Quantum mechanics and bonding theories
branch of science which deals with the matters behavior and also explain atomic
and subatomic scale .It explain the qualities of atoms, molecules their constituents
For example electron protons and neutrons. The matters
behavior and radiations on atomic scales are very complicated and very
difficult to understand and it cannot also be believed. There are many reasons
for which we study and apply the quantum mechanics.
Firstly it is used to illustrate the necessary
methodology of physics and the second reason for it is that it is successful in
giving correct results in every application where it is applied.
Historical Background of Quantum Mechanics:
As we know that the both radiation and matter have the characteristics
of particles and waves and some scientists recognize that the radiation have
the particle like properties. The most of the physics of eighteenth century
were believed that the light consists of particles.
The development of quantum mechanics was begin
in 20th century when the scientists started studying molecular and
atomic phenomenon and discovered the classical mechanics and wave theory of
light did not explain their experiments results. Classical mechanics is based
on the newton’s law of motion and Maxwell’s wave theory was able to explain
phenomenon related to the large object. However it was fails when it was
applied to small particles such as electrons atoms molecule etc. For example
according to classical mechanics it should be possible to determine the
position and velocity of a moving particle but this is given by Heisenberg
uncertainty principle. Similarly classical mechanics was assume that the energy
is emitted or absorb whereas the Planks quantum theory that the energy is not
absorbed or emitted continuously but it is discontinuously in the form of
energy packets that are called photons or quanta. Further the concept of the
quantum mechanics was introduced to explain the concept of the atomic spectra.
A few phenomenon for which the classical mechanics theory was fail to give the
satisfactory explanation are black body radiations photoelectric effect heat
capacities of solids and atomic and molecular spectra.
of the classical mechanical theory to explain the phenomenon associated with
microparticals a new mechanics has been put forward to explain these
phenomenon. One of these is called the Matrix Mechanics given forwarded by
Heisenberg in 1925.It is purely mathematical and does not assume any atomic
model. The other is called the wave mechanics put forwarded by Schrodinger in
1926.It is based on the de Broglie concept of dual character of the matter and thus takes into
account the particle as wave nature of material particles. However it has been
shown that the both the mechanics are essentially equivalent so for as the
basic physical concept are concerned. Wave mechanics is being competitively
simpler and more useful in the application of chemistry. It is also called
particle mechanics or quantum mechanics .Because it with the problem that are
arise when particles such as electrons atoms nuclei and molecules etc. are
subjected to force. The quantum mechanics take the concept of de’broglic
concept of dual nature of matter and Planck’s quantum mechanics. It is also
able to explain the phenomenon that is related to small particles
The important applications of the
It helps the scientist to calculate energy
levels and other properties of atoms and molecule.
It also enables the scientist to understand the
periodic variations in properties like ionization, electron affinity and atomic
It enables to understand the nature of chemical
bonding in molecules.
The energy level bond angles and bond lengths
can be calculated accurately for many molecules and compounds. The increasing
power of computer has made these calculations more and more accurate.
Quantum mechanical principles together with
symmetry idea of molecules can help to predict that the molecule has dipole
moment or not.
Quantum mechanics also give the basis for
understanding the results of measurement of spectroscopy. Spectroscopy is useful
for the identification of molecules and there concentration is also determined
.It is especially used in physical chemistry because it yield information about
the properties of molecules. Microwave and infrared spectroscopy yield
information about bond angles and bond length.IR and Raman spectroscopy yield
the information about vibrational motion of the molecules.UV visible
spectroscopy provides information on dissociation energies bond energies and
excited state of the electrons.
also counts properties of individual molecule with the thermodynamics
properties of the bulk matter though statistical mechanics are chemical statistics
or quantum statistics mechanics having information obtained from the method or
In classical mechanics we study
about the larger particles each having certain mass .It is based on the newton
law of motion
1. An object will stay at rest and will
moving with constant speed until an unbalanced force act on that object
2. If an unbalanced force act on the
body an object will accelerate in the direction of force the acceleration is
directly proportional to the force and inversely proportional to the mass of
3. Action and reaction are equal in
magnitude but opposite direction.
Difference between quantum mechanics and classical mechanics
Classical mechanics 1.In
classical mechanics we study the macroscopic objects e. g. planets stars etc.
2. It based on the newton
law of motion.
3. It study only the
particle nature of the object.
4. Classical mechanics accuracy is 100%.
5. We can measure two observable at a time.
6. Normally large units
are used for the measurement.
7. Classical cannot explain the advance
1. It is based on the Schrodinger wave
2. It deals with the micro particle
study like atom electrons etc.
3. It deals with the dual nature of the
4. Its accuracy cannot be 100%.
5. Two observable cannot be measure
6. Small units are used like nm, mm, and
7. It is the science of the future and
discuss many advance problems of both physical and medical sciences.
Theories of chemical bonding:
bonding theories that are currently accepted allow us to predict structures and
properties that are usually accurate. Here we discuss three bonding theories.
The first is the valence shell electron pair repulsion (VESPER) theory which
assumes that electrons pairs are arranged around the central atom in such a way
that there is maximum separation among the different electrons pairs.
second theory is the valance bond theory (VBT) which explain the bonding in
overlapping atomic orbitals. The third theory is called molecular orbital (MO)
theory which assumes that the atomic orbitals of the original unbounded atoms
become replaced by the new set of molecular energy levels that are called
molecular orbitals. And the occupancy of these orbitals determines properties
of the resulting molecule.
Valance shell electron pair repulsion (VSPER)
main idea of the vesper theory is that:
The electron pairs surrounding the central atom must be arranged in
space as far apart as possible to minimize the electrostatic repulsion between them.
A central atom is any atom that is bonded to two or more than two atoms. The
first and the most important rule of the VESPER theory is that the bond angle
about a central atom are those that minimize the total repulsion between the
electron pairs in the valance shell of the atom while working out the shapes of
molecules from this theory the following rules are necessary:
A lone pair of electron occupy most space than a bonding
pair. This is because the lone pair of electrons is under the influence of only
one nucleus of the central atom they are expected to fill more space with a
greater electron density than the bond pair electrons which are under the
influence of two neucli.Thus decreasing order of repulsion is:
Lone pair –lone pair > lone pair-bond pair >bond
Repulsive forces decrease sharply with increasing
inter pair angle. They are strong at 90 much weaker at 120 and they are very
weaken at 180.
The influence of bonding electrons decrease with the
increasing value of electro negativity of an atom forming a molecule.
Multiple bonds behave as a single electrons pair for
the purpose of VSPER theory.
The two electrons pairs of a double bond or three
electrons pair of a triple bond occupy more space than the one electron pair of
a single bond.
The lone pairs repel bond pairs giving rise to some
distortion in the shape of molecule. The distortion may also result due to the
different atoms in the molecules.
Application of VSPER theory:
Let us now apply the valance shell electron pair repulsion theory to
predict the shape of molecules. The first step in the VSPER method for
determining the geometry of the molecule is to write down its Lewis structure
in order to determine the no of electron pairs around the central atom. The
second step is to determine the total no of electron pair around the central
atom. The second step is to determine the no and location of lone pair.
scientist Gillespie propose some rule for the explanation of shape of inorganic
1: If the central atom of a molecule is surrounded only by bonding electron
pair and not by non-bonding electron pair called lone pair. The geometry of the
molecule will be regular. It will be linear triangular and planner tetrahedral
trigon by pyramid and regular octahedron for 2,3,4,5 and 6 bonding electron
Rule 2: when
the central atom in a molecule is surrounded by both bps and lps , the molecule
does not have a regular shape. The alternation or distortion in shape is due to
the alternation in bond angles which arises due to presence of on the central
Rule 3. B-A-B bond angle decreases with the
increase in electronegativity of atom B in AB molecule where in A in the
central atom. This is due to the fact that with the increase in electronegativity of atom B’ the average
position of bonding electron –pair moves farther from the central atom A and
hence the repulsion exerted by bonding electron pair on the electron pair on
atom A decreases.
Rule 4. Bond angles involving multiple bonds
multiple bonds are generally larger than those involving only single bonds.
However the multiple bonds do not affect the geometry of a molecule.
Repulsion between electron- pairs in filled shells are larger than the
repulsion between electron pairs in completely filled shells.
The valance shell electron pair repulsion model
predicts the shapes of molecules and ions in which valance shell electron pairs
are arranged about each atom so that electron – pair repulsions. That even
though VSPER suggests pairs of electrons region can exist really refers to
electron domains or regions. An electron region can exist as a single electron,
two electrons pair and bond pair, four electron bond, or six electrons. However
when we determine the geometry of a molecule, we locate the positions of the
atoms, not the electron pairs. For the general molecular formula, A refers to
central atom, B refers to atoms attached to central atom, and E refers to
unbounded electron pairs.
AB2; Molecules with two electron pairs around a
There are several molecules and ions that consists
of a central pair plus two atoms of another element in which there are no lone
pairs on the central atom. This type of molecule is abbreviated as AB2.
In the solid state, Beryllium chloride, BeCl2,
molecules are bonded to each other in polymeric solid. However, BeCl3 exists as
Valance bond theory:
The vesper theory is quite successful in and the in
explaining and predicting molecular geometry but does not describe how and
where bonding occur as well where lone pairs of valence electrons are directed
.also it does not permit a prediction of bond energies bond lengths etc. In
order to find the answer to these questions the molecules have been employed.
Two approaches have been used for the purpose of describing the covalent bond
and electronic structures of molecules. Each approach employed quantum mechanics.
The first approach called the valance bond theory and second called the
molecular orbital theory. Both approaches are based on the concepts of
The valance bond theory is based on the assumption that the half-filled
atomic orbitals of combining atoms interact to form bigger new orbitals of
combining atoms interact to form bigger new orbitals called molecular orbitals.
These new orbitals are responsible for making the system to be a stable one.
Hitler and London
(1927) proposed that the electrons wave of the valance orbitals on one atom
overlaps the electrons wave of the other bonding orbitals to form a covalent bond.
The essential condition for the overlap of electron waves of orbitals are:
two overlapping orbitals must be valance orbitals must be half filled and must
retain their identities. All other orbitals on the atoms remain undistributed.
half-filled valence orbitals of the atoms should approach sufficiently close to
one another with the axis of their orbitals in proper alignment.
Let us see how valance bond theory explain the formation of
hydrogen molecule starting from H atoms.
We begin with two hydrogen atoms are far apart so that no
interaction occur. If electron 1 occupies atom A and electron 2 occupies atom B
the wave function for the pair is:
Note that the wave function
of the separate system are multiplied to produce the overall function. This is
an accurate description when the atoms are infinity separated
As the two hydrogen atoms
approach each other the electron of one atom is attached to the nucleus of the
other .However the repulsion between electron –electron and nucleus also become
important. The attractive and repulsive forces are balanced at an internuclear
distance of 0.074 nm and the actual distance between the nuclei of the hydrogen
atom has its lowest energy 436KJ/mol which is most stable arrangement. The valance
bond theory give the explanation when the atoms are at equilibrium separation
in the molecule. In the electrostatic analysis we treat the electrons as
separate electrons. It tell us that we really do not know which electron is
Sigma bond and pi bond in VBT:
A molecular orbital that is
symmetrical about the line joining the two nuclei and that is occupied by the
pair of the electron is called sigma molecular orbital and the linkage that is
formed thus is called sigma bond. Although the electrons have the freedom with
in the entire region of the molecular orbital. The probability of finding the
electrons is higher between the two nuclei on the bond axis. A straight line
that is joining the two nuclei of bonded atoms is called the bond axis. All
single bonds are sigma bonds and they are formed by the end to end or head on
overlap of the atomic orbitals.
A bond in which the distribution of the electron is concentrated along
the internuclear axis and possesses axial symmetry is called sigma bond. And
these bonds are required for the formation of different compounds which are
explained by the valance bond theory.
Postulates of valance bond theory:
atom that are to be unite to form a molecule having their complete
covalent bond is formed by the overlap of atomic orbitals. If the two atoms
each having one unpaired electrons, came together, the atomic orbitals
according these unpaired electrons overlap and the spin of the two electrons get
mutually neutralized resulting in the formation of a covalent bond which is
localized between two atoms. If the electron in AO are of parallel spin, no
bond formation will take place.
the atomic orbitals possess, more than one unpaired electrons, formation of
more than one covalent bonds is possible.
shell electrons which are already paired cannot make covalent bonds unless they
are unpaired. Unparing of electrons necessary energy. However the energy
removed by bond formation usually compensate the unpairing energy.
strength of a covalent bond roughly on the extent of atomic orbitals overlap
bond extent of overlap, stronger is the covalent bond.
Molecular orbital theory (MOT)
valance bond theory is based upon the assumption that the formation of molecule
includes relationship between the electron waves of only the atomic orbitals
taking part atoms which are half filled. These bonding orbitals migrate into
one another to give a new orbital of a larger size which is responsible for the
stability of the system. All other orbitals on the atoms remain undividable.
to the molecular orbital theory (developed by Hund, Mullikan and Hackle), all
the valance electrons in molecule are associated with all the nuclei concerned.
In other Words, all the valance electrons have an influence on the stability of
molecule. Furthermore MO theory considered that valance shell atomic orbital
cease to exist when a molecule is formed. They are replaced by a new set of
energy levels with corresponding new charge- cloud distributions. These new
energy levels are a property of a molecule as a whole and are called,
consequently molecular orbitals. An electronic energy level in a molecule and a
corresponding charge- cloud distribution in species called molecular orbital.
Molecular orbitals may be obtained by the linear combination of atomic orbitals
(LC AO method) belonging to each atom in the molecule. The wave functions of
the atomic orbitals are combined mathematically to produce wave functions for
the resulting molecular orbitals. The molecular orbitals are polycentric and
not monocentric as in the case of an atom. The number of original atomic
orbitals combined. The rules for filling the electrons in these molecular
orbitals are the same as for filling the atomic orbitals.
us consider the example of the simple homonuclear diatomic molecule such as
hydrogen molecule in which two identical atoms are linked by an electron pair.Alhough
the atoms are identical but it will be convenient to distinguish the two atoms
by writing the