electron.
• The value of n starts with 1
n = 1, 2, ...etc
• Maximum number of
electrons in any shell =2n2
At n=1 , # electrons = 2x(1)2 = 2
At n=2 , # electrons = 2x(2)2 = 8
At n=3 , # electrons = 2x(3)2 = 18
Principal quantum (n)
Valence shell is the outermost shell of every
element.
Open shell is a valence shell which is not
completely filled with electrons
Closed shell is obtained with a completely filled
valence shell.
Core electrons are the electrons in an atom that
are present in inner shells (not valence
electrons) and do not participate in chemical
bonding
Valence electron is an outer shell electron that
is associated with an atom
• Chlorine has got 7 electrons in its outermost
shell. Potassium has 1 valence electrons
Open and closed shells
Octet rule is a chemical rule of thumb that reflects the theory that
main-group elements tend to bond in such a way that each atom has
eight electrons in its valence shell, giving it the same electronic
configuration as a noble gas.
Closed shells
Noble gas configuration is the electron configuration of noble gases.
The basis of all chemical reactions is the tendency of atoms to acquire
stability through bond formation in order to attain noble gas
Know how to write electron
configuration (Octet rule)
configuration up to period 3
Azimuthal quantum number (ℓ)
• Azimuthal quantum number describes the shape of an
orbital in a subshell.
• The value of the azimuthal quantum number ranges
between 0 and (n-1).
Azimuthal quantum number (ℓ)
Relationship between principal (n) and Azimuthal quantum
number (ℓ)
Azimuthal quantum number (ℓ)
Each of the different angular momentum states have 2ℓ + 1 orbitals and
can take 2(2ℓ + 1) electrons. The maximum number of electrons in a
subshell (s, p, d, or f) is equal to 2(2ℓ+1) where ℓ = 0, 1, 2, 3...
Magnetic quantum number (mℓ)
• Used to calculate the orientation
of orbital in space present in
azimuthal quantum number
• Distinguishes the orbitals
available within a subshell
• For l = 0, ml = 0. This represents
an s orbital, which is spherical in
shape.
• For an s orbital, the orbital
angular momentum is zero and it
does not point in any specific
directions
spherical
Magnetic quantum number (mℓ)
The value of ml can range from -ℓ to +ℓ including zero
For l = 1, ml = {−1, 0, 1}. Each value represents a p orbital.
When ml = 0, it is the pz orbital. It is aligned along the zdirection having each lobe on either of the origin. ml = ±1 are
the px and py orbitals. px and py rest on x- and y-axes.
Magnetic quantum number (mℓ)
Magnetic Quantum Number Shown here are the shapes of the
“d” orbitals
Magnetic quantum number (mℓ)
The value of ml can range from -ℓ to +ℓ, including zero
Spin quantum number (s)
• Every electron has a
spin. This a spin is
either in the
direction of "up" or
"down," denoted by
the arrows ↑ and
↓ respectively.
Aufbau principle
• The Aufbau principle dictates
the order in which electrons
are filled in the atomic orbitals
of an atom in its ground state.
• It state that Atomic Orbitals
with the lowest energy levels
are occupied first before those
with higher energy levels.
• The electron configuration of
an element describes how
electrons are distributed in its
atomic orbitals.
Aufbau principle
Orbital energy diagram
• Orbitals with the lowest energy levels are occupied before
those with higher energy levels.
Aufbau principle
Pauli exclusion principle
Two electrons cannot have the
same four quantum numbers
• Two electrons reside in the
same orbital will have same
n, ℓ, and mℓ values,
therefore their ms must be
different
• Electrons must have
opposite half-integer spin
projections of 1/2 and −1/2.
• Therefore an orbital contains
maximum of two electrons
Hund's rule of maximum multiplicity
• Degenerate orbitals
are filled singly before
filling in pairs.
Definition: Degenerate orbitals are
orbitals having the same energy
levels
Pauli exclusion principle
Hund's rule of maximum multiplicity
An orbital filling diagram is the more visual way to represent the
arrangement of all the electrons in an atom.
Hund's rule of maximum multiplicity
An atomic orbital energy diagram is the more visual way to represent
the relative energy of orbitals in a an atom.
Molecular Orbital Theory
• Three types of Molecular orbitals:
• Bonding orbitals
– Have an energy lower than the energy of the atomic orbitals
which formed them
– Promote the chemical bonds which hold the molecule
together
• Antibonding orbitals
– Have an energy higher than the energy of their constituent
atomic orbitals
– Oppose the bonding of the molecule
• Nonbonding orbitals
– Have the same energy as their constituent atomic orbitals
– Have no effect on the bonding of the molecule. Eg of non
bonding orbitals are lone pairs in Lewis structure
Molecular Orbital Theory
• Nonbonding orbitals
– The energy level of a non-bonding orbital is typically in
between the lower energy of a valence shell bonding
orbital and the higher energy of a corresponding anti
bonding orbital
Molecular Orbital Theory
• Bond order is defined as half the difference
between the number of bonding electrons and the
number of anti-bonding electrons
The higher the bond order, the stronger the bond.
Molecular Orbital Theory
Molecular orbital energy-level diagram is a diagram that
shows the relative energies of molecular orbitals
NOTE: An analogous higher energy anti-bonding orbital is also
formed anytime two atomic orbitals combine to give a lowerenergy bonding orbital
• Bonding lowers the energy of the system. Proffered
Molecular Orbital Theory
Molecular Orbitals for the H2 Molecule
Hybridization of Molecular Orbitals
Formation of sigma bonds
AO
AO
MO
Molecular Orbitals for sigma bond
Molecular Orbitals of Sigma bonds (σ)
sigma bond
Highest energy
High energy
Lower energy
Molecular Orbitals of Sigma bonds (σ)
sigma bond
S orbital
p orbital
S orbital
p orbital
s-s overlap
p-p overlap
Sigma bonds (σ) are the strongest type of covalent bond,
formed by head-on overlapping of atomic orbitals.
Molecular Orbitals of Sigma bonds (σ)
S orbital
p orbital
s-p overlap
Sigma bonds (σ) are the strongest type of covalent bond,
formed by head-on overlapping of atomic orbitals.
Hybridization of Molecular Orbitals
Hybrid orbitals formed from s and p-orbitals
Hybridization of Molecular Orbitals
Hybrid orbitals formed from p and p-orbitals
Molecular Orbitals for Sigma bonds (σ)
Molecular Orbitals for sigma bond
Sigma bonds (σ) are the strongest type of covalent bond,
formed by head-on overlapping of atomic orbitals.
Molecular Orbitals of Pi bonds (π)
Pi bonds (π) are a type of covalent bond formed by sideways
or lateral overlapping of atomic orbitals.
Molecular Orbitals of Pi bonds (π)
Pi bonds (π) are a type of covalent bond formed by sideways
or lateral overlapping of atomic orbitals.
Molecular Orbitals of Pi bonds (π)
Pi bonds (π) are a type of covalent bond formed by sideways
or lateral overlapping of atomic orbitals.
Molecular Orbitals of Pi bonds (π)
Pi bonds (π) are a type of covalent bond formed by sideways
or lateral overlapping of atomic orbitals.
Hybridization of Molecular Orbitals
Formation of Pi bonds
Pi bonds (π) are a type of covalent bond formed by sideways
or lateral overlapping of atomic orbitals.
Hybridization of Molecular Orbitals
Molecular Orbitals for pi bond
END OF LECTURE 1
HW 1
1. Define the following terms
a. Hybridization
b. Atomic orbitals
c. Molecular orbitals
d. Electron configuration
e. Aufbau principle
f. Hund’s rule
g. Pauli exclusion principle
2. What is the difference between the following terms
a. Open shell and close shell
b. Core electrons and valence electrons
c. Octet rule and noble gas configuration
HW 2
1. Define four quantum numbers that describe the electron
in a atom
2. Calculate the maximum number of electrons the third
shell of an atom can accommodate
3. Draw the shapes of s, p and d orbitals
4. Draw all the p orbitals that are present in magnetic
quantum number
5. Calculate the value of n when ℓ = 0, 1, 2 and 3
6. Name all the orbitals that are present in principal
quantum number 4
7. Calculate the number of orbitals and maximum number of
electrons that are present in Azimuthal quantum number
1,2 and 3
HW 3
Fill the tables below
HW 4
Fill the tables below
HW 5
1. What are the 3 rules for orbital diagrams?
2. Write (a) the electron configuration, (b) orbital filling
diagram and (c) orbital energy diagram of the following
elements
a.
Hydrogen
b.
Boron
c.
Carbon
d.
Nitrogen
e.
Sulfur
f.
Chlorine
h.
Argon
HW 6
1. Draw the molecular orbital diagrams the following
molecules
a. H2
b. He2
c. He2+
d. Be2
e. Methane
2. Calculate the bond order(s) of the molecule above
3. Explain why H2 exists while He2 doesn't
HW 7
1. Show orbital overlap that gives sigma and pi bonds
2. Show the hybrid orbital formed by combination of (a) s
and p orbitals and (b) p and p orbitals
3. Show the molecular orbital diagram of pi bonds in ethane
molecule (CH2=CH2)
END OF HW QUESTIONS