Orbital (Modern) Concept of Covalent Bond
The Lewis Concept of Covalent
Bonding failed to explain the geometry
and magnetic properties of
molecules.
In 1927, Heitler and London put forward Valence Bond Theory (VBT). In 1930, Hund, Huckle and Mullikan put forward
Molecular Orbital Theory (MOT). Both theories account for bond energies, bond
length and shape of covalent molecules. According to both theories:
A Covalent Bond is formed by the
overlapping or interpenetrating (fusion) of two atomic orbitals, each
containing a single electron.
Valence Bond Theory (VBT)/ Atomic Orbital
Theory (AOT) of Covalent Bond
(Heitler-London’s Theory/ Pauling-Slater’s
theory)
Introduction
Valence Bond Theory (VBT) or
atomic orbital theory was first proposed in 1927 by Heitler and London and was
modified in 1931 by Pauling and Slater that accounts for the formation and
directional characteristics of covalent bond. Thus Pauling-Slater’s theory is the modified form of Heitler-London’s
theory.
Statement
Covalent Bond is formed by the overlapping or interpenetrating (fusion)
of two atomic orbitals of the valence shell each containing an unpaired
electron. OR A covalent bond between
two atoms results by the overlap of half-filled
atomic orbitals (AOs) belonging to their outermost shell giving rise to a single bond orbital occupied by both
the electrons with opposite spins.
According to VBT, the bonding
electrons occupy the atomic orbitals of the bonded atoms, and the shared
electron is influenced by one nucleus (monocentric).
According to VBT, atomic
orbitals which are involved in the bond formation maintain their individual
nature and identities.
In VBT, some of the valence
electrons are indicated as unshared and uninvolved in the formation of
molecule.
Molecular Orbital Theory (MOT)/ Hund- Mulliken
Theory/ LCAO-MO Theory
Introduction
Molecular orbital theory (MOT)
was mainly developed in 1930 (1932) by Hund, Huckle and Mulliken. This theory
is also sometimes called Hund-Mulliken’s
Theory. This theory is based on the Linear
Combination of Atomic Orbitals (LCAO) of the atoms constituting the
molecule or ion and hence is also called LCAO-MO
Theory.
Statement
A covalent bond between two atoms results by the overlap of half-filled
atomic orbitals (AOs) belonging to their outermost shells which get mixed up to
give an equivalent number new molecular orbitals containing the two bonding
electrons with opposite spin and are influenced by two or more nuclei (i.e.
they are polycentric). OR A covalent bond is formed by the
overlapping or interpenetrating (fusion) of two half-filled atomic orbitals and
the bonding (shared) electrons occupy the molecular orbitals which are
polycentric and influenced by more than one nucleus.
According to MOT, the bonding
electrons occupy the molecular orbital and the shared electron is influenced by
more than one nucleus (polycentric).
According to MOT, atomic
orbitals which form molecular orbitals do not retain their individual nature.
In MOT, all of the valence electrons take part in the bonding of molecules.
Explanation
Internuclear
axis/Bond Axis
The line joining the nuclei of
atomic orbitals of both the atoms is called internuclear axis (INA) or bond
axis or molecular axis. It is an imaginary line joining the two nuclei of
atomic orbitals.
Overlapping
The interpenetration or fusion
of half-filled atomic orbitals (or hybrid orbitals) is called Overlapping. The overlapping of atomic orbitals takes
place if they have similar signs on their lobes. + and - signs of the lobes of atomic orbitals are
only geometric signs of the atomic orbital wave function and should not be
confused with + and - charges. The wave functions either have + and - sign. The + sign shows that these orbitals are
spherically symmetrical and electron cloud is concentrated in that orbital (or
lobe) while - sign indicates that electron cloud is less concentrated in that
orbital or lobe.
Types of Overlapping according to internuclear axis
There are two types of
overlapping:
(a) Head-on (i.e. End to end) overlapping (results in (σ-bond).
(b) Side-ways (i.e. lateral)
overlapping (results in (p-bond).
(a) Head-on OR End to End
Overlapping
The overlapping of two
half-filled atomic orbitals along the internuclear (molecular) axis giving
sigma molecular orbitals resulting in sigma bond is called Head-to-Head or Head-on
or End-on or Linear or Axial or Linear-axis overlapping. The various
types of linear axis overlapping to form sigma bond are given below:
Atomic-atomic
orbitals overlapping
1. s-s orbitals overlap
2. s-px orbitals overlap
3. px-px orbitals overlap
Atomic-hybridized
orbitals overlapping
4. s-sp3 (hybrid) orbital overlap
5. s-sp2 (hybrid) orbital overlap
6. s-sp (hybrid) orbital overlap
7. px -sp3 (hybrid) orbital overlap
8. px -sp3 (hybrid) orbital overlap
9. px -sp3 (hybrid) orbital overlap
Hybridized-hybridized
orbitals overlapping
10. sp3-sp3 (hybrid)orbital
11. sp2-sp2 (hybrid)orbital
12. sp-sp (hybrid)orbital
(b) Side-Wise OR Side to Side
Overlapping
The overlapping of two
half-filled p-atomic orbitals along a line perpendicular to the internuclear
(molecular) axis giving pi molecular orbitals resulting in pi bond is called sideways or sidewise or side-to-side
or lateral or parallel overlapping. The lateral overlapping takes place only
between two py or pz atomic orbitals.
Types of Overlapping according to LCAO
Method
According to MOT, the linear
combination of atomic orbitals (LCAO) gives rise to two types of overlapping:
(a) Additive overlap/ Positive overlap/ ++ overlap
(b) Subtractive overlap/ Negative overlap/+ - overlap
(a) Additive
overlap/ Positive overlap/ ++ overlap
The linear additive overlap
(also called positive overlap or ++ overlap) involves the overlapping of the
positive lobe of an atomic orbital with the positive lobe of another atomic
orbital to form a molecular orbital having a lower energy than each of the
combining atomic orbitals exerting attraction between the two nuclei by
concentrating the electron density between them. This attraction between the
two nuclei and occupation of this molecular orbital by two electrons with
opposite spins results in the bond formation. Hence this molecular orbital is
called bonding molecular orbital (BMO).
(b) Subtractive
overlap/ Negative overlap/+ - overlap
The linear subtractive overlap
(also called Negative overlap/+ -
overlap) involves the overlapping of the positive lobe of an atomic
orbital with the negative lobe of another atomic orbital to form a molecular
orbital having a higher energy than each of the combining atomic orbitals
exerting repulsion between the two nuclei by concentrating the electron density
away from the region between the two nuclei so that nuclei are exposed and face
each other. This repulsion opposes bond formation and this molecular orbital is
unoccupied with electrons. Hence this molecular orbital is called antibonding
molecular orbital (AMO).
Difference between Atomic Orbital and
Molecular Orbital
1. An
atomic orbital is defined as the region of space round the nucleus in an atom
in which there is maximum probability of finding the electron A molecular orbital is defined as the region
of space round the two or more nuclei in a molecule.
2. An atomic orbital belongs to one nucleus only and hence is
monocentric. A molecular orbital belongs
to two or more nuclei and hence is polycentric.
3. An atomic orbital may contain one or two electrons. A
molecular orbital always contain two electrons
or no electrons at all.
4.Atomic orbital may be pure or hybridized. Molecular orbital
may be bonding or antibonding.
5. Pure atomic orbitals are designated by s, p, d, and
f-orbitals and hybrid atomic orbitals are designated
by sp3, sp2, sp etc. Molecular orbitals are designated as
(s and p-orbitals).
6. Atomic orbitals have a simple shape like sphere, dumb-bell,
double dumb-bell etc. Molecular orbitals
have complicated shapes.
Types of Molecular Orbitals according to LCAO Method
According to MOT, the Linear
Combination of Atomic Orbitals (LCAO) by additive overlap (or positive overlap
or ++ overlap) and subtractive overlap (or negative overlap /+ - overlap) gives
rise to two types of molecular orbitals, one of lower energy and the other of
higher energy than the average energy of the two isolated overlapping atomic
orbitals:
(a) Bonding Molecular Orbital (BMO)
(b) Antibonding Molecular Orbital (AMO)
(a) Bonding Molecular Orbital
The molecular orbital in which
there is a maximum electronic cloud density between the centers of two nuclei
and which has lower energy than the total energy of the atomic orbitals from
which it is derived is called a Bonding Molecular Orbital (BMO).
If the two electrons of the
atomic orbitals, occupy the lower energy molecular orbital, the electron
density is concentrated in the region between the two nuclei, exerting
attraction on both the nuclei.
Therefore, occupation of this
orbital by two electrons results in the bond formation. Hence, this molecular
orbital is called Bonding Molecular Orbital.
(b) Antibonding Molecular Orbital
The molecular orbital in which
there is a minimum electron cloud density between the centers of two nuclei and
which has higher energy than the energy of the separate atomic orbitals from
which it is derived is called Antibonding Molecular Orbital (AMO).
If the two electrons of the
atomic orbitals, occupy the higher energy molecular orbital, the electron
density is away from region between the two nuclei, so that nuclei are exposed
and face each other, resulting in strong repulsion between them.
This opposes bond formation. Hence
this molecular orbital is called Antibonding Molecular Orbital.
Energy diagram of
Bonding and Antibonding Molecular Orbitals
1. An
energy diagram for the molecular orbitals (for hydrogen) is shown below in
which two atomic orbitals approach each other to form two molecular orbitals.
2. The molecular orbital with less energy than
its parent atomic orbitals is more stable and occupied
with two electrons of opposite spin and is called Bonding Molecular Orbital.
This is the Lowest Electronic
Energy State or Ground State of (Hydrogen) Molecule.
3. The molecular orbital with high energy than
its parent atomic orbitals is less stable and unoccupied
with electrons and is called Antibonding Molecular Orbital (AMO).An electron
may occupy AMO in excited
state. This state is achieved when electrons in ground state absorbs a photon of light of proper energy.
Types of Molecular Orbitals
There are two types of molecular
orbitals:
1. Sigma Molecular Orbital (σ-MO)
[which has sigma (σ) bond].
2.
Pi-Molecular Orbital (p--MO) [which has sigma (p) bond].
Sigma Bond/σ-Bond
Definition of
Sigma Bond
A covalent bond which is formed by the head on overlapping of
half-filled atomic orbitals (or hybrid orbitals) along a internuclear axis
giving rise to sigma bonding and sigma antibonding (σ*)
molecular orbitals is called a sigma (σ)
bond and the electrons that occupy sigma orbital (bond) are called sigma
electrons. In other words, a sigma bond is a (bonding) molecular orbital which
is symmetrical about a line joining the two nuclei (internuclear axis). Sigma bond is produced (assuming
x-axis to be the molecular axis) by s-s-overlap (as in H2), s-px
overlap (as in HF, HCl, HBr, HI, H2O, NH3 etc) and px-px
overlap (as in F2, Cl2, Br2, and I2).
A sigma bond is also produced when a hybrid orbital overlaps with atomic
orbital or two hybrid orbitals overlap together along the internuclear axis.
Various
Combinations of Linear overlapping giving sigma bonds
The linear axis overlapping of
different orbitals leading to sigma bond formation is given below:
Atomic-atomic orbitals overlapping
1. s-s orbitals overlap
2. s-px orbitals overlap
3. px-px orbitals overlap
Atomic-hybridized orbitals overlapping
4. s-sp3 (hybrid) orbital overlap
5. s-sp2 (hybrid) orbital overlap
6. s-sp (hybrid) orbital overlap
7. px -sp3 (hybrid) orbital overlap
8. px -sp3 (hybrid) orbital overlap
9. px -sp3 (hybrid) orbital overlap
Hybridized-hybridized
orbitals overlapping
10. sp3-sp3 (hybrid)orbital
11. sp2-sp2 (hybrid)orbital
12. sp-sp (hybrid)orbital
Example of Sigma
Bond Formation
(1). Formation of Sigma Bond in
Hydrogen (H2) Molecule
Each
hydrogen atom has one half-filled 1s-orbital. In the formation of H2
molecule, 1s-orbitals of both hydrogen atoms containing an unpaired electron
overlap with each other along internuclear axis (s-s- overlap) to form a H – H
sigma bond (which constitutes a single covalent bond in H2
molecule). The antibonding orbital remains vacant.
(2). Formation of Sigma Bond in Fluorine (F2)
Molecule
Each fluorine atom has one
half-filled 2p-orbital. In the formation of F2 molecule, 2px-orbitals
of both fluorine atoms containing an unpaired electron overlap with each other
along internuclear axis (px-px- overlap) to form a F – F
sigma bond (which constitutes a single covalent bond in F2
molecule). The antibonding orbital remains vacant.
(3). Formation of Sigma Bond in
Hydrogen fluoride (HF) Molecule
Hydrogen atom has one
half-filled 1s-orbital and fluorine atom has one half-filled 2p-orbital. In the
formation of HF molecule, 1s-orbital of hydrogen atom and 2px-orbital
of fluorine atom containing an unpaired electron overlap with each other along
internuclear axis (s-px-overlap) to form a H – F sigma bond (which
constitutes a single covalent bond in H–F molecule). The antibonding orbital
remains vacant.
Characteristics of
Sigma Bond
1. A
sigma bond results from end to end overlap of atomic orbitals giving two types
of molecular orbitals (as when atomic orbitals combine an equivalent number of
new molecular orbitals is formed), one of lower energy and other of higher
energy than the combining atomic orbitals called sigma-bonding (sbMO OR s-orbital) and sigma-antibonding (s*MO or s*-orbital) molecular orbitals
respectively. Sigma bonding molecular orbital denoted as (sbMO OR s-orbital) is obtained when the + lope of one atomic orbital
overlaps with the + lope of another atomic orbital having a single region of
electron density in between the two nuclei of atomic orbitals, and thus s-bonding orbital is occupied with two electrons of
opposite spin. Sigma antibonding molecular orbital denoted as s*MO or s*-orbital is obtained when the +
lobe of one atomic orbital overlaps with the - lobe of another atomic orbital
having negligible electron density in between the two nuclei of atomic orbitals
and hence the nuclei fly apart and so s*orbital is unoccupied with electrons. The electrons
may occupy s*orbital in excited state.
2. sb-orbital and s*-orbitals both have cylindrical
symmetry around the internuclear axis. It is for this reason that these molecular orbitals are called sigma
molecular orbitals.
3. s-orbital has no node while s*-orbital has one node.
4. There is free rotation of s-orbital about the bond axis. Thus if an atomic
orbital (which forms s-orbital)
is rotated on the internuclear axis, the extent of overlap region does not
change i.e. electronic
distribution and bond length do not change in case of sigma bonds. Thus s-bond (or s-orbital) decides the direction of the bond and the
bond length.
5. The s-orbitals as well as p-orbitals can
overlap in linear axis or along internuclear axis to form sigma bond. The hybrid orbitals can also form sigma bond by
linear overlap along internuclear axis.
6. The extent of overlapping in sigma bond is
sufficient (due to end to end overlap of atomic orbitals) resulting in a strong bond between two atoms
(i.e. less reactive and more stable) with higher
bond energy.
7. The
relative strength of sigma is related to the extent of overlap of atomic
orbitals. This is known as the
Principle of Maximum Overlap. The
relative strength of the sigma bonds obtained
by various overlapping of atomic orbitals is as s s < sp < pp (i.e. the
relative bond strength is
p p > s p > s
s). Thus sigma bond formed by s-s overlap is relatively weak since s-orbitals have spherical distribution of
electron density. On the other hand, sigma bond formed by p-p or p-s overlap is relatively stronger since
p-orbitals are concentrated in a particular
direction and their lobes are longer than the radius of the corresponding
s-orbital.
8. Sigma bond is formed independently
because atoms always combine first with a sigma bond.
9. Only one sigma bond exists between two
atoms.
10. A sigma bond is equivalent to a single
bond.
11. Sigma electrons in a sigma bond are
localized i.e. confined to only two atoms.
12. In sigma bond formation, one lobe of
p-orbital stretches while the other lobe reduces in size.
Pi (p) Bond
Definition
A covalent bond which is formed
by the side-ways overlapping of two half-filled p-atomic orbitals (belonging to
the same atom) whose axes are common along a line perpendicular to the
internuclear axis giving rise to pi-bonding and pi-antibonding (p*) molecular orbitals is called
a pi (p) bond and the electrons that occupy pi-orbital (bond) are called
pi-electrons.
Explanation
1. A pi bond results from lateral overlap of two
p-atomic orbitals at the two sides of the lobe giving two types of molecular
orbitals (as when atomic orbitals combine an equivalent number of new molecular
orbitals is formed), one of lower energy and other of higher energy than the
combining atomic orbitals called pi-bonding (pbMO) and pi-antibonding (p* or p*MO) molecular
orbitals respectively. pi bonding
molecular orbital denoted as (pbMO) or (p-orbital is obtained when the + lope of one p-atomic
orbital overlaps with the + lope of another p-atomic orbital having two regions
of electron density above and below the nodal plane (i.e. place where two
orbitals coincide), and thus (p-bonding orbital is occupied with two electrons of
opposite spin. pi antibonding
molecular orbital denoted as (p*MOor p*-orbital is obtained when the + lobe of one p-atomic
orbital overlaps with the - lobe of another p-atomic orbital having negligible
electron density in between the two nuclei of atomic orbitals and hence the
nuclei fly apart and so p*-orbital is unoccupied with electrons. The electrons
may occupy p*orbital in excited state.
2. pbMO orbital and p*orbitals both have
unsymmetrical electronic distribution around the internuclear axis.
3. pbMO orbital has one node while p*orbital has two nodes.
4. There is restriction of free rotation of
pbMO orbital about the bond axis. Thus if an atomic
orbital (which forms pbMO -orbital) is rotated on the
internuclear axis, the extent of overlap region decreases (further rotation leads to cease the
overlapping of two orbitals) i.e. electronic distribution
and bond length changes incase
ofp-bond. This
increases the potential energy of the
molecule and hence its reactivity is increased. Thus it does not decide the
direction of bond but shortens
the bond length. The formation of two pi-bonds
(as in a triple bond) shortens the bond
length to a greater extent than the formation of one pi-bond (as in a double
bond).
5. The s-orbitals cannot take part in
pi-bond formation. Only p-orbitals can form pi-bond by py-py
or pz-pz
overlaps.
6. The
extent of overlapping in pi bond is less i.e. it has less extent of overlapping
(due to parallel overlap of atomic orbitals in which electron density is
maximum above and below the line joining the nuclei.) resulting in a weak bond
between two atoms (i.e. more reactive and less stable) with lower bond energy.
7.Pi-bond
is not formed independently because a p-bond is only formed when the two different overlapping p-orbitals are on two
atoms which are already bonded by sigma bond.
8. One or two pi-bonds can be formed
between two sigma-bonded atoms [as in O2 (one (p-bond) and in N2 (two p-bonds)].
9. A pi bond is equivalent to a double
bond and two pi-bonds are equivalent to a triple bond.
10.Pi electrons in a pi bond may be localized (i.e. confined to
only two atoms) or delocalized.
11.Both
lobes of p-orbitals take part in pi-bond formation. They retain their shape
i.e. (p-bonding orbital has a
shape similar to that of p-orbital (dumbbell shape).
Difference between Sigma and Pi Bond
1. It is formed by the head on overlapping of two half filled pure
atomic orbitals or hybrid orbitals along the internuclear axis. It is formed by
the side-wise overlapping of two half-filled pure atomic orbitals in the form
of p-orbitals along a line perpendicular to internuclear axis.
2. It is stronger bond (i.e.
more stable and less reactive) due to greater or maximum overlapping of
orbitals. It is a weaker bond (i.e. less stable and more reactive) due to
lesser overlapping of orbitals.
3. It has only one region of
electron cloud density around the bond axis. It has two regions of electron
cloud density, one above and one below the sigma-bond axis.
4. It has symmetrical electron
cloud density around the bond axis. It has unsymmetrical electron cloud density
around the bond axis.
5. Sigma bond can form between s-orbitals (s-s overlap) as well as s
and p-orbitals (s-px and px and px-px
overlap). s-orbitals cannot take part in making pi bond. Only p-orbitals can
form pi bond py-py or pz-pz
overlaps.
6. One lobe of p-orbital taking
part in sigma bond formation, stretches while the other lobe reduces in size.
Both lobes of p-orbitals take part in pi-bond formation. They retain their
shape.
7. It is formed alone and
independently as atoms always combine first with a sigma bond. It is always
formed only between two atoms which are already bonded by a sigma bond.
8. Only one sigma bond exists
between two atoms. One or two pi bonds can be formed between two sigma-bonded
atoms.
9. All single bonds are sigma
bonds. A double bond consists of one sigma and a pi bond, a triple bond
consists of one sigma and two pi bonds.
10. It determines the direction
of bond and bond length. It does not decide the direction of bond but shortens
the bond length. The formation of two pi bonds (as in a triple bond) shortens
the bond length to a greater extent than the formation of one pi bond (as in a
double bond).
11. Sigma electrons in a sigma
bond are localized. Pi electrons in a pi bond may be localized or delocalized.
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