1. CHAPTER 1: THE NATURE OF
COVALENT BOND
COVALENT BOND, ATOMIC AND
MOLECULAR ORBITALS
LECTURE 1
B Y
D R A Y E S H A M O H Y - U D - D I N
D E P A R T M E N T O F C H E M I S T R Y
S C H O O L O F S C I E N C E
U N I V E R S I T Y O F M A N A G E M E N T A N D T E C H N O L O G Y , L A H O R E
IN THE NAME OF ALLAH, THE
BENEFICENT THE MERCIFUL
2. 2
Atomic Structure
Structure of an atom
Positively charged nucleus (very dense, protons and neutrons) and
small (10-15
m)
Negatively charged electrons are in a cloud (10-10
m) around nucleus
Diameter is about 2 10-10
m (200 picometers (pm) [the unit
angstrom (Å) is 10-10
m = 100 pm]
3. Atomic Structure
As far as Organic Chemistry was concerned we are
only interested in the arrangement of electron
around the nucleus in “Because it determine the
chemistry of that atom”
Previously it was believed that atom is like a solar
system as discussed by Neil Bohr in 1913
4. Atomic Structure
Using this wave nature De broglie presented its
atomic model based on wave nature of electron in
1924
5. Atomic Structure
Waves can undergo constructive and Destructive
interference, hence come the factor Probability
6. Atomic Structure
In 1926 the Austrian physicist Erwin Schrodinger
took the models one step further he use new
quantum theory to write and solve a mathematical
equation describing the location and energy of
electron in hydrogen atom, hence giving the most
accurate picture of atoms
Equation ???
7. Interpretation of Schrodinger equation
It is actually as differential equation and its solutions
are simple equation which can be plotted as 3D
graphs of probability of electrons and there densities
this shows atomic orbital's which then clarified by
quantum numbers
Please Observe the video !!!
8. Quantum Theory and the Electronic Structure of
Atoms
Quantum Numbers
Principal Quantum Number (n)
Angular Momentum Quantum Number (l)
Magnetic Quantum Number (ml)
Electron Spin Quantum Number (ms)
Atomic Orbitals
s Orbitals
p Orbitals
d Orbitals and other High-Energy Orbitals
Energies of Orbitals
Electron Configuration
Energies of Atomic Orbitals in Many-Electron Systems
The Pauli Exclusion Principle
Aufbau Principle
Hund’s Rule
General Rules for Writing Electron Configurations
Electron Configurations and the Periodic Table
9. Quantum Mechanics
Erwin Schrödinger derived a complex mathematical formula to incorporate the wave and
particle characteristics of electrons.
Wave behavior is described with the wave function ψ.
The probability of finding an
electron in a certain area of
space is proportional to ψ2
and
is called electron density.
10. The Schrödinger equation specifies possible energy
states an electron can occupy in a hydrogen atom.
The energy states and wave functions are
characterized by a set of quantum numbers.
Instead of referring to orbits as in the Bohr model,
quantum numbers and wave functions describe
atomic orbitals.
Quantum Mechanics
11. Quantum numbers are required to describe the distribution of
electron density in an atom.
There are three quantum numbers necessary to describe an atomic
orbital and fourth to characterize the electron further
The principal quantum number (n) – designates size
The Azimuthal/ angular moment quantum number (l) –
describes shape
The magnetic quantum number (ml) – specifies orientation
The spin quantum number (s) – specifies clockwise or
anticlockwise spin
No two electrons in an atom can have same set of values of all 4
quantum numbers
Quantum Mechanics
12. The principal quantum number (n) designates the size of the
orbital.
Larger values of n correspond to larger orbitals.
The allowed values of n are integral numbers: 1, 2, 3 and so forth.
The value of n corresponds to the value of n in Bohr’s model of the
hydrogen atom.
A collection of orbitals with the same value of n is frequently
called a shell.
Quantum Mechanics
13. Quantum Numbers
The Azimuthal/angular moment quantum number (l) describes
the shape of the orbital.
The values of l are integers that depend on the value of the
principal quantum number
The allowed values of l range from 0 to n – 1.
Example: If n = 2, l can be 0 or 1.
A collection of orbitals with the same value of n and l is referred to
as a subshell.
l 0 1 2 3
Orbital designation s p d f
14. The magnetic quantum number (ml) describes the orientation of
the orbital in space.
The values of ml are integers that depend on the value of the
angular moment quantum number:
– l,…0,…+l
Quantum Mechanics
15. The electron spin quantum number
(s) is used to specify an electron’s
spin.
There are two possible directions of
spin.
Allowed values of ms are +½ and
−½.
That is the spin can be clockwise or
counterclockwise
Quantum Mechanics
16. A beam of atoms is split by a magnetic field.
Statistically, half of the electrons spin clockwise, the other half spin counterclockwise.
Quantum Mechanics
18. To summarize quantum numbers:
principal (n) – size
angular (l) – shape
magnetic (ml) – orientation
electron spin (s) direction of spin
Required to describe an atomic orbital
Required to describe an
electron in an atomic
orbital
2px
principal (n = 2)
angular momentum (l = 1)
related to the magnetic
quantum number (ml )
Quantum Mechanics
19. Atomic Orbitals
All s orbitals are spherical in shape but differ in size:
1s < 2s < 3s
2s
angular momentum
quantum number (l = 0)
ml = 0; only 1 orientation
possible
principal
quantum number
(n = 2)
20. Atomic Orbitals
The p orbitals:
Three orientations:
l = 1 (as required for a p orbital)
ml = –1, 0, +1
21. Atomic Orbitals
The d orbitals:
Five orientations:
l = 2 (as required for a d orbital)
ml = –2, –1, 0, +1, +2
22. Strategy Consider the significance of the number and the letter in the 4d
designation and determine the values of n and l. There are multiple values for ml,
which will have to be deduced from the value of l.
List the values of n, l, and ml for each of the orbitals in a 4d subshell.
Solution 4d
Possible ml are -2, -1, 0, +1, +2.
Setup The integer at the beginning of the orbital designation is the principal
quantum number (n). The letter in an orbital designation gives the value of the
angular momentum quantum number (l). The magnetic quantum number (ml) can
have integral values of – l,…0,…+l.
principal quantum
number, n = 4
angular momentum
quantum number, l = 2
23. Electron Configurations
According to the Pauli exclusion principle, no two electrons in an
atom can have the same four quantum numbers.
1s2
1s
2s
2p 2p 2p
Energy
The ground state electron
configuration of helium
Quantum number
Principal (n)
Angular moment (l)
Magnetic (ml)
Electron spin (ms)
1
0
0
+ ½
1
0
0
‒ ½
describes the 1s orbital
describes the electrons in the 1s orbital
24. Electron Configurations
The Aufbau principle states that electrons are added to the lowest energy
orbitals first before moving to higher energy orbitals.
The Hund,
s rule states when electrons occupy the orbitals of equal energy, the
most stable arrangement is the one that contains maximum possible number of
unpaired electrons.
1s2
2s1
1s
2s
2p 2p 2p
Energy
The ground state electron
configuration of Li
The 1s orbital can only accommodate 2
electrons (Pauli exclusion principle)
The third electron must go in the
next available orbital with the
lowest possible energy.
Li has a total of 3 electrons
25. Molecular Orbital
Atomic orbital consist of only one nucleus but molecular
orbital contains more then one nuclei.
As with atomic orbitals, Schrodinger equations can be
written for electrons in molecules. Approximate solutions
to these equations can be constructed from linear
combinations of atomic orbitals (LCAO), which are the
sums and differences of the atomic wave functions
26. MMG Skills Lecture Series
26
Linear combinations: Molecular Orbitals
Both atomic orbitals and
hybrids centred on different
atoms combine to form covalent
bonds.
σ-bonds (sigma-bonds) are
made up from overlapping
orbitals directed along the
bond direction.
π-bonds (pi-bonds) are made
up from overlapping orbitals
at an angle to the inter-
nuclear direction
27. MMG Skills Lecture Series
27
Overlapping of Atomic Orbitals: Molecular Orbitals
28. Today’s Culture Moment (Extra)
Schrödinger's cat
It is a famous thought
experiment that
demonstrates the idea in
quantum physics that tiny
particles can be in two
states at once until they're
observed. It asks you to
imagine a cat in a box with
a mechanism that might
kill it. Until you look inside,
the cat is both alive and
dead at the same time
![2
Atomic Structure
Structure of an atom
Positively charged nucleus (very dense, protons and neutrons) and
small (10-15
m)
Negatively charged electrons are in a cloud (10-10
m) around nucleus
Diameter is about 2 10-10
m (200 picometers (pm) [the unit
angstrom (Å) is 10-10
m = 100 pm]](https://image.slidesharecdn.com/lecture1ch206spring2025-250401124958-ba39c2cd/85/Lecture-1-CH-206-Spring-2025-pptxgcfgvug-2-320.jpg)
