CHEMICAL BONDING II
HbR
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Lecture Outline
Brief Introduction to :
•Quantum Numbers
•Atomic Orbital
•Pauli Exclusion Principle
•Energy of Orbital
•Hund’s Rule
•Lewis Symbol Review
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Quantum Numbers
 In quantum mechanics, four quantum numbers are
required to describe the distribution of electrons in
hydrogen and other atoms.
 They are the principal quantum number (n),
 the angular momentum /azimuthal quantum number (l),
 the magnetic quantum number (m)
 The spin quantum number( s)
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The Principal Quantum Number (n)
 The principal quantum number ( n ) can have integral
values 1, 2, 3,…
 the value of n determines the energy of an orbital
 It also relates to the average distance of the electron
from the nucleus in a particular orbital.
 The larger n is, the greater the average distance of
an electron in the orbital from the nucleus and
therefore the larger the orbital.
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The Angular Momentum Quantum Number (l)
 Tells the “shape” of the orbitals.
 The values of l depend on the value of the principal
quantum number, n .
 For a given value of n , l has possible integral values from
0 to ( n - 1).
 If n = 1, l = (1-1) = 0, So, l has one value “0”.
 If n = 2, there are two values of l, given by 0 and 1.
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The Magnetic Quantum Number (m)
 m depends on l. it is (2l +1) integral values.
-l , (-l +1), ……,0,……(+l-1), l
Ex: l= 1, m= -1, 0, +1
 It tells about the orientation of the eThere is another “magnetic spin quantum number(s).
It tells spinning motion of electron if one is
clockwise the other is counter-clockwise.
It has 2 values: +1/2 and -1/2.
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Atomic Orbitals (s, p, d, f)
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Shapes and orientation of d
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Spin quantum number
Clockwise and anticlockwise spins of electrons about their
own axis produce opposite magnetic fields.
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Which of the of quantum
numbers are not allowable?
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The Pauli Exclusion Principle
 “No two electrons in an atom can have the
same set of four quantum numbers.”
 If two electrons in an atom should have the
same n , l and m values then they must have
different values of s
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 Let us find out the maximum number of
electrons that can be accommodated if n=2
Imply the Pauli Exclusion principle
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Energies of Orbital
H atom (energy depends on n)
Many e- atom (energy depends on n, l)
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Emission Spectrum of H Atom
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Emission Spectrum of H Atom
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Emission Spectrum of H Atom
RH is the Rydberg constant: 2.18 x 10-18 J.
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h = 6.63 x 10-34 J.s
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The order of sub-shell filling
1s<2s<2p< 3s<3p<4s <3d . . . .
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Puzzle around the 4s and 3d sub-shells

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K-1s22s22p63s23p64s1
But….
Fe 1s22s22p63s23p63d64s2
Fe3+ 1s22s22p63s23p63d5
Can you see any discrepancy?
As the 3d sublevel becomes populated with electrons, the relative energies of the 4s
and 3d fluctuate relative to one another and the 4s ends up higher in energy as the
3d sublevel fills. This is why when electrons are lost from the orbitals of the
transition metals, they are lost from the 4s first because it is higher in energy.
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Hund’s Rule
 “The most stable arrangement of electrons in
subshells is the one with the greatest number
of parallel spins. ”
 The electron configuration of carbon ( Z = 6)
is 1s2s22p2 . The following are different ways of
distributing two electrons among three p
orbitals:
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So, in summary
 Each electron shell can hold a maximum of
2n2 electrons where n is the shell number
 These electrons are accommodated in s, p, d
and f orbitals, the maximum number of
electrons in each type of orbitals being
determined by its electron-holding capacity
(for s = 2, p = 6, d = 10 and f = 14)
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So, in summary
 In the ground state of an atom, the electrons
tend to occupy the available orbitals in the
increasing order of energies, the orbitals of lower
energy being filled first (Aufbau Principle)
 Any orbital may have one or two electrons at the
most
 When several orbitals of equal energy
(degenerate orbitals) are available, electrons
prefer to occupy separate orbitals rather than
getting paired in the same orbital
Such electrons tend to have same spins (Hund’s
rule)
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New topics:
 Bond Energy, Bond Order, Bond length
 Molecular orbital
 Hybridization
 Geometry of Molecular Orbital
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Quick Definitions:
 Bond Energy:
In chemistry, bond energy (E) is the measure of bond
strength in a chemical bond. It is the heat required to
break one mole of molecules into their individual atoms.
 Bond Order:
Bond order is the number of chemical bonds between a pair
of atoms.
For example,
in diatomic nitrogen N≡N the bond order is 3,
in acetylene H−C≡C−H the bond order between the
two carbon atoms is also 3,the C−H bond order is 1.
Bond order gives an indication of the stability of a bond. 25
Quick Definitions:
 Bond Length:
bond length or bond distance is the average
distance between nuclei of two bonded atoms in
a molecule.
 Molecular Orbital:
A molecular orbital (or MO) is a mathematical
function describing the wave-like behavior of
an electron in a molecule.
This function can be used to calculate chemical and
physical properties such as the probability of
finding an electron in any specific region.
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Hybridization – mixing of two or more atomic
orbitals to form a new set of hybrid orbitals
1. Mix at least 2 non-equivalent atomic orbitals (e.g. s
and p). Hybrid orbitals have very different shape from
original atomic orbitals.
2. Number of hybrid orbitals are equal to number of pure
atomic orbitals used in the hybridization process.
3. Covalent bonds are formed by:
a. Overlap of hybrid orbitals with atomic orbitals
b. Overlap of hybrid orbitals with other hybrid orbitals
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Formation of sp3 Hybrid Orbitals
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sp3-Hybridized N Atom in NH3
N – 1s22s22p3
3 H – 1s1
sp3
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Formation of Covalent Bonds in CH4
C – 1s22s22p2
4 H – 1s1
sp3
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Formation of sp Hybrid Orbitals
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Formation of sp2 Hybrid Orbitals
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How do I predict the hybridization of the central atom?
1.
Draw the Lewis structure of the molecule.
2.
Count the number of lone pairs AND the number of atoms bonded to the
central atom
# of Lone Pairs
+
# of Bonded Atoms
Hybridization
Examples
2
sp
BeCl2
3
sp2
BF3
4
sp3
5
sp3d
PCl5
6
sp3d2
SF6
CH4, NH3, H2O
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Hybridization in Molecules Containing
Double and Triple Bonds
sp2 Hybridization of Carbon
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Unhybridized 2pz orbital (gray), which is perpendicular to the plane of the
hybrid (green) orbitals.
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Bonding in Ethylene, C2H4
Sigma bond (s) – electron density between the 2 atoms
Pi bond (p) – electron density above and below plane of nuclei of the bonding atoms
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Another View of p Bonding in Ethylene, C2H4
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sp Hybridization of Carbon
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Bonding in Acetylene, C2H2
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Another View of the Bonding in Ethylene, C2H4
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Describe the bonding in CH2O
H
C
O
H
C – 3 bonded atoms, 0 lone pairs
C – sp2
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Sigma (s) and Pi Bonds (p)
Single bond
1 sigma bond
Double bond
1 sigma bond and 1 pi bond
Triple bond
1 sigma bond and 2 pi bonds
How many s and p bonds are in the acetic acid (vinegar) molecule CH3COOH?
O
H
s bonds = 6
H
C
C
O
H
+1=7
p bonds = 1
H
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Let’s start with a confusion!
A hybrid orbital is an
atomic orbital or molecular
orbital
In the molecule the orbital of the central atom getting
mixed mathematically to become a hybridATOMIC
orbital
NOT a molecular orbital
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Valence Bond theory
• Valence Bond theory proposed by Heitler and
London in 1927 explains the bonding in simple
molecules
• According to this theory a covalent bond is formed
by the sharing of electron between the participating
atoms
• The overlapping between the half filled atomic
orbitals takes place and the strength of the bond
formed depends upon the extent of overlapping
between the atomic orbitals of two atoms
But comes with certain limitations……!!!
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Why O2 is paramagnetic???
Attracted to a magnetic field!
O
O
No unpaired eShould have been diamagnetic, isn’t it?
Lets learn the basics
before explaining…
We will come back..
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Molecular Orbital Theory
(1) A molecule is quite different from its constituent
atoms. All the electrons belongs to constituent atom and
are considered to be moving under the influence of all
nuclei.
(2) Atomic orbitals of individual atoms combine to form
molecular orbitals and these MOs are filled up in the
same way as atomic orbitals are formed. In other words,
Pauli’s exclusion principle, Aufbau principle and Hund’s
rule
(3) The molecular orbitals have definite energy levels.
(4) The shapes of MOs formed depend upon the shape of
combining atomic orbitals.
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Formation of molecular
orbitals from two 1s
orbitals of hydrogen atoms
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Constructive and Destructive Interference
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Energy levels of bonding and antibonding molecular
orbitals in hydrogen (H2).
A bonding molecular orbital has lower energy and
greater stability than the atomic orbitals from
which it was formed.
An antibonding molecular orbital has higher energy and lower stability than the
atomic orbitals from which it was formed.
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Possible Interactions Between Equivalent p Orbitals
Constructive
Destructive
Constructive
Destructive
So….
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In Summary….
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Molecular Orbital (MO) Configurations
1.
The number of molecular orbitals (MOs) formed is always equal to the number of
atomic orbitals combined.
2.
The more stable the bonding MO, the less stable the corresponding antibonding MO.
3.
The filling of MOs proceeds from low to high energies.
4.
Each MO can accommodate up to two electrons.
5.
Use Hund’s rule when adding electrons to MOs of the same energy.
6.
The number of electrons in the MOs is equal to the sum of all the electrons on the
bonding atoms.
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Lets get back to the O2
It is the lone electron that creates a magnetic field
around it due to its spin…So….
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bond order =
1
2
(
Number of
electrons in
bonding MOs
-
Number of
electrons in
antibonding
MOs
)
Imply the rule to O2 to calculate bond order….
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Using the Molecular
Orbital Model, Can
you explain why He2
Molecules Do Not
Exist???
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Difference in sigma and pi bond
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Thank you
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