Contributed by:
The matter is made up of one or different types of elements. Under normal conditions, no other element exists as an
independent atom in nature, except noble gases. However, a group of atoms is found to exist together as one species
having characteristic properties.
Scientists are constantly discovering new compounds, orderly
arranging the facts about them, trying to explain with the
existing knowledge, organising to modify the earlier views or
After studying this Unit, you will be evolve theories for explaining the newly observed facts.
able to
• understand K Ö ssel-Lewis
approach to chemical bonding;
• explain the octet rule and its Matter is made up of one or different type of elements.
limitations, draw Lewis Under normal conditions no other element exists as an
structures of simple molecules;
independent atom in nature, except noble gases. However,
• explain the formation of different a group of atoms is found to exist together as one species
types of bonds; having characteristic properties. Such a group of atoms is
• describe the VSEPR theory and called a molecule. Obviously there must be some force
predict the geometry of simple which holds these constituent atoms together in the
molecules; molecules. The attractive force which holds various
• explain the valence bond constituents (atoms, ions, etc.) together in different
approach for the formation of chemical species is called a chemical bond. Since the
covalent bonds; formation of chemical compounds takes place as a result
of combination of atoms of various elements in different
• predict the directional properties
of covalent bonds; ways, it raises many questions. Why do atoms combine?
Why are only certain combinations possible? Why do some
• explain the different types of atoms combine while certain others do not? Why do
hybridisation involving s, p and
d orbitals and draw shapes of molecules possess definite shapes? To answer such
simple covalent molecules; questions different theories and concepts have been put
forward from time to time. These are Kössel-Lewis
• describe the molecular orbital
theory of homonuclear diatomic approach, Valence Shell Electron Pair Repulsion (VSEPR)
molecules; Theory, Valence Bond (VB) Theory and Molecular Orbital
(MO) Theory. The evolution of various theories of valence
• explain the concept of hydrogen
bond. and the interpretation of the nature of chemical bonds have
closely been related to the developments in the
understanding of the structure of atom, the electronic
configuration of elements and the periodic table. Every
system tends to be more stable and bonding is nature’s
way of lowering the energy of the system to attain stability.
4.1 KÖSSEL-LEWIS APPROACH TO the number of valence electrons. This number
CHEMICAL BONDING of valence electrons helps to calculate the
In order to explain the formation of chemical common or group valence of the element. The
bond in terms of electrons, a number of group valence of the elements is generally
attempts were made, but it was only in 1916 either equal to the number of dots in Lewis
when Kössel and Lewis succeeded symbols or 8 minus the number of dots or
independently in giving a satisfactory valence electrons.
explanation. They were the first to provide Kössel, in relation to chemical bonding,
some logical explanation of valence which was drew attention to the following facts:
based on the inertness of noble gases.
• In the periodic table, the highly
Lewis pictured the atom in terms of a electronegative halogens and the highly
positively charged ‘Kernel’ (the nucleus plus electropositive alkali metals are separated
the inner electrons) and the outer shell that by the noble gases;
could accommodate a maximum of eight
electrons. He, further assumed that these • The formation of a negative ion from a
halogen atom and a positive ion from an
eight electrons occupy the corners of a cube
alkali metal atom is associated with the
which surround the ‘Kernel’. Thus the single
gain and loss of an electron by the
outer shell electron of sodium would occupy
respective atoms;
one corner of the cube, while in the case of a
noble gas all the eight corners would be • The negative and positive ions thus
occupied. This octet of electrons, represents formed attain stable noble gas electronic
a particularly stable electronic arrangement. configurations. The noble gases (with the
Lewis postulated that atoms achieve the exception of helium which has a duplet
stable octet when they are linked by of electrons) have a particularly stable
chemical bonds. In the case of sodium and outer shell configuration of eight (octet)
chlorine, this can happen by the transfer of electrons, ns2np6.
an electron from sodium to chlorine thereby

• The negative and positive ions are
giving the Na+ and Cl ions. In the case of stabilized by electrostatic attraction.
other molecules like Cl2, H2, F2, etc., the bond For example, the formation of NaCl from
is formed by the sharing of a pair of electrons sodium and chlorine, according to the above
between the atoms. In the process each atom scheme, can be explained as:
attains a stable outer octet of electrons. Na → Na+ + e

Lewis Symbols: In the for mation of a [Ne] 3s1 [Ne]
molecule, only the outer shell electrons take –
Cl + e → Cl–
part in chemical combination and they are
known as valence electrons. The inner shell [Ne] 3s2 3p5 [Ne] 3s2 3p6 or [Ar]
– –
electrons are well protected and are generally Na+ + Cl → NaCl or Na+Cl
not involved in the combination process. Similarly the formation of CaF2 may be
G.N. Lewis, an American chemist introduced shown as:
simple notations to represent valence –
Ca → Ca2+ + 2e
electrons in an atom. These notations are
called Lewis symbols. For example, the Lewis [Ar]4s2 [Ar]
– –
symbols for the elements of second period are F +e → F
as under: [He] 2s2 2p5 [He] 2s2 2p6 or [Ne]
– –
Ca2+ + 2F → CaF2 or Ca2+(F )2
The bond formed, as a result of the
Significance of Lewis Symbols : The electrostatic attraction between the
number of dots around the symbol represents positive and negative ions was termed as
the electrovalent bond. The electrovalence chlorine atoms attain the outer shell octet of
is thus equal to the number of unit the nearest noble gas (i.e., argon).
charge(s) on the ion. Thus, calcium is The dots represent electrons. Such
assigned a positive electrovalence of two, structures are referred to as Lewis dot
while chlorine a negative electrovalence of structures.
The Lewis dot structures can be written
Kössel’s postulations provide the basis for for other molecules also, in which the
the modern concepts regarding ion-formation combining atoms may be identical or
by electron transfer and the formation of ionic different. The important conditions being that:
crystalline compounds. His views have proved
• Each bond is formed as a result of sharing
to be of great value in the understanding and
of an electron pair between the atoms.
systematisation of the ionic compounds. At
the same time he did recognise the fact that • Each combining atom contributes at least
a large number of compounds did not fit into one electron to the shared pair.
these concepts. • The combining atoms attain the outer-
shell noble gas configurations as a result
4.1.1 Octet Rule
of the sharing of electrons.
Kössel and Lewis in 1916 developed an
• Thus in water and carbon tetrachloride
important theory of chemical combination
molecules, formation of covalent bonds
between atoms known as electronic theory
can be represented as:
of chemical bonding. According to this,
atoms can combine either by transfer of
valence electrons from one atom to another
(gaining or losing) or by sharing of valence
electrons in order to have an octet in their
valence shells. This is known as octet rule.
4.1.2 Covalent Bond
Langmuir (1919) refined the Lewis
postulations by abandoning the idea of the
stationary cubical arrangement of the octet, Thus, when two atoms share one
and by introducing the term covalent bond. electron pair they are said to be joined by
The Lewis-Langmuir theory can be a single covalent bond. In many compounds
understood by considering the formation of we have multiple bonds between atoms. The
the chlorine molecule,Cl2. The Cl atom with formation of multiple bonds envisages
electronic configuration, [Ne]3s 2 3p5, is one sharing of more than one electron pair
electron short of the argon configuration. between two atoms. If two atoms share two
The formation of the Cl2 molecule can be pairs of electrons, the covalent bond
understood in terms of the sharing of a pair between them is called a double bond. For
of electrons between the two chlorine atoms, example, in the carbon dioxide molecule, we
each chlorine atom contributing one electron have two double bonds between the carbon
to the shared pair. In the process both and oxygen atoms. Similarly in ethene
molecule the two carbon atoms are joined by
a double bond.
or Cl – Cl
Covalent bond between two Cl atoms Double bonds in CO2 molecule
in subtraction of one electron from the total
number of valence electrons. For example,
for the CO3 ion, the two negative charges
indicate that there are two additional
electrons than those provided by the
neutral atoms. For NH 4 ion, one positive
charge indicates the loss of one electron
C2H4 molecule from the group of neutral atoms.
• Knowing the chemical symbols of the
When combining atoms share three
combining atoms and having knowledge
electron pairs as in the case of two
of the skeletal structure of the compound
nitrogen atoms in the N2 molecule and the
(known or guessed intelligently), it is easy
two carbon atoms in the ethyne molecule,
to distribute the total number of electrons
a triple bond is formed.
as bonding shared pairs between the
atoms in proportion to the total bonds.
• In general the least electronegative atom
occupies the central position in the
molecule/ion. For example in the NF3 and
N2 molecule CO3 , nitrogen and carbon are the central
atoms whereas fluorine and oxygen
occupy the terminal positions.
• After accounting for the shared pairs of
electrons for single bonds, the remaining
electron pairs are either utilized for multiple
C2H2 molecule
bonding or remain as the lone pairs. The
4.1.3 Lewis Representation of Simple basic requirement being that each bonded
Molecules (the Lewis Structures) atom gets an octet of electrons.
The Lewis dot structures provide a picture Lewis representations of a few molecules/
of bonding in molecules and ions in terms ions are given in Table 4.1.
of the shared pairs of electrons and the
octet rule. While such a picture may not Table 4.1 The Lewis Representation of Some
explain the bonding and behaviour of a Molecules
molecule completely, it does help in
understanding the formation and properties
of a molecule to a large extent. Writing of
Lewis dot structures of molecules is,
therefor e, very useful. The Lewis dot
structures can be written by adopting the
following steps:
• The total number of electrons required for
writing the structures are obtained by
adding the valence electrons of the
combining atoms. For example, in the CH4
molecule there are eight valence electrons
available for bonding (4 from carbon and
4 from the four hydrogen atoms).
• For anions, each negative charge would
mean addition of one electron. For * Each H atom attains the configuration of helium (a duplet
cations, each positive charge would result of electrons)
Problem 4.1 each of the oxygen atoms completing the
octets on oxygen atoms. This, however,
Write the Lewis dot structure of CO
does not complete the octet on nitrogen
if the remaining two electrons constitute
Solution lone pair on it.
Step 1. Count the total number of
valence electrons of carbon and oxygen
atoms. The outer (valence) shell
configurations of carbon and oxygen Hence we have to resort to multiple
atoms are: 2s 2 2p 2 and 2s 2 2p 4 , bonding between nitrogen and one of the
respectively. The valence electrons oxygen atoms (in this case a double
available are 4 + 6 =10. bond). This leads to the following Lewis
Step 2. The skeletal structure of CO is dot structures.
written as: C O
Step 3. Draw a single bond (one shared
electron pair) between C and O and
complete the octet on O, the remaining
two electrons are the lone pair on C.
This does not complete the octet on
carbon and hence we have to resort to
multiple bonding (in this case a triple 4.1.4 Formal Charge
bond) between C and O atoms. This Lewis dot structures, in general, do not
satisfies the octet rule condition for both represent the actual shapes of the molecules.
atoms. In case of polyatomic ions, the net charge is
possessed by the ion as a whole and not by a
particular atom. It is, however, feasible to
assign a formal charge on each atom. The
formal charge of an atom in a polyatomic
molecule or ion may be defined as the
Problem 4.2
difference between the number of valence
Write the Lewis structure of the nitrite electrons of that atom in an isolated or free

ion, NO2 . state and the number of electrons assigned
to that atom in the Lewis structure. It is
expressed as :
Step 1. Count the total number of
valence electrons of the nitrogen atom, Formal charge (F.C.)
on an atom in a Lewis =
the oxygen atoms and the additional one structure
negative charge (equal to one electron).
N(2s2 2p3), O (2s2 2p4)
5 + (2 × 6) +1 = 18 electrons total number of valence total number of non
electrons in the free — bonding (lone pair)

Step 2. The skeletal structure of NO2 is atom electrons
written as : O N O total number of
Step 3. Draw a single bond (one shared — (1/2) bonding(shared)
electron pair) between the nitrogen and
The counting is based on the assumption 4.1.5 Limitations of the Octet Rule
that the atom in the molecule owns one The octet rule, though useful, is not universal.
electron of each shared pair and both the It is quite useful for understanding the
electrons of a lone pair. structures of most of the organic compounds
Let us consider the ozone molecule (O3). and it applies mainly to the second period
The Lewis structure of O3 may be drawn as : elements of the periodic table. There are three
types of exceptions to the octet rule.
The incomplete octet of the central atom
In some compounds, the number of electrons
surrounding the central atom is less than
eight. This is especially the case with elements
having less than four valence electrons.
The atoms have been numbered as 1, 2 Examples are LiCl, BeH2 and BCl3.
and 3. The formal charge on:
• The central O atom marked 1
1 Li, Be and B have 1,2 and 3 valence electrons
=6–2– (6) = +1
2 only. Some other such compounds are AlCl3
• The end O atom marked 2 and BF3.
Odd-electron molecules
=6–4– (4) = 0 In molecules with an odd number of electrons
like nitric oxide, NO and nitrogen dioxide,
• The end O atom marked 3 NO2, the octet rule is not satisfied for all the
1 atoms
=6–6– (2) = –1
Hence, we represent O3 along with the
The expanded octet
formal charges as follows:
Elements in and beyond the third period of
the periodic table have, apart from 3s and 3p
orbitals, 3d orbitals also available for bonding.
In a number of compounds of these elements
there are more than eight valence electrons
around the central atom. This is termed as
We must understand that formal charges the expanded octet. Obviously the octet rule
do not indicate real charge separation within does not apply in such cases.
the molecule. Indicating the charges on the
Some of the examples of such compounds
atoms in the Lewis structure only helps in
are: PF 5 , SF 6 , H 2 SO 4 and a number of
keeping track of the valence electrons in the
coordination compounds.
molecule. For mal charges help in the
selection of the lowest energy structure from
a number of possible Lewis structures for a
given species. Generally the lowest energy
structure is the one with the smallest
formal charges on the atoms. The formal
charge is a factor based on a pure covalent
view of bonding in which electron pairs
are shared equally by neighbouring atoms.
Interestingly, sulphur also forms many Obviously ionic bonds will be formed
compounds in which the octet rule is obeyed. more easily between elements with
In sulphur dichloride, the S atom has an octet comparatively low ionization enthalpies
of electrons around it. and elements with comparatively high
negative value of electron gain enthalpy.
Most ionic compounds have cations
derived from metallic elements and anions
Other drawbacks of the octet theory
from non-metallic elements. The
• It is clear that octet rule is based upon +
ammonium ion, NH4 (made up of two non-
the chemical inertness of noble gases. metallic elements) is an exception. It forms
However, some noble gases (for example the cation of a number of ionic compounds.
xenon and krypton) also combine with
Ionic compounds in the crystalline state
oxygen and fluorine to form a number of
consist of orderly three-dimensional
compounds like XeF2, KrF2, XeOF2 etc.,
arrangements of cations and anions held
• This theory does not account for the shape
together by coulombic interaction energies.
of molecules.
These compounds crystallise in different
• It does not explain the relative stability of
crystal structures determined by the size
the molecules being totally silent about
of the ions, their packing arrangements and
the energy of a molecule.
other factors. The crystal structure of
4.2 IONIC OR ELECTROVALENT BOND sodium chloride, NaCl (rock salt), for
From the Kössel and Lewis treatment of the example is shown below.
formation of an ionic bond, it follows that the
for mation of ionic compounds would
primarily depend upon:
• The ease of formation of the positive and
negative ions from the respective neutral
• The arrangement of the positive and
negative ions in the solid, that is, the
lattice of the crystalline compound.
The formation of a positive ion involves
ionization, i.e., removal of electron(s) from
the neutral atom and that of the negative ion
involves the addition of electron(s) to the Rock salt structure
neutral atom.

In ionic solids, the sum of the electron
M(g) → M+(g) + e ; gain enthalpy and the ionization enthalpy
Ionization enthalpy may be positive but still the crystal
– –
X(g) + e → X (g) ; structure gets stabilized due to the energy
Electron gain enthalpy released in the formation of the crystal

M+(g) + X (g) → MX(s) lattice. For example: the ionization
The electron gain enthalpy, ∆eg H, is the enthalpy for Na (g) formation from Na(g)
enthalpy change (Unit 3), when a gas phase atom is 495.8 kJ mol –1 ; while the electron gain

in its ground state gains an electron. The enthalpy for the change Cl(g) + e →
– –1
electron gain process may be exothermic or Cl (g) is, – 348.7 kJ mol only. The sum
endothermic. The ionization, on the other hand, of the two, 147.1 kJ mol -1 is more than
is always endothermic. Electron affinity, is the compensated for by the enthalpy of lattice
negative of the energy change accompanying for mation of NaCl(s) (–788 kJ mol –1 ).
electron gain. Therefore, the energy released in the
processes is more than the energy absorbed.
Thus a qualitative measure of the
stability of an ionic compound is
provided by its enthalpy of lattice
formation and not simply by achieving
octet of electrons around the ionic species
in gaseous state.
Since lattice enthalpy plays a key role
in the formation of ionic compounds, it is
important that we learn more about it.
4.2.1 Lattice Enthalpy
The Lattice Enthalpy of an ionic solid is
defined as the energy required to
completely separate one mole of a solid
ionic compound into gaseous constituent
ions. For example, the lattice enthalpy of NaCl
Fig. 4.1 The bond length in a covalent
is 788 kJ mol–1. This means that 788 kJ of
molecule AB.
energy is required to separate one mole of
R = rA + rB (R is the bond length and rA and rB
solid NaCl into one mole of Na+ (g) and one are the covalent radii of atoms A and B
mole of Cl– (g) to an infinite distance. respectively)
This process involves both the attractive covalent bond in the same molecule. The van
forces between ions of opposite charges and der Waals radius represents the overall size
the repulsive forces between ions of like of the atom which includes its valence shell
charge. The solid crystal being three- in a nonbonded situation. Further, the van
dimensional; it is not possible to calculate der Waals radius is half of the distance
lattice enthalpy directly from the interaction between two similar atoms in separate
of forces of attraction and repulsion only. molecules in a solid. Covalent and van der
Factors associated with the crystal geometry Waals radii of chlorine are depicted in Fig.4.2
have to be included.
rc = 99 pm 19
4.3.1 Bond Length
Bond length is defined as the equilibrium
distance between the nuclei of two bonded
atoms in a molecule. Bond lengths are
measured by spectroscopic, X-ray diffraction
and electron-diffraction techniques about
r vd
which you will learn in higher classes. Each
atom of the bonded pair contributes to the
bond length (Fig. 4.1). In the case of a covalent
bond, the contribution from each atom is
called the covalent radius of that atom.
The covalent radius is measured
approximately as the radius of an atom’s Fig. 4.2 Covalent and van der Waals radii in a
core which is in contact with the core of chlorine molecule. The inner circles
an adjacent atom in a bonded situation. correspond to the size of the chlorine atom
The covalent radius is half of the distance (r vdw and r c are van der Waals and
covalent radii respectively).
between two similar atoms joined by a
Some typical average bond lengths for Table 4.2 Average Bond Lengths for Some
single, double and triple bonds are shown in Single, Double and Triple Bonds
Table 4.2. Bond lengths for some common
Bond Type Covalent Bond Length
molecules are given in Table 4.3.
The covalent radii of some common
elements are listed in Table 4.4. O–H 96
C–H 107
4.3.2 Bond Angle N–O 136
It is defined as the angle between the orbitals C–O 143
C–N 143
containing bonding electron pairs around the
C–C 154
central atom in a molecule/complex ion. Bond C=O 121
angle is expressed in degree which can be N=O 122
experimentally determined by spectroscopic C=C 133
methods. It gives some idea regarding the C=N 138
distribution of orbitals around the central C≡N 116
atom in a molecule/complex ion and hence it C≡C 120
helps us in determining its shape. For
Table 4.3 Bond Lengths in Some Common
example H–O–H bond angle in water can be
represented as under :
Molecule Bond Length
H2 (H – H) 74
F2 (F – F) 144
4.3.3 Bond Enthalpy Cl2 (Cl – Cl) 199
It is defined as the amount of energy required Br2 (Br – Br) 228
to break one mole of bonds of a particular I2 (I – I) 267
type between two atoms in a gaseous state. N2 (N ≡ N) 109
The unit of bond enthalpy is kJ mol–1. For O2 (O = O) 121
example, the H – H bond enthalpy in hydrogen HF (H – F) 92
molecule is 435.8 kJ mol–1. HCl (H – Cl) 127
H2(g) → H(g) + H(g); ∆aH = 435.8 kJ mol–1 HBr (H – Br) 141
HI (H – I) 160
Similarly the bond enthalpy for molecules
containing multiple bonds, for example O2 and
Table 4.4 Covalent Radii, *rcov/(pm)
N2 will be as under :
O2 (O = O) (g) → O(g) + O(g);
∆aH = 498 kJ mol–1
N2 (N ≡ N) (g) → N(g) + N(g);
∆aH = 946.0 kJ mol–1
It is important that larger the bond
dissociation enthalpy, stronger will be the
bond in the molecule. For a heteronuclear
diatomic molecules like HCl, we have
HCl (g) → H(g) + Cl (g); ∆aH = 431.0 kJ mol–1
In case of polyatomic molecules, the
measurement of bond strength is more
complicated. For example in case of H 2O * The values cited are for single bonds, except where
molecule, the enthalpy needed to break the otherwise indicated in parenthesis. (See also Unit 3 for
two O – H bonds is not the same. periodic trends).
H2O(g) → H(g) + OH(g); ∆aH1 = 502 kJ mol–1 equally represented by the structures I and II
V shown below:
OH(g) → H(g) + O(g); ∆aH2 = 427 kJ mol –1
The difference in the ∆aH value shows that
the second O – H bond undergoes some change
because of changed chemical environment.
This is the reason for some difference in energy
of the same O – H bond in different molecules
like C2H5OH (ethanol) and water. Therefore in
polyatomic molecules the term mean or
average bond enthalpy is used. It is obtained
by dividing total bond dissociation enthalpy
by the number of bonds broken as explained
below in case of water molecule,
502 + 427
Average bond enthalpy =
2 Fig. 4.3 Resonance in the O3 molecule
= 464.5 kJ mol –1
(structures I and II represent the two canonical
forms while the structure III is the resonance
4.3.4 Bond Order hybrid)
In the Lewis description of covalent bond, In both structures we have a O–O single
the Bond Order is given by the number of bond and a O=O double bond. The normal
bonds between the two atoms in a O–O and O=O bond lengths are 148 pm and
molecule. The bond order, for example in H2 121 pm respectively. Experimentally
(with a single shared electron pair), in O2 determined oxygen-oxygen bond lengths in
(with two shared electron pairs) and in N2 the O3 molecule are same (128 pm). Thus the
(with three shared electron pairs) is 1,2,3 oxygen-oxygen bonds in the O3 molecule are
respectively. Similarly in CO (three shared intermediate between a double and a single
electron pairs between C and O) the bond bond. Obviously, this cannot be represented
order is 3. For N2, bond order is 3 and its by either of the two Lewis structures shown
∆a H V is 946 kJ mol–1; being one of the above.
highest for a diatomic molecule. The concept of resonance was introduced
Isoelectronic molecules and ions have to deal with the type of difficulty experienced
identical bond orders; for example, F2 and in the depiction of accurate structures of
O2 have bond order 1. N2, CO and NO+ molecules like O3. According to the concept
have bond order 3. of resonance, whenever a single Lewis
structure cannot describe a molecule
A general correlation useful for
accurately, a number of structures with
understanding the stablities of molecules
similar energy, positions of nuclei, bonding
is that: with increase in bond order, bond
and non-bonding pairs of electrons are taken
enthalpy increases and bond length
as the canonical structures of the hybrid
which describes the molecule accurately.
4.3.5 Resonance Structures Thus for O3, the two structures shown above
constitute the canonical structures or
It is often observed that a single Lewis
resonance structures and their hybrid i.e., the
structure is inadequate for the representation
III structure represents the structure of O3
of a molecule in confor mity with its
more accurately. This is also called resonance
experimentally determined parameters. For
hybrid. Resonance is represented by a double
example, the ozone, O 3 molecule can be
headed arrow.
Some of the other examples of resonance
structures are provided by the carbonate ion
and the carbon dioxide molecule.
Fig. 4.5 Resonance in CO2 molecule, I, II
Problem 4.3
and III represent the three
Explain the structure of CO3 ion in terms canonical forms.
of resonance.
In general, it may be stated that
• Resonance stabilizes the molecule as the
The single Lewis structure based on the
energy of the resonance hybrid is less
presence of two single bonds and one
than the energy of any single cannonical
double bond between carbon and oxygen
structure; and,
atoms is inadequate to represent the
molecule accurately as it represents • Resonance averages the bond
unequal bonds. According to the characteristics as a whole.
experimental findings, all carbon to Thus the energy of the O 3 resonance
oxygen bonds in CO32– are equivalent. hybrid is lower than either of the two
Therefore the carbonate ion is best cannonical froms I and II (Fig 4.3).
described as a resonance hybrid of the
canonical forms I, II, and III shown below. Many misconceptions are associated
with resonance and the same need to be
dispelled. You should remember that :
• The cannonical forms have no real
• The molecule does not exist for a
certain fraction of time in one
cannonical for m and for other
Fig.4.4 Resonance in CO32–, I, II and fractions of time in other cannonical
III represent the three forms.
canonical forms.
• There is no such equilibrium between
Problem 4.4 the cannonical forms as we have
Explain the structure of CO2 molecule. between tautomeric forms (keto and
Solution enol) in tautomerism.
The experimentally determined carbon • The molecule as such has a single
to oxygen bond length in CO 2 is structure which is the resonance
115 pm. The lengths of a nor mal hybrid of the cannonical forms and
carbon to oxygen double bond (C=O) which cannot as such be depicted by
and carbon to oxygen triple bond (C≡O) a single Lewis structure.
are 121 pm and 110 pm respectively.
The carbon-oxygen bond lengths in 4.3.6 Polarity of Bonds
CO2 (115 pm) lie between the values The existence of a hundred percent ionic or
for C=O and C≡O. Obviously, a single covalent bond represents an ideal situation.
Lewis structure cannot depict this In reality no bond or a compound is either
position and it becomes necessary to completely covalent or ionic. Even in case of
write more than one Lewis structures covalent bond between two hydrogen atoms,
and to consider that the structure of there is some ionic character.
CO2 is best described as a hybrid of When covalent bond is formed between
the canonical or resonance forms I, II two similar atoms, for example in H2, O2, Cl2,
and III. N2 or F2, the shared pair of electrons is equally
attracted by the two atoms. As a result electron In case of polyatomic molecules the dipole
pair is situated exactly between the two moment not only depend upon the individual
identical nuclei. The bond so formed is called dipole moments of bonds known as bond
nonpolar covalent bond. Contrary to this in dipoles but also on the spatial arrangement of
case of a heteronuclear molecule like HF, the various bonds in the molecule. In such case,
shared electron pair between the two atoms the dipole moment of a molecule is the vector
gets displaced more towards fluorine since the sum of the dipole moments of various bonds.
electronegativity of fluorine (Unit 3) is far For example in H2O molecule, which has a bent
greater than that of hydrogen. The resultant structure, the two O–H bonds are oriented at
covalent bond is a polar covalent bond. an angle of 104.50. Net dipole moment of 6.17
As a result of polarisation, the molecule × 10–30 C m (1D = 3.33564 × 10–30 C m) is the
possesses the dipole moment (depicted resultant of the dipole moments of two O–H
below) which can be defined as the product bonds.
of the magnitude of the charge and the
distance between the centres of positive and
negative charge. It is usually designated by a
Greek letter ‘µ’. Mathematically, it is expressed
as follows :
Dipole moment (µ) = charge (Q) × distance of
separation (r)
Dipole moment is usually expressed in Net Dipole moment, µ = 1.85 D
Debye units (D). The conversion factor is –30 –30
= 1.85 × 3.33564 × 10 C m = 6.17 ×10 C m
1 D = 3.33564 × 10–30 C m The dipole moment in case of BeF2 is zero.
where C is coulomb and m is meter. This is because the two equal bond dipoles
Further dipole moment is a vector quantity point in opposite directions and cancel the
and by convention it is depicted by a small effect of each other.
arrow with tail on the negative centre and head
pointing towards the positive centre. But in
chemistry presence of dipole moment is
represented by the crossed arrow ( ) put
on Lewis structure of the molecule. The cross In tetra-atomic molecule, for example in
is on positive end and arrow head is on negative BF3, the dipole moment is zero although the
end. For example the dipole moment of HF may o
B – F bonds are oriented at an angle of 120 to
be represented as : one another, the three bond moments give a
net sum of zero as the resultant of any two is
H F equal and opposite to the third.
This arrow symbolises the direction of the
shift of electron density in the molecule. Note
that the direction of crossed arrow is opposite
to the conventional direction of dipole moment
Peter Debye, the Dutch chemist
received Nobel prize in 1936 for
his work on X-ray diffraction and Let us study an interesting case of NH3
dipole moments. The magnitude and NF3 molecule. Both the molecules have
of the dipole moment is given in pyramidal shape with a lone pair of electrons
Debye units in order to honour him. on nitrogen atom. Although fluorine is more
electronegative than nitrogen, the resultant
dipole moment of NH3 ( 4.90 × 10–30 C m) is in terms of the following rules:
greater than that of NF3 (0.8 × 10–30 C m). This • The smaller the size of the cation and the
is because, in case of NH3 the orbital dipole larger the size of the anion, the greater the
due to lone pair is in the same direction as the covalent character of an ionic bond.
resultant dipole moment of the N – H bonds, • The greater the charge on the cation, the
whereas in NF3 the orbital dipole is in the greater the covalent character of the ionic bond.
direction opposite to the resultant dipole • For cations of the same size and charge,
moment of the three N–F bonds. The orbital the one, with electronic configuration
dipole because of lone pair decreases the effect (n-1)dnnso, typical of transition metals, is
of the resultant N – F bond moments, which more polarising than the one with a noble
results in the low dipole moment of NF3 as gas configuration, ns2 np6, typical of alkali
represented below : and alkaline earth metal cations.
The cation polarises the anion, pulling the
electronic charge toward itself and thereby
increasing the electronic charge between
the two. This is precisely what happens in
a covalent bond, i.e., buildup of electron
charge density between the nuclei. The
polarising power of the cation, the
polarisability of the anion and the extent
of distortion (polarisation) of anion are the
factors, which determine the per cent
Dipole moments of some molecules are covalent character of the ionic bond.
shown in Table 4.5. 4.4 THE VALENCE SHELL ELECTRON
Just as all the covalent bonds have PAIR REPULSION (VSEPR) THEORY
some partial ionic character, the ionic As already explained, Lewis concept is unable
bonds also have partial covalent to explain the shapes of molecules. This theory
character. The partial covalent character provides a simple procedure to predict the
of ionic bonds was discussed by Fajans shapes of covalent molecules. Sidgwick
Table 4.5 Dipole Moments of Selected Molecules
Type of Example Dipole Geometry
Molecule Moment, µ(D)
Molecule (AB) HF 1.78 linear
HCl 1.07 linear
HBr 0.79 linear
HI 0.38 linear
H2 0 linear
Molecule (AB2) H2O 1.85 bent
H2 S 0.95 bent
CO2 0 linear
Molecule (AB3) NH3 1.47 trigonal-pyramidal
NF3 0.23 trigonal-pyramidal
BF3 0 trigonal-planar
Molecule (AB4) CH4 0 tetrahedral
CHCl3 1.04 tetrahedral
CCl4 0 tetrahedral
and Powell in 1940, proposed a simple theory result in deviations from idealised shapes and
based on the repulsive interactions of the alterations in bond angles in molecules.
electron pairs in the valence shell of the atoms. For the prediction of geometrical shapes of
It was further developed and redefined by molecules with the help of VSEPR theory, it is
Nyholm and Gillespie (1957). convenient to divide molecules into two
The main postulates of VSEPR theory are categories as (i) molecules in which the
as follows: central atom has no lone pair and (ii)
molecules in which the central atom has
• The shape of a molecule depends upon
one or more lone pairs.
the number of valence shell electron pairs
(bonded or nonbonded) around the central Table 4.6 (page114) shows the
atom. arrangement of electron pairs about a central
atom A (without any lone pairs) and
• Pairs of electrons in the valence shell repel
geometries of some molecules/ions of the type
one another since their electron clouds are
AB. Table 4.7 (page 115) shows shapes of some
negatively charged.
simple molecules and ions in which the central
• These pairs of electrons tend to occupy atom has one or more lone pairs. Table 4.8
such positions in space that minimise (page 116) explains the reasons for the
repulsion and thus maximise distance distortions in the geometry of the molecule.
between them. As depicted in Table 4.6, in the
• The valence shell is taken as a sphere with compounds of AB2, AB3, AB4, AB5 and AB6,
the electron pairs localising on the the arrangement of electron pairs and the B
spherical surface at maximum distance atoms around the central atom A are : linear,
from one another. trigonal planar, tetrahedral, trigonal-
• A multiple bond is treated as if it is a single bipyramidal and octahedral, respectively.
electron pair and the two or three electron Such arrangement can be seen in the
pairs of a multiple bond are treated as a molecules like BF3 (AB3), CH4 (AB4) and PCl5
single super pair. (AB5) as depicted below by their ball and
stick models.
• Where two or more resonance structures
can represent a molecule, the VSEPR
model is applicable to any such structure.
The repulsive interaction of electron pairs
decrease in the order:
Lone pair (lp) – Lone pair (lp) > Lone pair (lp)
– Bond pair (bp) > Bond pair (bp) – Fig. 4.6 The shapes of molecules in which
Bond pair (bp) central atom has no lone pair
Nyholm and Gillespie (1957) refined the The VSEPR Theory is able to predict
VSEPR model by explaining the important geometry of a large number of molecules,
difference between the lone pairs and bonding especially the compounds of p-block elements
pairs of electrons. While the lone pairs are accurately. It is also quite successful in
localised on the central atom, each bonded pair determining the geometry quite-accurately
is shared between two atoms. As a result, the even when the energy difference between
lone pair electrons in a molecule occupy more possible structures is very small. The
space as compared to the bonding pairs of theoretical basis of the VSEPR theory
electrons. This results in greater repulsion regarding the effects of electron pair repulsions
between lone pairs of electrons as compared on molecular shapes is not clear and
to the lone pair - bond pair and bond pair - continues to be a subject of doubt and
bond pair repulsions. These repulsion effects discussion.
Table 4.6 Geometry of Molecules in which the Central Atom has No Lone Pair of Electrons
Table 4.7 Shape (geometry) of Some Simple Molecules/Ions with Central Ions having One or
More Lone Pairs of Electrons(E).
Table 4.8 Shapes of Molecules containing Bond Pair and Lone Pair
Molecule No. of No. of Arrangement Shape Reason for the
type bonding lone of electrons shape acquired
pairs pairs
AB2E 4 1 Bent Theoretically the shape
should have been triangular
planar but actually it is found
to be bent or v-shaped. The
reason being the lone pair-
bond pair repulsion is much
more as compared to the
bond pair-bond pair repul-
sion. So the angle is reduced
to 119.5° from 120°.
AB3E 3 1 Trigonal Had there been a bp in place
pyramidal of lp the shape would have
been tetrahedral but one
lone pair is present and due
to the repulsion between
lp-bp (which is more than
bp-bp repulsion) the angle
between bond pairs is
reduced to 107° from 109.5°.
Bent The shape should have been
AB2E2 2 2 tetrahedral if there were all bp
but two lp are present so the
shape is distorted tetrahedral
or angular. The reason is
lp-lp repulsion is more than
lp-bp repulsion which is more
than bp-bp repulsion. Thus,
the angle is reduced to 104.5°
from 109.5°.
AB4E 4 1 See- In (a) the lp is present at axial
saw position so there are three
lp—bp repulsions at 90°. In(b)
the lp is in an equatorial
position, and there are two
lp—bp repulsions. Hence,
arrangement (b) is more
stable. The shape shown in (b)
is described as a distorted
tetrahedron, a folded square or
(More stable)
a see-saw.
Molecule No. of No. of Arrangement Shape Reason for the
type bonding lone of electrons shape acquired
pairs pairs
AB3E2 3 2 T-shape In (a) the lp are at
equatorial position so
there are less lp-bp
repulsions as
compared to others in
which the lp are at
axial positions. So
structure (a) is most
stable. (T -shaped).
4.5 VALENCE BOND THEORY knowledge of atomic orbitals, electronic
As we know that Lewis approach helps in configurations of elements (Units 2), the
writing the structure of molecules but it fails overlap criteria of atomic orbitals, the
to explain the formation of chemical bond. It hybridization of atomic orbitals and the
also does not give any reason for the difference principles of variation and superposition. A
in bond dissociation enthalpies and bond rigorous treatment of the VB theory in terms
lengths in molecules like H2 (435.8 kJ mol-1, of these aspects is beyond the scope of this
74 pm) and F 2 (155 kJ mol -1 , 144 pm), book. Therefore, for the sake of convenience,
although in both the cases a single covalent valence bond theory has been discussed in
bond is formed by the sharing of an electron terms of qualitative and non-mathematical
pair between the respective atoms. It also gives treatment only. To start with, let us consider
no idea about the shapes of polyatomic the formation of hydrogen molecule which is
molecules. the simplest of all molecules.
Similarly the VSEPR theory gives the Consider two hydrogen atoms A and B
geometry of simple molecules but approaching each other having nuclei NA and
theoretically, it does not explain them and also N B and electrons present in them are
it has limited applications. To overcome these represented by eA and eB. When the two atoms
limitations the two important theories based
are at large distance from each other, there is
on quantum mechanical principles are
no interaction between them. As these two
introduced. These are valence bond (VB) theory
atoms approach each other, new attractive and
and molecular orbital (MO) theory.
repulsive forces begin to operate.
Valence bond theory was introduced by
Attractive forces arise between:
Heitler and London (1927) and developed
further by Pauling and others. A discussion (i) nucleus of one atom and its own electron
of the valence bond theory is based on the that is NA – eA and NB– eB.
(ii) nucleus of one atom and electron of other hydrogen atoms are said to be bonded together
atom i.e., NA– eB, NB– eA. to form a stable molecule having the bond
Similarly repulsive forces arise between length of 74 pm.
(i) electrons of two atoms like e A – e B , Since the energy gets released when the
(ii) nuclei of two atoms NA – NB. bond is formed between two hydrogen atoms,
Attractive forces tend to bring the two the hydrogen molecule is more stable than that
atoms close to each other whereas repulsive of isolated hydrogen atoms. The energy so
forces tend to push them apart (Fig. 4.7). released is called as bond enthalpy, which is
corresponding to minimum in the curve
depicted in Fig. 4.8. Conversely, 435.8 kJ of
energy is required to dissociate one mole of
H2 molecule.
H2(g) + 435.8 kJ mol–1 → H(g) + H(g)
Fig. 4.8 The potential energy curve for the
formation of H2 molecule as a function of
internuclear distance of the H atoms. The
minimum in the curve corresponds to the
most stable state of H2.
4.5.1 Orbital Overlap Concept
In the formation of hydrogen molecule, there
is a minimum energy state when two hydrogen
atoms are so near that their atomic orbitals
undergo partial interpenetration. This partial
Fig. 4.7 Forces of attraction and repulsion during merging of atomic orbitals is called overlapping
the formation of H2 molecule. of atomic orbitals which results in the pairing
Experimentally it has been found that the of electrons. The extent of overlap decides the
magnitude of new attractive force is more than strength of a covalent bond. In general, greater
the new repulsive forces. As a result, two the overlap the stronger is the bond formed
atoms approach each other and potential between two atoms. Therefore, according to
energy decreases. Ultimately a stage is orbital overlap concept, the formation of a
reached where the net force of attraction covalent bond between two atoms results by
balances the force of repulsion and system pairing of electrons present in the valence shell
acquires minimum energy. At this stage two having opposite spins.
4.5.2 Directional Properties of Bonds
As we have already seen, the covalent bond is
formed by overlapping of atomic orbitals. The
molecule of hydrogen is formed due to the
overlap of 1s-orbitals of two H atoms.
In case of polyatomic molecules like CH4,
NH3 and H2O, the geometry of the molecules is
also important in addition to the bond
formation. For example why is it so that CH4
molecule has tetrahedral shape and HCH bond
angles are 109.5°? Why is the shape of NH3
molecule pyramidal ?
The valence bond theory explains the
shape, the formation and directional properties
of bonds in polyatomic molecules like CH4, NH3
and H 2 O, etc. in terms of overlap and
hybridisation of atomic orbitals.
4.5.3 Overlapping of Atomic Orbitals
When orbitals of two atoms come close to form
bond, their overlap may be positive, negative
or zero depending upon the sign (phase) and
direction of orientation of amplitude of orbital
wave function in space (Fig. 4.9). Positive and
negative sign on boundary surface diagrams
in the Fig. 4.9 show the sign (phase) of orbital
wave function and are not related to charge.
Fig.4.9 Positive, negative and zero overlaps of
Orbitals forming bond should have same sign
s and p atomic orbitals
(phase) and orientation in space. This is called
positive overlap. Various overlaps of s and p hydrogen.The four atomic orbitals of carbon,
orbitals are depicted in Fig. 4.9. each with an unpaired electron can overlap
The criterion of overlap, as the main factor with the 1s orbitals of the four H atoms which
for the formation of covalent bonds applies are also singly occupied. This will result in the
uniformly to the homonuclear/heteronuclear formation of four C-H bonds. It will, however,
diatomic molecules and polyatomic molecules. be observed that while the three p orbitals of
We know that the shapes of CH4, NH3, and H2O carbon are at 90° to one another, the HCH
molecules are tetrahedral, pyramidal and bent angle for these will also be 90°. That is three
respectively. It would be therefore interesting C-H bonds will be oriented at 90° to one
to use VB theory to find out if these geometrical another. The 2s orbital of carbon and the 1s
shapes can be explained in terms of the orbital orbital of H are spherically symmetrical and
overlaps. they can overlap in any direction. Therefore
Let us first consider the CH4 (methane) the direction of the fourth C-H bond cannot
molecule. The electronic configuration of be ascertained. This description does not fit
carbon in its ground state is [He]2s2 2p2 which in with the tetrahedral HCH angles of 109.5°.
in the excited state becomes [He] 2s1 2px1 2py1 Clearly, it follows that simple atomic orbital
2pz1. The energy required for this excitation is overlap does not account for the directional
compensated by the release of energy due to characteristics of bonds in CH4. Using similar
overlap between the orbitals of carbon and the procedure and arguments, it can be seen that in the
case of NH3 and H2O molecules, the HNH and charged clouds above and below the plane
HOH angles should be 90 ° . This is in of the participating atoms.
disagreement with the actual bond angles of
107 ° and 104.5 ° in the NH 3 and H 2 O
molecules respectively.
4.5.4 Types of Overlapping and Nature of
Covalent Bonds
The covalent bond may be classified into two
types depending upon the types of
(i) Sigma(σ) bond, and (ii) pi(π) bond 4.5.5 Strength of Sigma and pi Bonds
(i) Sigma(σ σ) bond : This type of covalent bond Basically the strength of a bond depends upon
is formed by the end to end (head-on) the extent of overlapping. In case of sigma bond,
overlap of bonding orbitals along the the overlapping of orbitals takes place to a
internuclear axis. This is called as head larger extent. Hence, it is stronger as compared
on overlap or axial overlap. This can be to the pi bond where the extent of overlapping
formed by any one of the following types occurs to a smaller extent. Further, it is
of combinations of atomic orbitals. important to note that in the formation of
• s-s overlapping : In this case, there is multiple bonds between two atoms of a
overlap of two half filled s-orbitals along molecule, pi bond(s) is formed in addition to a
the internuclear axis as shown below : sigma bond.
In order to explain the characteristic
geometrical shapes of polyatomic molecules
like CH4, NH3 and H2O etc., Pauling introduced
• s-p overlapping: This type of overlap the concept of hybridisation. According to him
occurs between half filled s-orbitals of one the atomic orbitals combine to form new set of
atom and half filled p-orbitals of another
equivalent orbitals known as hybrid orbitals.
Unlike pure orbitals, the hybrid orbitals are
used in bond formation. The phenomenon is
known as hybridisation which can be defined
as the process of intermixing of the orbitals of
slightly different energies so as to redistribute
their energies, resulting in the formation of new
• p–p overlapping : This type of overlap
set of orbitals of equivalent energies and shape.
takes place between half filled p-orbitals
For example when one 2s and three 2p-orbitals
of the two approaching atoms.
of carbon hybridise, there is the formation of
four new sp 3 hybrid orbitals.
Salient features of hybridisation: The main
features of hybridisation are as under :
(ii) pi(π ) bond : In the formation of π bond 1. The number of hybrid orbitals is equal to
the atomic orbitals overlap in such a way
the number of the atomic orbitals that get
that their axes remain parallel to each other
and perpendicular to the internuclear axis.
The orbitals formed due to sidewise 2. The hybridised orbitals are always
overlapping consists of two saucer type equivalent in energy and shape.
3. The hybrid orbitals are more effective in vacant 2p orbital to account for its bivalency.
forming stable bonds than the pure atomic One 2s and one 2p-orbital gets hybridised to
orbitals. form two sp hybridised orbitals. These two
4. These hybrid orbitals are directed in space sp hybrid orbitals are oriented in opposite
in some preferred direction to have direction forming an angle of 180°. Each of
minimum repulsion between electron the sp hybridised orbital overlaps with the
pairs and thus a stable arrangement. 2p-orbital of chlorine axially and form two Be-
Therefore, the type of hybridisation Cl sigma bonds. This is shown in Fig. 4.10.
indicates the geometry of the molecules.
Important conditions for hybridisation
(i) The orbitals present in the valence shell
of the atom are hybridised.
(ii) The orbitals undergoing hybridisation
should have almost equal energy.
(iii) Promotion of electron is not essential
condition prior to hybridisation.
(iv) It is not necessary that only half filled
orbitals participate in hybridisation. In
some cases, even filled orbitals of valence
shell take part in hybridisation.
4.6.1 Types of Hybridisation Fig.4.10 (a) Formation of sp hybrids from s and
p orbitals; (b) Formation of the linear
There are various types of hybridisation BeCl2 molecule
involving s, p and d orbitals. The different
(II) sp2 hybridisation : In this hybridisation
types of hybridisation are as under:
there is involvement of one s and two
(I) sp hybridisation: This type of p-orbitals in order to form three equivalent sp2
hybridisation involves the mixing of one s and hybridised orbitals. For example, in BCl3
one p orbital resulting in the formation of two molecule, the ground state electronic
equivalent sp hybrid orbitals. The suitable configuration of central boron atom is
orbitals for sp hybridisation are s and pz, if 1s22s22p1. In the excited state, one of the 2s
the hybrid orbitals are to lie along the z-axis. electrons is promoted to vacant 2p orbital as
Each sp hybrid orbitals has 50% s-character
and 50% p-character. Such a molecule in
which the central atom is sp-hybridised and
linked directly to two other central atoms
possesses linear geometry. This type of
hybridisation is also known as diagonal
The two sp hybrids point in the opposite
direction along the z-axis with projecting
positive lobes and very small negative lobes,
which provides more effective overlapping
resulting in the formation of stronger bonds.
Example of molecule having sp
BeCl 2 : The ground state electronic
configuration of Be is 1s22s2. In the exited state Fig.4.11 Formation of sp2 hybrids and the BCl3
one of the 2s-electrons is promoted to molecule
a result boron has three unpaired electrons. ground state is 2S 2 2 p1x 2 p1y 2 p1z having three
These three orbitals (one 2s and two 2p)
unpaired electrons in the sp3 hybrid orbitals
hybridise to form three sp2 hybrid orbitals. The
and a lone pair of electrons is present in the
three hybrid orbitals so formed are oriented in
fourth one. These three hybrid orbitals overlap
a trigonal planar arrangement and overlap with
with 1s orbitals of hydrogen atoms to form
2p orbitals of chlorine to form three B-Cl
three N–H sigma bonds. We know that the force
bonds. Therefore, in BCl3 (Fig. 4.11), the
of repulsion between a lone pair and a bond
geometry is trigonal planar with ClBCl bond
pair is more than the force of repulsion
angle of 120°.
between two bond pairs of electrons. The
(III) sp 3 hybridisation: This type of molecule thus gets distorted and the bond
hybridisation can be explained by taking the angle is reduced to 107° from 109.5°. The
example of CH4 molecule in which there is geometry of such a molecule will be pyramidal
mixing of one s-orbital and three p-orbitals of as shown in Fig. 4.13.
the valence shell to form four sp3 hybrid orbital
of equivalent energies and shape. There is 25%
s-character and 75% p-character in each sp3
hybrid orbital. The four sp3 hybrid orbitals so
formed are directed towards the four corners
of the tetrahedron. The angle between sp3
hybrid orbital is 109.5° as shown in Fig. 4.12.
Fig.4.13 Formation of NH3 molecule
In case of H2O molecule, the four oxygen
orbitals (one 2s and three 2p) undergo sp3
hybridisation forming four sp3 hybrid orbitals
out of which two contain one electron each and
the other two contain a pair of electrons. These
four sp3 hybrid orbitals acquire a tetrahedral
σ geometry, with two corners occupied by
hydrogen atoms while the other two by the lone
σ σ pairs. The bond angle in this case is reduced
to 104.5° from 109.5° (Fig. 4.14) and the
molecule thus acquires a V-shape or
angular geometry.
Fig.4.12 For mation of sp 3 hybrids by the
combination of s , px , py and pz atomic
orbitals of carbon and the formation of
CH4 molecule
The structure of NH3 and H2O molecules
can also be explained with the help of sp3
hybridisation. In NH3, the valence shell (outer)
electronic configuration of nitrogen in the Fig.4.14 Formation of H2O molecule
4.6.2 Other Examples of sp3, sp2 and sp sp2 hybrid orbitals of each carbon atom are
Hybridisation used for making sp2–s sigma bond with two
hydrogen atoms. The unhybridised orbital (2px
sp3 Hybridisation in C2H 6 molecule: In
or 2py) of one carbon atom overlaps sidewise
ethane molecule both the carbon atoms
with the similar orbital of the other carbon
assume sp3 hybrid state. One of the four sp3
atom to form weak π bond, which consists of
hybrid orbitals of carbon atom overlaps axially two equal electron clouds distributed above
with similar orbitals of other atom to form and below the plane of carbon and hydrogen
sp3-sp3 sigma bond while the other three atoms.
hybrid orbitals of each carbon atom are used
Thus, in ethene molecule, the carbon-
in forming sp3–s sigma bonds with hydrogen
carbon bond consists of one sp2–sp2 sigma
atoms as discussed in section 4.6.1(iii).
bond and one pi (π ) bond between p orbitals
Therefore in ethane C–C bond length is 154
which are not used in the hybridisation and
pm and each C–H bond length is 109 pm.
are perpendicular to the plane of molecule;
sp2 Hybridisation in C2H4: In the formation the bond length 134 pm. The C–H bond is
of ethene molecule, one of the sp2 hybrid sp2–s sigma with bond length 108 pm. The H–
orbitals of carbon atom overlaps axially with C–H bond angle is 117.6° while the H–C–C
sp2 hybridised orbital of another carbon atom angle is 121°. The formation of sigma and pi
to form C–C sigma bond. While the other two bonds in ethene is shown in Fig. 4.15.
Fig. 4.15 Formation of sigma and pi bonds in ethene
sp Hybridisation in C2H2 : In the formation 4.6.3 Hybridisation of Elements involving
of ethyne molecule, both the carbon atoms d Orbitals
undergo sp-hybridisation having two The elements present in the third period
unhybridised orbital i.e., 2py and 2px. contain d orbitals in addition to s and p
One sp hybrid orbital of one carbon atom orbitals. The energy of the 3d orbitals are
overlaps axially with sp hybrid orbital of the comparable to the energy of the 3s and 3p
orbitals. The energy of 3d orbitals are also
other carbon atom to form C–C sigma bond,
comparable to those of 4s and 4p orbitals. As
while the other hybridised orbital of each
a consequence the hybridisation involving
carbon atom overlaps axially with the half
either 3s, 3p and 3d or 3d, 4s and 4p is
filled s orbital of hydrogen atoms forming σ possible. However, since the difference in
bonds. Each of the two unhybridised p orbitals energies of 3p and 4s orbitals is significant, no
of both the carbon atoms overlaps sidewise to hybridisation involving 3p, 3d and 4s orbitals
form two π bonds between the carbon atoms. is possible.
So the triple bond between the two carbon The important hybridisation schemes
atoms is made up of one sigma and two pi involving s, p and d orbitals are summarised
bonds as shown in Fig. 4.16. below:
Shape of Hybridisation Atomic Examples
molecules/ type orbitals
Square dsp2 d+s+p(2) [Ni(CN)4]2–,
planar [Pt(Cl)4]2–
Trigonal sp3d s+p(3)+d PF5, PCl5
Square sp3d2 s+p(3)+d(2) BrF5
Octahedral sp3d2 s+p(3)+d(2) SF6, [CrF6]3–
d2sp3 d(2)+s+p(3) [Co(NH3)6]3+
(i) Formation of PCl5 (sp3d hybridisation):
The ground state and the excited state outer
electronic configurations of phosphorus (Z=15)
are represented below.
Fig.4.16 Formation of sigma and pi bonds in sp3d hybrid orbitals filled by electron pairs
ethyne donated by five Cl atoms.
Now the five orbitals (i.e., one s, three p and hybrid orbitals overlap with singly occupied
one d orbitals) are available for hybridisation orbitals of fluorine atoms to form six S–F sigma
to yield a set of five sp3d hybrid orbitals which bonds. Thus SF 6 molecule has a regular
are directed towards the five corners of a octahedral geometry as shown in Fig. 4.18.
trigonal bipyramidal as depicted in the Fig.
sp3d2 hybridisation
Fig. 4.17 Trigonal bipyramidal geometry of PCl5
It should be noted that all the bond angles
in trigonal bipyramidal geometry are not
equivalent. In PCl5 the five sp3d orbitals of
phosphorus overlap with the singly occupied
p orbitals of chlorine atoms to form five P–Cl
sigma bonds. Three P–Cl bond lie in one plane
and make an angle of 120° with each other;
these bonds are termed as equatorial bonds.
Fig. 4.18 Octahedral geometry of SF6 molecule
The remaining two P–Cl bonds–one lying
above and the other lying below the equatorial
plane, make an angle of 90° with the plane. 4.7 MOLECULAR ORBITAL THEORY
These bonds are called axial bonds. As the axial Molecular orbital (MO) theory was developed
bond pairs suffer more repulsive interaction by F. Hund and R.S. Mulliken in 1932. The
from the equatorial bond pairs, therefore axial salient features of this theory are :
bonds have been found to be slightly longer
and hence slightly weaker than the equatorial (i) The electrons in a molecule are present
bonds; which makes PCl5 molecule more in the various molecular orbitals as the
reactive. electrons of atoms are present in the
various atomic orbitals.
(ii) Formation of SF6 (sp3d2 hybridisation):
In SF6 the central sulphur atom has the (ii) The atomic orbitals of comparable
ground state outer electronic configuration energies and proper symmetry combine
3s23p4. In the exited state the available six to form molecular orbitals.
orbitals i.e., one s, three p and two d are singly (iii) While an electron in an atomic orbital is
occupied by electrons. These orbitals hybridise influenced by one nucleus, in a
to form six new sp3d2 hybrid orbitals, which molecular orbital it is influenced by two
are projected towards the six corners of a or more nuclei depending upon the
regular octahedron in SF6. These six sp3d2 number of atoms in the molecule. Thus,
an atomic orbital is monocentric while a Mathematically, the formation of molecular
molecular orbital is polycentric. orbitals may be described by the linear
(iv) The number of molecular orbital formed combination of atomic orbitals that can take
is equal to the number of combining place by addition and by subtraction of wave
atomic orbitals. When two atomic functions of individual atomic orbitals as
orbitals combine, two molecular orbitals shown below :
are formed. One is known as bonding ψMO = ψA + ψB
molecular orbital while the other is
called antibonding molecular orbital. Therefore, the two molecular orbitals
σ and σ* are formed as :
(v) The bonding molecular orbital has lower
energy and hence greater stability than σ = ψA + ψB
the corresponding antibonding σ* = ψA – ψB
molecular orbital. The molecular orbital σ formed by the
(vi) Just as the electron probability addition of atomic orbitals is called the
distribution around a nucleus in an bonding molecular orbital while the
atom is given by an atomic orbital, the molecular orbital σ* formed by the subtraction
electron probability distribution around of atomic orbital is called antibonding
a group of nuclei in a molecule is given molecular orbital as depicted in Fig. 4.19.
by a molecular orbital.
(vii) The molecular orbitals like atomic
orbitals are filled in accordance with the
aufbau principle obeying the Pauli’s
exclusion principle and the Hund’s rule.
4.7.1 Formation of Molecular Orbitals
Linear Combination of Atomic
σ* = ψA – ψB
Orbitals (LCAO)
According to wave mechanics, the atomic
orbitals can be expressed by wave functions ψA ψB
(ψ ’s) which represent the amplitude of the
electron waves. These are obtained from the σ = ψA + ψB
solution of Schrödinger wave equation.
However, since it cannot be solved for any
system containing more than one electron,
molecular orbitals which are one electron wave
functions for molecules are difficult to obtain Fig.4.19 For mation of bonding (σ) and
directly from the solution of Schrödinger wave antibonding (σ*) molecular orbitals by the
equation. To overcome this problem, an linear combination of atomic orbitals ψA
approximate method known as linear and ψB centered on two atoms A and B
combination of atomic orbitals (LCAO) has respectively.
been adopted.
Qualitatively, the formation of molecular
Let us apply this method to the orbitals can be understood in terms of the
homonuclear diatomic hydrogen molecule. constructive or destructive interference of the
Consider the hydrogen molecule consisting electron waves of the combining atoms. In the
of two atoms A and B. Each hydrogen atom in formation of bonding molecular orbital, the
the ground state has one electron in 1s orbital. two electron waves of the bonding atoms
The atomic orbitals of these atoms may be reinforce each other due to constructive
represented by the wave functions ψA and ψB. interference while in the formation of