4 chemical bonding.pptx

Chemical bond
 The attractive force which holds
various constituents (atoms, ions,
etc.) together in different chemical
species is called a chemical bond.

KÖSSEL-LEWIS APPROACH TO
CHEMICAL BONDING
 Lewis postulated that atoms achieve the
stable octet when they are linked by
chemical bonds.

Octet Rule = atoms tend to gain, lose or share
electrons so as to have 8 electrons
C would like to Gain 4 electrons
N would like to Gain 3 electrons
O would like to Gain 2 electrons

LEWIS (DOT) SYMBOLS
A Lewis dot structure for an atom consists
of the symbol for the element and one
dot for each valence electron. It is used
for the s and p block elements, the
representative elements.

LEWIS’S ELECTRON DOT STRUCTURES
Symbols of atoms with dots to represent the
valence-shell electrons
1 2 13 14 15 16 17 18
H He:
          
Li Be  B   C   N   O  : F  :Ne :
       
          
Na Mg  Al  Si  P S :Cl  :Ar :
       

Kössel: chemical bonding
 In the periodic table, the highly
electronegative halogens and the highly
electropositive alkali metals are separated
by the noble gases;
 The formation of a negative ion from a
halogen atom and a positive ion from an
alkali metal atom is associated with the gain
and loss of an electron by the respective
atoms;

 The negative and positive ions thus formed
attain stable noble gas electronic
configurations. The noble gases (with the
exception of helium which has a duplet of
electrons) have a particularly stable outer
shell configuration of eight (octet)
electrons, ns2np6.
 The negative and positive ions are stabilized
by electrostatic attraction.

Kossel’s scheme
 Na → Na+ + e–
 [Ne] 3s1 [Ne]
 Cl + e– → Cl–
 [Ne] 3s2 3p5 [Ne] 3s2 3p6 or [Ar]
 Na+ + Cl– → NaCl or Na+Cl–

Chemical bonds: an attempt to fill electron shells
1. Ionic bonds –
2. Covalent bonds –

Formation of Ions from Metals
Ionic compounds result when metals react with
nonmetals
Metals lose electrons to match the number of
valence electrons of their nearest noble gas
Positive ions form when the number of electrons
are less than the number of protons
Group 1 metals  ion 1+

Formation of Sodium Ion
Sodium atom Sodium ion
Na  – e  Na +
2-8-1 2-8 ( = Ne)
11 p+ 11 p+
11 e- 10 e-
0 1+

Formation of Magnesium Ion
Magnesium atom Magnesium ion

Mg  – 2e  Mg2+
2-8-2 2-8 (=Ne)
12 p+ 12 p+
12 e- 10 e-
0 2+

Some Typical Ions with Positive
Charges (Cations)
Group 1 Group 2 Group 13
H+ Mg2+ Al3+
Li+ Ca2+
Na+ Sr2+
K+ Ba2+

Ions from Nonmetal Ions
In ionic compounds, nonmetals in 15, 16, and
17 gain electrons from metals
Nonmetal add electrons to achieve the octet
arrangement
Nonmetal ionic charge:
3-, 2-, or 1-

Fluoride Ion
unpaired electron octet
    1 -
: F  + e : F :
   
2-7 2-8 (= Ne)
9 p+ 9 p+
9 e- 10 e-
0 1 -
ionic charge

Ionic Bond
 Between atoms of metals and nonmetals
with very different electronegativity
 Bond formed by transfer of electrons
 Produce charged ions all states. Conductors
and have high melting point.
 Examples; NaCl, CaCl2, K2O

Ionic Bonds: One Big Greedy
Thief Dog!

1). Ionic bond – electron from Na is transferred
to Cl, this causes a charge imbalance in each
atom. The Na becomes (Na+) and the Cl
becomes (Cl-), charged particles or ions.

Na Cl
NaCl
+ -
electron transfer
and the formation of ions
This is the formation of an ionic bond.
Cl
Cl
Cl2
This is the formation of a covalent bond.
sharing of a pair of electrons
and the formation of molecules

COVALENT BOND
bond formed by the
sharing of electrons

Covalent Bond
 Between nonmetallic elements of similar
electronegativity.
 Formed by sharing electron pairs
 Stable non-ionizing particles, they are not conductors
at any state
 Examples; O2, CO2, C2H6, H2O, SiC

More sharing examples
O2
N2
O O
N N
O O O O
N N N N N N
double bond (2 pairs)
triple bond (3 pairs)
Share until octet is complete.
octet complete

NH3
N
H
H
H
N
H
H
H
H+
NH4
+ NH3 + H+  NH4
+
coordinate covalent bond
(the pair of electrons from the same
atom)
normal covalent bond
(each atom supplies an
electron)
Some more sharing examples

ionic covalent
valence
electrons
Comparison of Bonding Types
sharing of
electrons
transfer of
electrons
ions
molecules
DEN > 1.7 DEN < 1.7
high mp low mp
molten salts
conductive
non-
conductive

Two types of covalent bonds
 Non-polar covalent bond
 Polar covalent bond

when electrons are
shared equally
NONPOLAR
COVALENT BONDS
H2 or Cl2

Covalent bonds- Two atoms share one or more
pairs of outer-shell electrons.
Oxygen Atom Oxygen Atom
Oxygen Molecule (O2)

when electrons are
shared but shared
unequally
POLAR COVALENT
BONDS
H2O

Polar Covalent Bonds: Unevenly
matched, but willing to share.

- water is a polar molecule because oxygen is
more electronegative than hydrogen, and
therefore electrons are pulled closer to oxygen.

Is the sharing of electrons in
molecules always equal?
X Y DEN = 0
X Y DEN = 0.3
X Y DEN = 0.6
X Y DEN = 0.9
X Y DEN = 1.2
ENY > ENX
Which element is more
electronegative?
non-polar
bond
increasing
polarity
of
bond
polar bond
0 < EN < 1.7
Direction of electron migration

Molecular Shape and Molecular Polarity

Lewis Representation of Simple
Molecules (the Lewis Structures)
 The Lewis dot structures provide a picture of
bonding in molecules and ions in terms of
the shared pairs of electrons and the octet
rule.

Limitations of the Octet Rule
The incomplete octet of the central atom
 LiCl, BeH2, BF3 have only 2,4 and 6 electrons
respectively
Odd-electron molecules
 Nitric oxide, NO and nitrogen dioxide, NO2,
the octet rule is not satisfied. (7 electrons)
The expanded octet
 PF5, SF6 have 10 and 12 electrons respectively.

Violations of the Octet Rule
Usually occurs with B and elements of
higher periods. Common exceptions
are: Be, B, P, S, and Xe.
BF3
SF4
Be: 4
B: 6
P: 10
S: 10, OR 12
Xe: 10, OR 12

Other drawbacks of the octet theory
 The octet rule is based upon the chemical
inertness of noble gases. However, some
noble gases also combine with oxygen and
fluorine to form a number of compounds
like XeF2, KrF2, XeOF2 etc.,
 This theory does not account for the shape
of molecules.
 It does not explain the relative stability of
the molecules being totally silent about the
energy of a molecule.

IONIC OR ELECTROVALENT BOND
The formation of ionic compounds would
primarily depend upon:
 The ease of formation of the positive and
negative ions from the respective neutral
atoms;
 The arrangement of the positive and
negative ions in the solid, that is, the lattice
of the crystalline compound.

 M(g) → M+(g) + e– ; Ionization enthalpy
 X(g) + e– → X– (g) ; Electron gain enthalpy
 M+(g) + X –(g) → MX(s) Overall reaction
 The electron gain process may be
exothermic or endothermic. The ionization,
on the other hand, is always endothermic.

 Ionic bonds will be formed more easily
between elements with comparatively low
ionization enthalpies and elements with
comparatively high negative value of
electron gain enthalpy.
 In ionic solids, the sum of the electron gain
enthalpy and the ionization enthalpy may
be positive but still the crystal structure gets
stabilized due to the energy released in the
formation of the crystal lattice.

 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.
 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.

Properties of the Chemical Bond
 Bond Length
 Bond length is defined as the equilibrium
distance between the nuclei of two bonded
atoms in a molecule.

 The covalent radius is half the distance
between the nuclei of two covalently bonded
diatomic element.
 The van der Waals radius represents the
overall size of the atom which includes its
valence shell in a nonbonded situation. It is
half the distance between the nuclei of two
adjacent nonbonded atoms

Bond Angle
 It is defined as the angle between the
orbitals containing bonding electron pairs
around the central atom in a
molecule/complex ion.
 H–O–H bond angle in water is 104.50

Bond Enthalpy
 It is defined as the amount of energy
required to break one mole of bonds of a
particular type between two atoms in a
gaseous state.
 The H – H bond enthalpy in hydrogen
molecule is 435.8 kJ mol–1.
 For 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

Bond Order
 The Bond Order is given by the number of bonds
between the two atoms in a molecule.
 H2,O2 and N2 has bond orders 1,2,3 respectively.
 Isoelectronic molecules and ions have identical
bond orders
 with increase in bond order, bond enthalpy
increases and bond length decreases.

THE VALENCE SHELL ELECTRON
PAIR REPULSION (VSEPR) THEORY
 The main postulates of VSEPR theory are:
 The shape of a molecule depends upon the
number of valence shell electron pairs
(bonded or nonbonded) around the central
atom.
 Pairs of electrons in the valence shell repel one
another since their electron clouds are
negatively charged.

Postulates of VSEPR theory (contd...)
 These pairs of electrons tend to occupy such
positions in space that minimise repulsion
and thus maximise distance between them.
 The valence shell is taken as a sphere with
the electron pairs localising on the spherical
surface at maximum distance from one
another.

Postulates of VSEPR theory (contd...)
 A multiple bond is treated as if it is a single
electron pair and the two or three electron
pairs of a multiple bond are treated as a
single super pair.
 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) – Bond pair (bp)

Some Common Geometries
Linear
Trigonal Planar Tetrahedral

BeCl2
 No. of valence electrons of Be = 2
 No. of bonds formed with Cl =2
 No. of bond pairs =2
 No. of lone pairs =0
 Total No. of electron pairs =2+0=2
 Shape of molecule LINEAR
 Bond angle 1800

BF3
 No. of valence electrons of B = 3
 No. of bonds formed with F =3
 Shape of molecule TRIGONAL PLANAR
 Bond angle 1200

CH4
 No. of valence electrons of C =4
 No. of bonds formed with H =4
 Shape of molecule TETRAHEDRAL
 Bond angle 109.50

PCl5
 No. of valence electrons of P = 5
 No. of bonds formed with Cl =5
 Shape of molecule TRIGONAL BIPYRAMIDAL
 Bond angle 1200 & 900

SF6
 No. of valence electrons of S = 6
 No. of bonds formed with F =6
 Shape of molecule OCTADEDRAL
 Bond angle 900

Structure Determination by VSEPR
Ammonia, NH3
Bond pairs=3 lone pairs=1 Total 4
The electron pair geometry is tetrahedral.
H
H
H
lone pair of electrons
in tetrahedral position
N
The MOLECULAR GEOMETRY — the positions of
the atoms — is TRIGONAL PYRAMID.

Structure Determination by VSEPR
Water, H2O The electron pair geometry is
TETRAHEDRAL
The molecular geometry is
BENT.
2 bond pairs
2 lone pairs

The Effect of Nonbonding Electrons
• By experiment, the H-X-H bond angle decreases on
moving from C to N to O:
• Since electrons in a bond are attracted by two
nuclei, they do not repel as much as lone pairs.
• Therefore, the bond angle decreases as the number
of lone pairs increases
VSEPR Model
104.5O
107O
N
H
H
H
C
H
H
H
H
109.5O
O
H
H

Towards Quantum Mechanical Model
 Lewis approach helps in writing the structure of
molecules but it fails to explain the formation of
chemical bond.
 The VSEPR theory gives the geometry of simple
molecules but it has limited applications. To
overcome these limitations the two important
theories based on quantum mechanical
principles are introduced. These are
 Valence Bond (VB) theory and
 Molecular Orbital (MO) theory.

VALENCE BOND THEORY
 Valence bond theory was introduced by
Heitler and London (1927) and developed
further by Pauling and others.
 To start with, let us consider the formation
of hydrogen molecule

 Consider two hydrogen atoms A and B
approaching each other having nuclei NA
and NB and electrons present in them are
represented by eA and eB.
Attractive forces arise between:
 nucleus of one atom and its own electron
that is NA – eA and NB– eB.
 nucleus of one atom and electron of other
atom i.e., NA– eB, NB– eA.

Similarly repulsive forces arise between
 electrons of two atoms like eA – eB,
 nuclei of two atoms NA – NB.
 Attractive forces tend to bring the two atoms
close to each other whereas repulsive forces
tend to push them apart

When H – H distance = 74 pm,
Repulsion = Attraction
 strongest bond
 optimal overlap
 lowest energy
74 pm

At H – H distance > 74 pm,
Repulsion < Attraction
 weaker bond
 too little overlap
 atoms come closer
74 pm
> 74 pm

At H – H distance < 74 pm,
Repulsion > Attraction
 weaker bond
 too much overlap
 atoms get further apart
74 pm
< 74 pm

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 merging of atomic orbitals is
called overlapping of atomic orbitals. In
general, greater the overlap the stronger is
the bond formed between two atoms.

Overlapping of Atomic Orbitals
 When two atoms come close to each other,
there is overlapping of atomic orbitals. This
overlap may be positive, negative or zero.

Dotted areas: representation of "electron cloud" for one electron
"Head-on Overlap"
Sigma Bond: merged orbital, 2 e's

Types of Overlapping and Nature of
Covalent Bonds
The covalent bond may be classified into two
types depending upon the types of overlapping:
(i) Sigma(σ) bond, and
(ii)Pi(π) bond
(i) Sigma(σ) bond : This type of covalent bond
is formed by the end to end (hand-on) overlap
of bonding orbitals along the internuclear axis.
This is called as head on overlap or axial
overlap.

Types of sigma bonds
 s-s overlapping : In this case, there is
overlap of two half filled s-orbitals along the
internuclear axis.
 s-p overlapping: This type of overlap occurs
between half filled s-orbitals of one atom
and half filled p-orbitals of another atom.
 p–p overlapping : This type of overlap takes
place between half filled p-orbitals of the
two approaching atoms.

pi(π ) bond
 In the formation of π bond the atomic
orbitals overlap in such a way that their axes
remain parallel to each other and
perpendicular to the internuclear axis. The
orbitals formed due to sidewise overlapping
consists of two saucer type charged clouds
above and below the plane of the
participating atoms.

Strength of Sigma and pi Bonds
 In case of sigma bond, the overlapping of
orbitals takes place to a larger extent. Hence,
it is stronger as compared to the pi bond
where the extent of overlapping occurs to a
smaller extent.
 Pi bond between two atoms is formed in
addition to a sigma bond. It is always
present in the molecules containing
multiple bond

HYBRIDISATION
 In order to explain the characteristic
geometrical shapes of polyatomic molecules,
Pauling introduced the concept of
hybridisation. According to him the atomic
orbitals combine to form new set of
equivalent orbitals known as hybrid orbitals.
Unlike pure orbitals, the hybrid orbitals are
used in bond formation.

Hybridisation
 Hybridisation 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
set of orbitals of equivalent energies and
shape.

Salient features of hybridisation
 The number of hybrid orbitals is equal to the
number of the atomic orbitals that get
hybridised.
 The hybridised orbitals are always equivalent in
energy and shape.
 The hybrid orbitals are more effective in forming
stable bonds than the pure atomic orbitals.
 These hybrid orbitals are directed in space in
some preferred direction to have minimum
repulsion between electron pairs and thus a
stable arrangement.

Important conditions for hybridisation
 The orbitals present in the valence shell of the
atom are hybridised.
 The orbitals undergoing hybridisation should
have almost equal energy.
 Promotion of electron is not essential condition
prior to hybridisation.
 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.

all s orbitals
all p orbitals
d orbitals
Orbital shapes, Individual (“isolated”) Atoms
Compare (next slide) to molecule, ion bonding shapes

trigonal tetrahedral
trigonal-bipyramidal octahedral

“sp” Hybridization: all 2 Region Species
BeCl2 Be
Cl Cl
Be 2
2Cl 14
16 e's/2= 8 prs
Be
Cl Cl (octet violator)
Number of regions around CENTRAL ATOM: 2
Be
Cl Cl shape : LINEAR
bond angles: 180o

Hybridization of Be in BeCl2
Atomic Be: 1s2 2s2
Valence e’s
2p
2s
Energy
separate
2p
2s
"hybridize"
"sp" "sp"
Hybrid sp orbitals:
1 part s, 1 part p

"arrange"
(VSEPR)
Be
Be is said to be
"sp hybridized"
FORMATION OF BeCl2:
Each Chlorine atom, 1s22s22p63s23p5 , has one
unshared electron in a p orbital. The half filled
p orbital overlaps head-on with a half full hybrid
sp orbital of the beryllium to form a sigma bond.

Be
Cl Cl
Be
Cl Cl
Be
Cl Cl
sp hybridized, linear, 180o
bond angles

“sp2” Hybridization: All 3 Region Species
BF3 B
F F
B 3
3F 21
24 e's/2= 12 prs
B
F F (octet violator)
shape : TRIGONAL PLANAR
bond angles: 120o
F
F
B
F F
F

Hybridization of B in BF3
Atomic B : 1s2 2s2 2p1
Valence e’s
2p
2s
Energy
separate
2p
2s
"hybridize"
"sp
2
" "sp
2
" "sp
2
"
Hybrid sp2 orbitals:
1 part s, 2 parts p

FORMATION OF BF3:
Each fluorine atom, 1s22s22p5, has one unshared
electron in a p orbital. The half filled p orbital
overlaps head-on with a half full hybrid sp2 orbital
of the boron to form a sigma bond.
"arrange"
(VSEPR)
B
B is said to be
"sp2
hybridized"

F F
sp2
hybridized, TRIGONAL PLANAR,
120o
bond angles
B
F
F F
B
F

“sp3” Hybridization: All 4 Region Species
CH4
C
H H
C 4
4H 4
shape : TETRAHEDRAL
bond angles: 109.5o
H
H
8
8 e's /2 = 4 pr
H
C
H
H
H

Hybridization of C in CH4
Atomic C : 1s2 2s2 2p2
Valence e’s
2p
2s
Energy
separate
2p
2s
"hybridize"
"sp
3
" "sp
3
" "sp
3
" "sp
3
"
Hybrid sp3 orbitals:
1 part s, 3 parts p

FORMATION OF CH4:
Each hydrogen atom, 1s1, has one unshared
electron in an s orbital. The half filled s orbital
of the carbon to form a sigma bond.
"arrange"
(VSEPR)
C
C is said to be
"sp3
hybridized"

sp3
hybridized, TETRAHEDRAL,
109.5o
bond angles
C
H
H
H
H
C
H
H
H
H

Unshared Pairs, Double or Triple Bonds
Unshared pairs occupy a hybridized orbital the
same as bonded pairs: See the example of NH3
that follows.
Double and triple bonds are formed from
electrons left behind and unused in p orbitals.
Since all multiple bonds are formed on top of
sigma bonds, the hybridization of the single ()
bonds determine the hybridization and shape of
the molecule...

NH3 N
H H
N 5
3H 3
8e's/2=4 prs
shape : TETRAHEDRAL
bond angles: < 109.5o
N
H H
H
N
H H
H
H

Hybridization of N in NH3
Atomic N: 1s2 2s2 2p3
Valence e’s
2p
2s
Energy
"hybridize"
"sp3
" "sp3
" "sp3
" "sp3
"

FORMATION OF NH3:
Each hydrogen atom, 1s1, has one unshared
electron in an s orbital. The half filled s orbital
of the nitrogen to form a sigma bond.
"arrange"
(VSEPR)
N
N is said to be
"sp3
hybridized"

sp3
hybridized, TETRAHEDRAL,
~107o
bond angles
N
H
H
H
N
H
H
H

“sp3d” Hybridization: All 5 Region Species
PF5
P
F F
P 5
5F 35
shape : TRIGONAL BIPYRAMIDAL
bond angles: 90, 120, 180o
F
F
40
40 e's /2 = 20 pr
P
F
P
F F
F
F
F
F
F
F
F
F

Hybridization of P in PF5 P: 1s2 2s2 2p6 3s2 3p3
3p
3s
Energy
separate
3p
3s
"hybridize"
"sp
3
d" "sp
3
d" "sp
3
d" "sp
3
d"
3d 3d
"sp
3
d"

FORMATION OF PF5:
overlaps head-on with a half full hybrid sp3d
orbital of the phosphorus to form a sigma bond.
"arrange"
(VSEPR)
P is said to be
"sp3
d hybridized"
P

sp3
d hybridized, TRIGONAL BIPYRAMIDAL,
90, 120, 180o
bond angles
P
F
F
F
F
F
P
F
F
F
F
F

“sp3d2” Hybridization: All 6 Region Species
SF6
S
F F
S 6
6F 42
shape : OCTAHEDRAL
bond angles: 90, 180o
F
F
48
48 e's /2 = 24 pr
S
F
S
F F
F
F F
F
F
F
F
F
F
F
F

Hybridization of S in SF6 S: 1s2 2s2 2p6 3s2 3p4
3p
3s
Energy
separate
3p
3s
"hybridize"
"sp3
d2
"
3d 3d

FORMATION OF SF6:
overlaps head-on with a half full hybrid sp3d2
orbital of the phosphorus to form a sigma bond.
"arrange"
(VSEPR)
S is said to be
"sp3
d2
hybridized"
S

sp3
d hybridized, TRIGONAL BIPYRAMIDAL,
90, 120, 180o
bond angles
S
F
F
F
F
F
S
F
F
F
F
F F
F

Summary: Regions, Shapes and Hybridization
#, regions shape hybridization
2 linear sp
3 trigonal
planar
sp2
4 tetrahedral sp3
5 trigonal
bipyramidal
sp3
d
6 octahedral sp3
d2

2s 2px 2pz
2py
1s sp3 sp3 sp3 sp3
109.5o
Promote Hybridize
x
z
y
Methane: Carbon

2s 2px 2pz
2py
1s sp2 sp2 sp2
120o
Hybridized
Formaldehyde: Carbon
Promoted
120o
Trigonal
Planar
2s + 2px + 2pz

2s 2px 2pz
2py
1s sp2 sp2 sp2
120o
Hybridized
Formaldehyde: Oxygen
120o
Trigonal
Planar
Lone Pairs
2s + 2px + 2pz

Formaldehyde
Sigma bond
2 Lone
Pairs
 bond

2s 2px 2pz
2py
1s sp sp
Promoted Hybridized
Hydrogen Cyanide: Carbon
2s + 2px
Linear

2s 2px 2pz
2py
1s sp sp
Hybridized
Hydrogen Cyanide: Nitrogen
2s + 2px
Linear

3s 3px 3pz
3py
2
Neon
120o
Hybridized
Phosphorus Pentachloride: Phosphorus
Trigonal
Bipyrimidal
sp3d sp3d sp3d sp3d sp3d
dxz dyz dxy dx2-y2 dz2
120o
90o
Promoted

Molecular Orbital Theory
 Molecular orbital (MO) theory was
developed by F. Hund and R.S. Mulliken in
1932.
 The salient features of this theory are :
 The electrons in a molecule are present in
the various molecular orbitals as the
electrons of atoms are present in the various
atomic orbitals.

 The atomic orbitals of comparable energies
and proper symmetry combine to form
molecular orbitals.
 While an electron in an atomic orbital is
influenced by one nucleus, in a molecular
orbital it is influenced by two or more
nuclei depending upon the number of
atoms in the molecule. Thus, an atomic
orbital is monocentric while a molecular
orbital is polycentric.

 The number of molecular orbital formed is
equal to the number of combining atomic
orbitals. When two atomic orbitals combine,
two molecular orbitals are formed. One is
known as bonding molecular orbital
while the other is called antibonding
molecular orbital.
 The bonding molecular orbital has lower
energy and hence greater stability than the
corresponding antibonding molecular
orbital.

 Just as the electron probability distribution
around a nucleus in an atom is given by an
atomic orbital, the electron probability
distribution around a group of nuclei in a
molecule is given by a molecular orbital.
 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.

Formation of Molecular Orbitals: Linear
Combination of Atomic Orbitals (LCAO)
The formation of molecular orbitals may be
described by the linear combination of atomic
orbitals that can take place by addition and by
subtraction of wave functions of individual
atomic orbitals as shown below:
MO = A ± B
Therefore, the two molecular orbitals  and *
are formed as:
 = A + B
* = A – B

 The molecular orbital  formed by the
addition of atomic orbitals is called the
bonding molecular orbital while the
molecular orbital * formed by the
subtraction of atomic orbital is called
antibonding molecular orbital as
depicted in Fig.

H
Energy
H
H2
1s 1s
g
u*

 In the formation of bonding molecular
orbital, the two electron waves of the
bonding atoms reinforce each other due to
constructive interference while in the
formation of antibonding molecular orbital,
the electron waves cancel each other due
to destructive interference.

 A bonding molecular orbital always
possesses lower energy than either of the
atomic orbitals that have combined to form
it. In contrast, the electrons placed in the
antibonding molecular orbital destabilise
the molecule. This is because the mutual
repulsion of the electrons in this orbital is
more than the attraction between the
electrons and the nuclei, which causes a
net increase in energy.

Conditions for
the Combination of Atomic Orbitals
The linear combination of atomic orbitals to
form molecular orbitals takes place only if
the following conditions are satisfied:
 The combining atomic orbitals must
have the same or nearly the same energy.
This means that 1s orbital can combine with
another 1s orbital but not with 2s orbital
because the energy of 2s orbital is
appreciably higher than that of 1s orbital.

 The combining atomic orbitals must have
the same symmetry about the molecular
axis.
 It is important to note that atomic orbitals
having same or nearly the same energy will
not combine if they do not have the same
symmetry. For example, 2pz orbital of one
atom can combine with 2pz orbital of the
other atom but not with the 2px or 2py
orbitals because of their different
symmetries.

 The combining atomic orbitals must
overlap to the maximum extent.
 Greater the extent of overlap, the greater
will be the electron-density between the
nuclei of a molecular orbital.

Types of Molecular Orbitals
 Molecular orbitals of diatomic molecules are
designated as  (sigma),  (pi) etc.
 In this nomenclature, the sigma ()
molecular orbitals are symmetrical around
the bond-axis while pi () molecular orbitals
are not symmetrical.

Energy Level Diagram for
Molecular Orbitals
 1s atomic orbitals on two atoms form two
molecular orbitals designated as 1s and *1s. In
the same manner, the 2s and 2p atomic orbitals
(eight atomic orbitals on two atoms) give rise to
the following eight molecular orbitals:
 Antibonding MOs *2s *2pz *2px *2py
 Bonding MOs 2s 2pz 2px 2py

 The energy levels of these molecular orbitals
have been determined experimentally from
spectroscopic data for homonuclear
diatomic molecules of second row elements
of the periodic table. The increasing order of
energies of various molecular orbitals for O2
and F2 is given below:
 1s < *1s < 2s < *2s <2pz<( 2px =
2py)< ( *2px=  *2py)<*2pz

F
Energy
F
F2
2s 2s
2g
2u*
2p
2p
3g
3u*
1u
1g*
MO diagram for F2
(px,py)
pz

 However, this sequence of energy levels of
molecular orbitals is not correct for the
remaining molecules. For instance, it has
been observed experimentally that for
molecules such as B2, C2, N2 etc. the
increasing order of energies of various
molecular orbitals is
 1s < *1s < 2s < *2s < ( 2px = 2py)
<2pz< ( *2px=  *2py) < *2pz

B
Energy
B
B2
2s 2s
2g
2u*
2p
2p
3g
3u*
1u
1g*
MO diagram for B2
(px,py)
pz
HOMO
LUMO

Electronic Configuration and
Molecular Behaviour
 The distribution of electrons among various
molecular orbitals is called the electronic
configuration of the molecule. From the
electronic configuration of the molecule, it
is possible to get important information
about the molecule as discussed below

 Stability of Molecules: If Nb is the number of
electrons occupying bonding orbitals and Na
the number occupying the antibonding
orbitals, then
i. the molecule is stable if Nb is greater than Na,
ii. the molecule is unstable if Nb is less than Na.
 In (i) more bonding orbitals are occupied and
so the bonding influence is stronger and a
stable molecule results. In (ii) the antibonding
influence is stronger and therefore the
molecule is unstable.

 Bond order
 Bond order (b.o.) is defined as one half the
difference between the number of electrons
present in the bonding and the antibonding
orbitals i.e.,
 Bond order (b.o.) = ½ (Nb–Na)
 Nature of the bond
 Integral bond order values of 1, 2 or 3
correspond to single, double or triple bonds
respectively as studied in the classical
concept.

 Bond-length
 The bond order between two atoms in a
molecule may be taken as an approximate
measure of the bond length. The bond length
decreases as bond order increases.
 Magnetic nature
 If all the molecular orbitals in a molecule are
doubly occupied, the substance is diamagnetic
(repelled by magnetic field). However if one or
more molecular orbitals are singly occupied it
is paramagnetic (attracted by magnetic field),
e.g., O2 molecule.

BONDING IN SOME HOMONUCLEAR
DIATOMIC MOLECULES
 1. Hydrogen molecule (H2): It is formed by the combination of
two hydrogen atoms. Each hydrogen atom has one electron in
1s orbital. Therefore, in all there are two electrons in hydrogen
molecule which are present in 1s molecular orbital. So
electronic configuration of hydrogen molecule is H2: (1s)2
 The bond order of H2 molecule can be calculated as given
below:
 Bond order = (Nb-Na)/2 = (2-0)/2=1
 This means that the two hydrogen atoms are bonded together
by a single covalent bond. Since no unpaired electron is present
in hydrogen molecule, it is diamagnetic.

 Helium molecule (He2): The electronic
configuration of helium atom is 1s2. Each helium
atom contains 2 electrons, therefore, in He2
molecule there would be 4 electrons.
 These electrons will be accommodated in 1s and
*1s molecular orbitals leading to electronic
configuration: He2: (1s)2 (*1s)2
 Bond order of He2 is ½(2 – 2) = 0
 He2 molecule is therefore unstable and does not
exist.

He
Energy
He
He2
1s 1s
g
u*

Lithium molecule (Li2)
 The electronic configuration of lithium is 1s2, 2s1.
There are six electrons in Li2. The electronic
configuration of Li2 molecule, therefore, is Li2:
(1s)2 (*1s)2 (2s)2
 From the electronic configuration of Li2 molecule
it is clear that there are four electrons present in
bonding molecular orbitals and two electrons
present in antibonding molecular orbitals. Its
bond order, therefore, is ½ (4 – 2) = 1. It means
that Li2 molecule is stable and since it has no
unpaired electrons it should be diamagnetic.

Li
Energy
Li
Li2
1s 1s
1g
1u*
2s 2s
2g
2u*

Be2 Molecule
 The electronic configuration of Be is 1s2, 2s2. There
are eight electrons in Be2.
 MO: (1s)2( *1s)2(2s)2( *2s)2
 The bond order in Be2 is (4-4)/2 = 0, so the
molecule can not exist.

Be
Energy
Be
Be2
1s 1s
1g
1u*
2s 2s
2g
2u*
Be2 Molecule

B2 molecule
 The electronic configuration of boron is 1s2 2s2 2p1. There
are ten electrons in B2. The electronic configuration of B2
molecule, therefore, is
 B2: (1s)2( *1s)2(2s)2( *2s)2 2px1 2py1
 The bond order of B2 is ½(6 – 4) = 1 and B2 should be
paramagnetic.

B
Energy
B
B2
2s 2s
2g
2u*
2p
2p
3g
3u*
1u
1g*
(px,py)
pz
HOMO
LUMO

Carbon molecule (C2)
 The electronic configuration of carbon is 1s2 2s2 2p2.
There are twelve electrons in C2. The electronic
configuration of C2 molecule, therefore, is
 C2: (1s)2( *1s)2(2s)2( *2s)2 2px2 2py2
 The bond order of C2 is ½(8 – 4) = 2 and C2 should be
diamagnetic. The bonding in N2 molecule is similar.

Nitrogen molecule
 The electronic configuration of nitrogen is 1s2 2s2 2p3.
There are 14 electrons in N2. The electronic configuration
of N2 molecule, therefore, is
 N2: (1s)2( *1s)2(2s)2( *2s)2 2px2 2py2 (2pz)2
 The bond order of N2 is ½(10 – 4) = 3. so there is a
triple bond and N2 should be diamagnetic.

Oxygen molecule (O2)
 The electronic configuration of oxygen atom is 1s2
2s2 2p4.
 Each oxygen atom has 8 electrons; hence, in O2
molecule there are 16 electrons.
 The electronic configuration of O2 molecule,
therefore, is
 (1s)2( *1s)2(2s)2( *2s)2 (2pz)2 (2px)2 (2py)2
(*2px)1 (*2py)1
 Bond order = (10-6)/2 =2
 So in oxygen molecule, atoms are held by a double
bond. O2 molecule should be paramagnetic

F
Energy
F
F2
2s 2s
2g
2u*
2p
2p
3g
3u*
1u
1g*
MO diagram for F2
(px,py)
pz
Total No. of Electrons =18
MO Electronic configuration
(1s)2( *1s)2(2s)2( *2s)2
(2pz)2 (2px)2 (2py)2
(*2px)2 (*2py)2
Bond order = (10-8)/2 =1
Diamagnetic

Neon molecule
 Total No. of Electrons =20
 MO Electronic configuration
 (1s)2( *1s)2(2s)2( *2s)2 (2pz)2 (2px)2
(2py)2 (*2px)2 (*2py)2 (*2pz)2
 Bond order = (10-10)/2 =0
 Molecule does not exist

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