QUANTUM CHEMISTRY
(SIMPLIED AND HIGHLY UNDERSTANDABLE)
Table of Contents
1.0 INTRODUCTION .......................................................................................................................................1
2.0 THE WAVE FUNCTION (Ψ) .....................................................................................................................1
3.0 QUANTUM NUMBERS .............................................................................................................................2
3.1 Principal quantum number (n) .................................................................................................................2
3.2 Azimuthal quantum number (Ɩ) ................................................................................................................2
3.3 Magnetic quantum number (MƖ) ..............................................................................................................2
3.4 Spin quantum number (Ms)......................................................................................................................3
4.0 Hund’s rule ..................................................................................................................................................3
4.1 Madelung’s rule ...........................................................................................................................................3
4.2 Pauli Exclusion Principle .............................................................................................................................5
5.0 The electron arrangement (electron configuration) .....................................................................................6
6.0 WAVE-PARTICLE DUALITY OF AN ELECTRON..............................................................................10
6.1 The particle characteristics of an electron .............................................................................................10
6.2 The wave characteristics of an electron .................................................................................................10
7.0 AN ORBITAL ...........................................................................................................................................10
7.1 The s and p orbitals shown in figure 11 .................................................................................................11
7.2 The d orbitals .........................................................................................................................................11
8.0 ORBITAL HYBRIDIZATION..................................................................................................................11
8.1 TYPES OF HYBRIDIZATION (They include; sp, sp2, sp3, sp3d, sp3d2) ..............................................12
8.11 sp hybridization................................................................................................................................12
8.12 sp2 hybridization ..............................................................................................................................14
8.13 sp3 hybridization ..............................................................................................................................16
8.14 sp3d hybridization ............................................................................................................................18
8.15 sp3d2 hybridization ...........................................................................................................................20
, 1
QUANTUM CHEMISTRY
1.0 INTRODUCTION
This is a branch of chemistry that explains the application of quantum mechanics to chemical
system. The arrangement of electrons is herein explained and the effect of spatial arrangement on
the electronic energies explained in details. The wavelike character (see wave duality section
below) of an electron makes it difficult to use classical equations to describe the motion of an
electron. It therefore necessitates the need for a new approach that would account for the wave
nature of electrons. Erwin Schrödinger developed the wave mechanics which is basically a
mathematical technique that explains the relationship between the, motion of a particle which is
wavelike to its allowed energies. The beautiful contribution by Schrödinger in quantum mechanics
enables scientist to describe the spatial arrangement of electrons and to quantify their energies. The
mathematical expression in quantum mechanics are sophisticated, however, you do not have to
know the details of it to understand the general conclusion.
2.0 THE WAVE FUNCTION (Ψ)
This is a mathematical expression that describes the location of a particle in space in relation to the
amplitude of its wave which is directly proportional to its energy. Schrödinger identified three
quantum numbers (n, Ɩ and MƖ) to specify a wave function. These quantum numbers provide
information about the distribution of electrons.
, 2
3.0 QUANTUM NUMBERS
3.1 Principal quantum number (n)
Principal quantum number is also known as energy level quantum number. It gives the
relative distance of an electron from the nucleus. This quantum number takes on integers from;
n = 1, 2, 3,….
3.2 Azimuthal quantum number (Ɩ)
It is also referred to as angular quantum number. It describes the shape of the electron cloud.
Azimuthal quantum number represents the sub shell (normally designated by s, p, d, f….). It
takes on integers from 0 to n-1 e.g. for an atom with n = 4, Ɩ can be 0, 1, 2 or 3. In this case, for Ɩ
= 0 is the first value of Ɩ and is named s orbital. For Ɩ =1 is p orbital, Ɩ =2 is the d orbital and Ɩ =3
is the f orbital.
3.3 Magnetic quantum number (MƖ)
Magnetic quantum number (number of orbitals), the value of this quantum number describes
the orientation of the orbitals with respect to applied magnetic field. The values of MƖ are
dependent on the value of Ɩ and it ranges from – Ɩ to + Ɩ e.g. for Ɩ = 1, MƖ = -1, 0, +1. Remember
from our discussion under angular quantum number (Ɩ), we had seen that Ɩ = 1 is the p orbital
and having three values of MƖ = -1, 0, +1 means that the p sub shell has 3 differently oriented
orbitals in space which are; Px, Py and Pz, these three orientations are shown in figure 1.
(SIMPLIED AND HIGHLY UNDERSTANDABLE)
Table of Contents
1.0 INTRODUCTION .......................................................................................................................................1
2.0 THE WAVE FUNCTION (Ψ) .....................................................................................................................1
3.0 QUANTUM NUMBERS .............................................................................................................................2
3.1 Principal quantum number (n) .................................................................................................................2
3.2 Azimuthal quantum number (Ɩ) ................................................................................................................2
3.3 Magnetic quantum number (MƖ) ..............................................................................................................2
3.4 Spin quantum number (Ms)......................................................................................................................3
4.0 Hund’s rule ..................................................................................................................................................3
4.1 Madelung’s rule ...........................................................................................................................................3
4.2 Pauli Exclusion Principle .............................................................................................................................5
5.0 The electron arrangement (electron configuration) .....................................................................................6
6.0 WAVE-PARTICLE DUALITY OF AN ELECTRON..............................................................................10
6.1 The particle characteristics of an electron .............................................................................................10
6.2 The wave characteristics of an electron .................................................................................................10
7.0 AN ORBITAL ...........................................................................................................................................10
7.1 The s and p orbitals shown in figure 11 .................................................................................................11
7.2 The d orbitals .........................................................................................................................................11
8.0 ORBITAL HYBRIDIZATION..................................................................................................................11
8.1 TYPES OF HYBRIDIZATION (They include; sp, sp2, sp3, sp3d, sp3d2) ..............................................12
8.11 sp hybridization................................................................................................................................12
8.12 sp2 hybridization ..............................................................................................................................14
8.13 sp3 hybridization ..............................................................................................................................16
8.14 sp3d hybridization ............................................................................................................................18
8.15 sp3d2 hybridization ...........................................................................................................................20
, 1
QUANTUM CHEMISTRY
1.0 INTRODUCTION
This is a branch of chemistry that explains the application of quantum mechanics to chemical
system. The arrangement of electrons is herein explained and the effect of spatial arrangement on
the electronic energies explained in details. The wavelike character (see wave duality section
below) of an electron makes it difficult to use classical equations to describe the motion of an
electron. It therefore necessitates the need for a new approach that would account for the wave
nature of electrons. Erwin Schrödinger developed the wave mechanics which is basically a
mathematical technique that explains the relationship between the, motion of a particle which is
wavelike to its allowed energies. The beautiful contribution by Schrödinger in quantum mechanics
enables scientist to describe the spatial arrangement of electrons and to quantify their energies. The
mathematical expression in quantum mechanics are sophisticated, however, you do not have to
know the details of it to understand the general conclusion.
2.0 THE WAVE FUNCTION (Ψ)
This is a mathematical expression that describes the location of a particle in space in relation to the
amplitude of its wave which is directly proportional to its energy. Schrödinger identified three
quantum numbers (n, Ɩ and MƖ) to specify a wave function. These quantum numbers provide
information about the distribution of electrons.
, 2
3.0 QUANTUM NUMBERS
3.1 Principal quantum number (n)
Principal quantum number is also known as energy level quantum number. It gives the
relative distance of an electron from the nucleus. This quantum number takes on integers from;
n = 1, 2, 3,….
3.2 Azimuthal quantum number (Ɩ)
It is also referred to as angular quantum number. It describes the shape of the electron cloud.
Azimuthal quantum number represents the sub shell (normally designated by s, p, d, f….). It
takes on integers from 0 to n-1 e.g. for an atom with n = 4, Ɩ can be 0, 1, 2 or 3. In this case, for Ɩ
= 0 is the first value of Ɩ and is named s orbital. For Ɩ =1 is p orbital, Ɩ =2 is the d orbital and Ɩ =3
is the f orbital.
3.3 Magnetic quantum number (MƖ)
Magnetic quantum number (number of orbitals), the value of this quantum number describes
the orientation of the orbitals with respect to applied magnetic field. The values of MƖ are
dependent on the value of Ɩ and it ranges from – Ɩ to + Ɩ e.g. for Ɩ = 1, MƖ = -1, 0, +1. Remember
from our discussion under angular quantum number (Ɩ), we had seen that Ɩ = 1 is the p orbital
and having three values of MƖ = -1, 0, +1 means that the p sub shell has 3 differently oriented
orbitals in space which are; Px, Py and Pz, these three orientations are shown in figure 1.
