Chapter 2 chemical_bonding_final

Many-electron atoms
Hartree proposed that the wave function could
be expressed simply as a product of spin orbitals,
one for each electron: ψ(1,2,…) = ψ1(1)ψ2(2)…..
ψ(1,2,…) = ψ1(1)ψ2(2)…..
Each orbital may be thought of as being hydrogen-
like with an effective nuclear charge.
configuration
the list of occupied orbitals
The orbital approximation allows us to express the electronic
structure of an atom in terms of its:

He
For example, if one disregards the inter-electronic
repulsion, the ground state wavefunction of He
may be written as
ψ(1,2) = (8/a0
3)1/2 e-2r1/a0 (8/a0
3)1/2 e-2r2/a0
corresponding to the configuration
1s2
with the 1s orbital being somewhat more compact
than in H (Nuclear charge being 2).

Li
Three electrons
First two electrons occupy as: 1s2
with the 1s orbital being more compact than in He (Z=3)
Next electron? 1s3? NO!!!
Pauli exclusion principle
No more than two electrons may occupy a given orbital, and if two
electrons do occupy one orbital, then their spins must be paired
This principle forms the basis of the electronic structure of atoms,
chemical periodicity, and molecular structure.

K SHELL COMPLETE! CLOSED SHEEL;[He]
Last electron in 2s or 2p??
Three electrons occupy as: 1s2 2s? or 1s2 2p?
The third electron in Li must enter the n = 2 shell,
Equivalently written as: [He] 2s? or [He] 2p?
Are the s and p orbitals degenerate?
• Degenerate in H
• Not in many electron systems
• 2s and 2p orbitals are non-degenerate
• p electrons are lower in energy, d,….
• S electrons are lower in energy than p,…
WHY?

In a many electron atom, each electron is shielded from the nucleus by
the others, and to a first approximation, each electron may be thought
of as experiencing an effective nuclear charge.
Shielding and Penetration
The effective nuclear charge experienced by an electron will be
determined by its probability density distribution, and this in turn by
its wave function.

‘s’ electron penetrates more than a ‘p’ electron of the same shell
‘s’ electron experiences a greater effective nuclear charge than a ‘p’
electron of the same shell
. The ‘p’ electron experienced greater effective nuclear charge than
that for a ‘d’ electron in the same shell.
In general therefore, in the same shell of a many-electron atom, the
order of energies of the orbitals is
s < p < d < f.
The ground electronic configuration of Li is therefore
1s22s1, or [He]2s1.

Building-up principle (aufbauprinzip)
Order of occupation of atomic orbitals. Rules:
1. 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 5d 4f 6p…
2. Each orbital may accommodate up to two
electrons (Pauli exclusion principle)

1s
2s
2p 2p 2p
C
Six electrons
First four electrons
occupy as: 1s22s2
Remaining two electrons
occupy as: 2p2
On the basis of
electrostatic repulsion
as: 2p1
x 2p1
y
1s22s2 2p1
x 2p1
y ; [He]2s2 2p1
x 2p1
y

Building-up (aufbau) principle
Rules:
3. Electrons occupy different orbitals of a given subshell before
doubly occupying any one of them.
4. In its ground state, atom adopts configuration with greatest
number of unpaired electrons (Hund’s rule of maximum
multiplicity).
Carbon
Friedrich
Hund
© Emilio segre visual archive

Eg., C 1s22s22px
12py
1 ; N 1s22s22px
12py
12pz
1
Origin of Hund’s rule:
Spin Correlation – Electrons in different orbitals with parallel spins
have a quantum mechanical tendency to stay apart. This allows slight
shrinkage, leading to greater attraction to nucleus.
So using the Building-up principles the configuration of
multielectron system can be written and their periodic properties
can be explained

Chapter 2: Chemical Bonding
Scheduled Lectures: 4

What is a Chemical Bond?
• Matter is made up of one or different type of elements.
• Under normal conditions no other element exists as an independent
atom in nature, except noble gases.
• The combination of atoms leads to the formation of a molecule that
has distinct properties different from that of the constituent atoms.
• Obviously there must be some force which holds these constituent
atoms together in the molecules.
• The attractive force which holds various constituents (atoms, ions,
etc.) together in different chemical species is called a chemical bond.

Since the formation of chemical compounds takes place as a result of
combination of atoms of various elements in different ways, it raises
many questions.
• Why do atoms combine?
• Why are only certain combinations possible?
• Why do some combine while certain others do not?
• Why do molecules possess definite shapes?
To answer such questions different theories and concepts have been put
forward from time to time.
• Kössel-Lewis approach
•Valence Shell Electron Pair Repulsion (VSEPR) Theory
•Valence Bond (VB) Theory
•Molecular Orbital (MO) Theory

Every system tends to be more stable and bonding is nature’s way of
lowering the energy of the system to attain stability.
Thus a chemical bond may be visualised as an effect that leads to the
decrease in the energy.
How do atoms achieve the decrease in energy to form the bond?
The answer lies in the electronic configuration.
The formation of a bond between two atoms may be visualised in
terms of their acquiring stable electronic configurations; they will do
so in such a way that they attain an electronic configuration of the
nearest noble gas.
The stable electronic configuration of the noble gases can be achieved
in a number of ways; by losing, gaining or sharing of electrons.
• Ionic or electrovalent bond
• Covalent bond
• Co-ordinate covalent bond

Why do atoms combine?
Every system tends to be more stable and bonding is nature’s way
of lowering the energy of the system to attain stability.
Balance of attractive and repulsive forces
• Consider an instantaneous configuration of two atoms
• When they are far: Attraction of A and e(1) + B and e(2)
• When close (R): [Attraction of A and e(1),e(2) + B and e(1), e(2)] + Repulsion
between A,B

Potential energy-separation curve: diatomic molecule
Low energy: stable state
High energy: unstable state
Large separation: Energy
of isolated atoms
Energetic advantage for
formation of a molecule

How do atoms achieve the decrease in energy to form the bond?
By losing, gaining or sharing of electrons.
• Ionic or electrovalent bond
• Covalent bond
• Co-ordinate covalent bond
Ionic and covalent bonds are idealized or extreme representations and though
one type generally predominates, in most substances the bond type is
somewhere between these extreme forms
LiCl: considered to be ionic but soluble in alcohol (covalent character)

Types of Chemical Bond
There are three (important) types of bonding exist among atoms.
 Metallic bonding
 Ionic bonding
 Covalent bonding
Covalent
CsF
F2, H2
Cs, Cu
Most of compounds have more than one type of bonding interaction.
18

Ionic bond: Transfer of electron(s) from one atom to another, and
the consequent attraction between the ions so formed
Electropositive element + Electronegative element  Ionic Bond
Some examples of ionic bonds and ionic compounds:
NaBr - sodium bromide NaF - sodium fluoride
KI - potassium iodide KCl - potassium chloride
CaCl2 - calcium chloride KBr - potassium bromide

Characteristics of Ionic Compounds
 Are polar; soluble in polar solvents (H2O and NH3) but insoluble
in non-polar solvents (CCl4 and C6H6)
 Are ionisable in solutions or in fused state
 Solutions of these compounds are good conductors of electricity
 Possess high melting and boiling points
 The polar linkages present in ionic compounds are non directional
• The ion pair “c+a” has a strong
residual electric field thereby
attracts other ion pairs and a large
number of ion pairs arrange within
an ionic crystal.
• The total energy released in this
process is called “lattice energy”

Metallic Bond: Metallic bond constitutes the electrostatic
attractive forces between the delocalized electrons,
called conduction electrons, gathered in an electron cloud and
the positively charged metal ions.

Melting points and boiling points
Metals tend to have high melting and boiling points because of the strength of the
metallic bond.
Electrical conductivity
Metals conduct electricity. The delocalised electrons are free to move throughout
the structure in 3-dimensions.
Thermal conductivity
Metals are good conductors of heat. Heat energy is picked up by the electrons as
additional kinetic energy.
Malleability and ductility
Metals are described as malleable (can be beaten into sheets) and ductile (can be
pulled out into wires). This is because of the ability of the atoms to roll over each
other into new positions without breaking the metallic bond.
Properties of metals

In CY101, we will concentrate on covalent bonding only!
Covalent bonding
Covalent bond is formed by sharing of the VALENCE ELECTRONS of each
atom in a bond.
Electrons are divided between core and valence electrons.
ATOM core valence
Br [Ar] 3d10 4s2 4p5 [Ar] 3d10 4s2 4p5
Br Br
Occurs between two or more electronegative atoms.
Covalent bonds are directional in nature.

24
Development of theories to understand covalent
bonding
Lewis Theory
G. N. Lewis
Valence bond theory
Linus Pauling
Molecular
Orbital Theory
Mulliken
Density
functional
theory
Kohn and
Pople
1916 1954 1966 1998
VSEPR theory
1957
Several theories were developed to explain shape and electronic
structure of covalent molecules.

25
G. N. Lewis
1875 - 1946
Lewis Theory
If two electrons are shared between two atoms, it
makes a bond and bind the atoms together.
Valence electrons are distributed as shared or BOND
PAIRS and unshared or LONE PAIRS.
Except for H, total no. of valence electrons:
#Bond Pairs + #Lone Pairs = 4 pairs or 8 electrons
Atoms in a molecule tends to have eight valence
electrons to form stable arrangement as in noble gases.
This is called as OCTET RULE.
••
Cl
••
••
shared or bond pair
Unshared or
lone pair (LP)
••
Cl
••
••
This is a LEWIS ELECTRON
DOT structure.

26
Step 2. Count valence electrons
S = 6
3 x O = 3 x 6 = 18
Negative charge = 2
TOTAL = 6 + 18 + 2 = 26 e- or 13 pairs
Step 1. Central atom = S
10 pairs of electrons are left.
Electron dot structure of Sulfite ion, SO3
2-
Step 3. Form three covalent bonds with three oxygen atoms
O O
O
S
Step 4: Remaining pairs become lone pairs,
first on outside atoms then on central atom.
•
• O O
O
S
••
••
•• ••
••
••
•
•
•
•
•
•Each atom is surrounded by an octet of electrons.

27
Count valence electrons
H = 1 and N = 5
Total = (3 x 1) + 5
= 8 electrons or 4 pairs
Electron Dot Structure of NH3
Ammonia, NH3
Form a sigma bond between the central atom
and surrounding atoms.
H H
H
N
Remaining electrons form LONE PAIRS
to complete octet as needed.
H
••
H
H
N
3 BOND PAIRS and 1 LONE PAIR
(Central atom = N; surrounding atoms = H)

•The incomplete octet of the central atom
BeH2 BF3
F B F
F
H Be H
Limitations of the Octet Rule
BF3
F••
•
•
••
F
F
B
••
••
•
•
•
•
•
•
•
•
Central atom = B
Valence electrons = 3 + 3*7 = 24 (12 electron pairs)
The B atom has a share in only 6 electrons
(or 3 pairs). B atom is electron deficient.

•Odd-electron molecules
•Expanded octet
NO N O
In a number of compounds there are more than eight valence electrons around the
central atom. PF5, SF6, H2SO4 and a number of coordination compounds.
F
••
•
•
••
F
F
S
••
••
•
•
•
•
•
• F••
••
••
••
••
5 pairs around
the S atom

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

Sidgwick – Powell Theory
In 1940 Sidgwick and Powell suggested that for molecules and
ions that contain only single bonds, the approximate shape can be
predicted from the number of electron pairs in the outer or valence
shell of the central atom.
• Bond pairs and lone pairs were taken as equivalent
• All electron pair take up some space
• All electron pairs repel each other
• Repulsion is minimized if the electron pairs are oriented in
space as far as possible.

Predicted molecular shapes from Sidgwick- Powell Theory:
No. of electron
pairs in outer
shell
Arrangement of electron pairs Electron-pair geometry Bond angles
2
3
4
5
6
Linear
Trigonal Planar
Tetrahedral
Trigonal bipyramid
Octahedral
180 0
120 0
109.50
900, 120 0
90 0

Valence Shell Electron Pair Repulsion (VSEPR)
Theory
33
 The theory was suggested by Sidgwick and Powell in 1940 and was developed
by Gillespie and Nyholm in 1957.
 VSEPR theory is based on the idea that the geometry of a molecule or polyatomic
ion is determined primarily by repulsion among the pairs of electrons associated
with a central atom.
 The pairs of electrons may be bonding or nonbonding (lone pairs).
 Only valence electrons of the central atom influence the molecular shape in a
meaningful way.
 The shape of the molecule is determined by repulsions between all of the electron
pairs present in the valence shell.
Trigonal planar Pyramidal

A lone pair of electrons takes up more space around the central atom than a bond
pair.
And hence, lp-lp repulsion > lp-bp repulsion > bp-bp repulsion
34
The bonds around the central atom and hence the shape of molecule
depends on number of electron pairs surrounds it.
For a given number of electron pairs in the valence shell of the central atom,
the preferred arrangement is that which minimizes their repulsion.
VSEPR theory may be summarized as:
The space occupied by a bond pair electron around the central atom decreases
with increase in electronegativity of ligand.
Double bond occupy more space around the central atom than single bond, and
triple bond occupy more space around central atom than double bond
lp belongs to central atom
bp belongs to both atoms

35
Effect of lone pair
A. Molecules with four electron pairs (steric numbers)
CH4 4 bp 0 lp Tetrahedral 109.5
degree
NH3 3 bp 1 lp Trigonal
pyramid
107.3
H2O 2 bp 2 lp Bent or
angular
104.5

36
Effect of lone pair
B. Molecules with five electron pairs (steric numbers)
I. PCl5 (5 bp + 0 lp) trigonal bipyramidal geometry (all bonds are identical)
P Cl
Cl
Cl
Cl
Cl
90 °
120 °
II. SF4
Valence electron of S = 6
Contribution from each 4F = 4 x 1
Total = 10 VE (4 bp + 1 lp)
There are two possible structure (a) lone pair at equatorial position or (b)
lone pair at axial position.
S ..
F
F F
F
S F
F
F F
..
(a) (b)

37
(a) (b)
lp-lp ---- ---
Lp-bp 2@120,
2@90
1@180, 3@90
If the angle is >120 , the repulsions have same effect on the structure. So
120 and 180 repulsions have same effect on the structure.
Since in structure (a), there are only 2@90 lp-bp repulsions, so it is the
preferred structure for SF4.
Effect of lone pair
II. SF4
III. ClF3 (Home work)

ClF3
Lewis model:
Shape : T shape
Lone pairs occupy equatorial positions of trigonal bipyramid
Cl
F
F
F

39
Effect of Electronegativity
If the ligand has larger electronegativity, the smaller is the bond angle.
If the central atom has larger electronegativity, the larger is the
bond angle.
NH3; bond angle 106.7
NF3; bond angle 102.2
H2O; bond angle 104.5
H2S; bond angle 92
•The high electronegativity of F pulls the bonding electrons
away from N in NF3 than in NH3
• Thus repulsion between bp-bp is less in NF3 than in NH3

40
Effect of Double bond
Double bond has very similar effect as that of the lone pair
because of the repulsive effect of  electrons.
CH3
C C
HCH3
H122.2
115.6
Q. Draw all possible structures of the following molecules and explain which
one is the preferred structure based on VSEPR theory.
(a) SO2Cl2, (b) ClOF3
S
O
O
Cl
Cl
120o
111o

Limitations of VSEPR Theory
It fails to predict the shapes of several isoelectronic species.
Two isoelectronic species, can differ in geometry despite the fact
that they have the same numbers of valence electrons
 It fails to predict the shapes of transition metal complexes
The model does not take relative size of substituents into account.
Atomic orbitals overlap cannot be explained by VSEPR theory
The theory makes no predictions about the lengths of the bonds,
which is another aspect of the shape of a molecule

Valence Bond Theory (VBT)-
• localized quantum mechanical approach
•Proposed by Heitler and London in 1927
• This theory was further developed by Linus Pauling (Nobel Prize 1954)
• The process of chemical bond formation can be visualized as the overlapping of
atomic orbitals of the two atoms as they approach each other.
• Bond regarded as being formed when electron in an orbital on one atom pairs its
spin with that of an electron in an orbital on another atom.
• The strength of the bond depends on the effectiveness or extent of the overlapping.
Greater the overlapping of the orbitals, stronger is the bond formed.
Consider the approach of two ground state hydrogen atoms and bond formation in H2:
A and B stand for the 1s orbitals centered on nucleus A and nucleus B respectively.
Nucleus A:
A
Nucleus B:
B

1HA
2HB
2HA
1HB
Ψ(1,2) = A(1)B(2) Ψ(1,2) = A(2)B(1)
A linear combination is appropriate:
Ψ(1,2) = [CIA(1)B(2) +CII A(2)B(1)] {(1)(2)- (1) (2)}
CI and CII: Mixing coefficients

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.
Positive overlap: Orbitals forming bond should have same sign (phase) and
orientation in space.

sigma bonds (σ bonds) are formed by head-on overlapping between atomic
orbitals.
Sigma bonds are cylindrically symmetric about the inter nuclear axis.
More overlap and hence the sigma bonds are strongest type of covalent
chemical bond.
Sigma (σ) bond
45

Pi bonds (π bonds) are formed by sideways overlap of orbitals.
Pi bonds have electron density in two lobes, one each side of the bond axis.
Pi (π ) bond
46
Overlap of 2 2p orbitals for the
formation of  bond
Nodal plane
Pi bond has one nodal plane containing the inter-nuclear axis and the sign
of the lobe changes across the axis.
Pi bond is not as strong as sigma - less overlap.

1s

1s
1s-1s overlap gives a H – H single bond
The 1s-2p overlap gives a H – F single bond
F 
2s 2p
 
1s
H
Non-bonding electrons
Three 2p-1s overlaps lead to the formation of three N – H single bonds.
N 
2s 2p
 3H 
1s
N
H
H
H

48
Single bond: must be one sigma bond
Double bond: one sigma + one pi bond (ethylene)
Triple bond: one sigma + two pi bonds (nitrogen molecule)
Sigma bonds and the lone pairs are responsible for shape/geometry
of molecule. Pi bond only shorten the bond distance.
Multiple bond

Limitations
(1) Poor prediction of bond angles
If the p orbitals are used for bonding in H2O and NH3 then the
bond angle should be 90.
(2) Inability to explain the tetra valence of carbon
C= 1s22s22px
12py
1
Promotion and hybridization
C= 1s22s22px
12py
1  C= 1s22s12px
12py
12pz
1
Promotion
Driving force: To attain more stability by forming more number
of bonds

50
sp 2 sp hybrid orbitals from mixing of a s and a p orbital
sp 2 3 sp2 hybrid orbitals from mixing of a s and 2 p orbital
sp3 4 sp4 hybrid orbitals from mixing of a s and 3 p orbital
sp3d 5 sp3d hybrid orbitals from mixing of a s and 3 p and a d orbital
The valence orbitals (of central atom) undergo hybridization before
making chemical bond.
Hybridization (A hypothetical concept for bonds)
A hybrid animal – Centaur – Greek myth with
head, arms and torso of a man united to the
body and legs of a horse

Consider n atomic orbitals with wave functions ψ1 …. ψn mix
Mixing : makes linear combination
n hybrid orbitals Ψ1 …. Ψn are formed
Ψ1 = C1,1 ψ1 + C1,2 ψ2 ………… + C1,nψn
………………………………………………………
………………………………………………………
Ψn = Cn,1 ψ1 + Cn,2 ψ2 ………… + Cn,nψn
How the coefficients are determined?
•They should be so that directional properties of resultant hybrid orbitals are
achieved
•Constructive and destructive interference of the wave characteristics of the
corresponding orbital
•Square of coefficients should also give proportion of each atomic orbital in
the hybrid

sp hybrids
Ψsp1 = (1/2) (ψs + ψpz
)
Ψsp2 = (1/2) (ψs – ψpz
)
Hybridization of one s and one p orbitals = 2 sp hybrid orbitals

53
H-C-C-H: three s bonds due to overlapping of 1sH – spC; spC – spC; and spC – 1sH.
Two  bonds in HCCH are due to overlapping of p orbitals results.
H H
sp hybrid orbitals
Two nodal planes of p bonds are perpendicular to each other.
in  bond
C
2s 2p 2p 2p
spsp 2p 2p
H-CC-H
Examples of sp Hybridization

The sp2 Hybrid Orbitals
Hybridization of one s and two p orbitals=3 sp2 hybrid orbitals
Ψ1 = (1/3)1/2ψs + (2/3)1/2ψpx
Ψ2 = (1/3)1/2 ψs – (1/6)1/2 ψpx
 (1/2)1/2 ψpy
Ψ3 = (1/3)1/2 ψs  (1/6)1/2 ψpx
+ (1/2)1/2 ψpy
These lie in a plane and point towards the corners of an equilateral
triangle.

sp2 hybrids: Ethene H2C=CH2
Uses the three sp2 orbitals to form s bonds with 2H atoms and the
other C atom.
Use the remaining unhybridized 2p orbitals on the two C atoms to form
a  bond

56
Compounds involving sp2 hybrid orbitals: BF3, CO3
2–, H2CO,
H2C=CH2, NO3
–, etc
examples of sp2 hybridization
Total number of hybrid orbitals = total number of sigma bonds (of central
atom) + lone pairs on central atom

The sp3 Hybridized Orbitals
The hybridization of a s and three p orbitals lead to 4 sp3 hybrid orbitals for bonding.
Ψ1 = (½) (ψ2s + ψ2px + ψ2py + ψ 2pz)
Ψ2 = (½) (ψ 2s + ψ 2px - ψ 2py - ψ 2pz )
Ψ3 = (½) (ψ 2s - ψ 2px - ψ 2py + ψ 2pz)
Ψ4 = (½) ( ψ 2s - ψ 2px + ψ 2py - ψ 2pz )
These arrange in a tetrahedral geometry with bond angle 109.5

58
Compounds involving sp3 hybrid orbitals: CF4, CH4, : NH3,
H2O::, SiO4
4–, SO4
2–, ClO4
–, etc
sp3 hybridization
Dr. Saroj L. Samal
Department of Chemistry
hybridization of s and px, py and pz orbitals = 4
sp3 hybrid orbitals (tetrahedral geometry)

59
hybridization of s and px, py , pz and dz2orbitals = 5 sp3d hybrid orbitals
(trigonal bipyramid)
The sp3d Hybridization
Some structures due to these type of
orbitals are PF5, PClF4, TeCl4, and
BrF3.

The sp3d2 Hybrid Orbitals
Hybridization of one s, three p, and two d orbitals results in 6 sp3d2
hybrid orbitals.
The arrangement of these orbitals is an octahedron.
Compounds using these type of orbitals are of the type:
AX6, AX5E, AX4E2

61
Bent’s Rule
Bent’s rule
More electronegative substituents prefer hybrid orbitals having less s-
character (small bond angle) and vice versa.
sp3d hybrid orbitals are combination of two sets of hybrid orbitals. spxpy
hybrids and pzdz2 hybrid orbitals.
sp2 hybrid orbitals are form stronger bond and are shorter than weak axial
pzdz2 hybrid orbitals.
Empirical rule proposed by H. A. Bent, in
the chloroflurides of phosphorous, 1960.
PCl5 has sp3d hybridization. When the electronegativities of the substituents on the
phosphorous atom differ (PCl5-xFx), it has been experimentally observed that the more
electronegative substituent occupies axial position.
In CH2Cl2, the H-C-H bond angle is more than 109.5o indicating
more than 25% s character where as the Cl-C-Cl bond angle
is less than 109.5o indicating less than 25% s character

62
Draw backs of VBT
1. Does not tell anything about the excited states of molecule.
Because of orbital overlap, the bonding
electrons localize in the region between
the bonding nuclei
2. Not able to explain paramagnetic nature of O2 molecule.
3. Can’t explain the delocalized pi-electrons in certain molecules.
Ex- benzene.
Paramagnetic compound: compounds/elements having unpaired electrons.
Diamagnetic compound: All electrons are paired up, no unpaired electron.

63
Molecular Orbital Theory
MOT is developed by Robert S. Mulliken (Got nobel prize in 1966).
Based on delocalized quantum mechanical approach.
Uses symmetry to describe the bonding in molecule.
Basic Principles of MOT
Describes the electrons in a molecule using wave functions called molecular orbitals.
A molecular orbital is a one electron wavefunction which spread over the entire
molecule
The atomic orbitals of different atoms combine to create molecular orbitals. The
symmetry and relative energy of atomic orbitals determine how they interact to form
molecular orbital.
These molecular orbitals are then filled with available electrons according to the
increasing order of energy.

64
VBT MOT
Electrons occupy orbitals,
localized to overlap region.
(localized electron pair concept)
Hybridization of A. O.s of same
atom to explain the geometry of
molecule.
Does not tell anything about the
excited states of molecule.
Electrons in molecular orbitals
belong to the molecule as a whole.
(Delocalized concept)
No concept of hybridization. It does
not tell anything about geometry of
molecule.
Better describe the excited states
of molecule.
MOT and VBT
MO theory more “accurately predict the bonding" than VB theory and also
the properties of molecules.

65
Types of Molecular Orbitals
Combination of atomic orbitals, gives following molecular orbitals:
• Bonding molecular orbital
• Antibonding molecular orbital
• Nonbonding molecular orbital
 Bonding molecular orbital
 When two orbitals with same sign overlaps, then there is
increase in electron density in the overlap region and a
bonding MO is formed.
 This is called as constructive interference of atomic
orbitals.
 lower energy than atomic orbital
 Cyllinderical symmetry.
Called s orbital

Overlap integral (S)
Represent the accumulation of electron
density between atoms
Probability density
Coefficients C – extent to which each AO contributes to the MO
A B
+. +. . .+
MO = CA A+ CBB
2
MO = cA
2 A
2 + 2cAcB A B + cB
2 B
2

67
 Antibonding molecular orbital
– Destructive interference leads exclusion of electrons for the
region between the nuclei
• Highest electron density is located on opposite sides of
the nuclei
– higher energy than atomic orbital
MO = CA A- CBB
2
MO = cA
2 A
2 - 2cAcB A B + cB
2 B
2

68
Nonbonding molecular orbitals have essentially same as that of the atomic orbitals.
These may exist in following situations:
1. Combination of atomic orbitals whose symmetry do not match and
remain unchanged in the molecule.
Ex: interaction of s with px or py or dxy or dyz etc
2. When there are three atomic orbitals of the same symmetry and
similar energy, three MOs are formed: bonding MO (lower energy),
antibonding MO (higher energy), and nonbonding MO (same energy as
atomic orbital).
 Nonbonding molecular orbital

69
Procedure for forming molecular orbitals
1. Identify set of symmetry related atomic orbitals with similar energy.
2. MOs form by linear combinations of the atomic orbitals (LCAO).
3. For poly atomic molecule, the LCs of ligands combine with the atomic
orbitals of central atom to form MOs.
Molecular Orbital Theory
Application of MOT
(a) Homonuclear diatomic molecule
(b) Heteronuclear diatomic molecule

70
Molecular orbitals from 1s atomic orbitals
MOs may be either sigma (σ) or pi (π) orbitals.
σ MO: MO which are symmetric to rotation about the inter-nuclear axis.
π MO: MO which have a nodal plane containing the inter-nuclear axis (not
symmetric to rotation about the inter-nuclear axis.)
ψA (1s) = 1s orbital wave function of A
ψB (1s) = 1s orbital wave function of B
Molecular orbitals are:
s1s = 1/2[ψA (1s) + ψB (1s)] (Bonding MO)
s*1s = 1/2[ψA (1s) − ψB (1s)] (Antibonding MO)
Homonuclear diatomic molecule
Note: In homonuclear diatomic molecule, the contribution from each
atom to the MO is equal.

First period diatomic molecules
s1s2
H
Energy
HH2
1s 1s
s1s g
s*1s
Bond order =
½ (bonding electrons –
antibonding electrons)
Bond order: 1
u
MO Diagram of H2

72
Bond order (strength of bond)
Bond order = (no. of bonding e- − no. of antibonding e-)
2
Single bond: bond order = 1
Double bond: bond order = 2
Triple bond: bond order = 3
Fractional bond orders also exist!
In MO Theory, the strength of a covalent bond can be related to its
bond order

s1s2, s*1s2He
Energy
HeHe2
1s 1s
Molecular Orbital theory is powerful because it allows us to predict whether
molecules should exist or not and it gives us a clear picture of the
electronic structure of any hypothetical molecule that we can imagine.
MO diagram of He2
Bond order: 0
s1s
s*1s

Second period diatomic molecules
s1s2, s*1s2, s2s2
Bond order: 1
Li
Energy
Li
Li2
1s 1s
2s 2s
s*1s
s1s
s2s
s*2s
Bond energy for
Li2 = 110 kJ.mol-1,
Compared to 436
kJ.mol-1 for H2.

s1s2, s*1s2, s2s2,
s*2s2
Bond order: 0
Be
Energy
BeBe2
1s 1s
2s 2s
Diatomic molecules: Homonuclear Molecules of the Second Period
s1s
s*1s
s2s
s*2s

76
Molecular orbitals from 2p atomic orbitals
Combination of 2p orbitals gives two sets of molecular orbitals based on symmetry.
If the inter nuclear axis is the z-axis, then the combination of 2pz atomic orbitals
[2pz(A) ± 2pz(B)] gives MOs that are symmetric about inter nuclear axis.
Shape
2pz 2pz
σ*2pz
σ2pz
σ2pz = 2pz(A) − 2pz(B)
σ*2pz = 2pz(A) + 2pz(B)
+
+
- −
- -
+
+ -

77
Molecular orbitals from 2p atomic orbitals
Combination of 2px atomic orbitals [2px(A) ± 2px(B)] gives molecular
orbitals having nodal plane containing internuclear axis. MOs are:
Shape
+
+
+
-
-
-
2px 2px
+ +
− −
Similarly, 2py atomic orbitals combine to give π2py and π*2py MOs.
π2px = 2px(A) + 2px(B)
π*2px = 2px(A) − 2px(B)
Since the 2px and 2py orbitals have identical energy, so the
resulting MOs also have same energy. These MOs differ only
in spatial orientation.

78
Molecular orbital diagram
An energy level diagram that shows the energy level of molecular orbitals
relative to the atomic orbitals from which they’re derived
 Draw the skeleton MOs
 Use only the valence electrons of the atoms
 Follow the aufbau principle
 Each MO can hold a maximum of 2 electrons
 Follow Hund’s rule.
Keep electrons unpaired until all MO’s having the
same energy have one e-.

Molecular Orbital Diagram of N₂
79
Number of valence electrons for two N atoms = 10
B. O. = (8−2)/2 = 3
Magnetic properties: Since all
the electrons are paired up, so
it is a diamagnetic compound.
HOMO
LUMO Frontier orbitals

80
Q. Draw the molecular orbital diagram of O2 molecule. Fill the valence
electrons and write down the energy order of MOs. Find out the bond order and
show that it is paramagnetic in nature.
Since there are two unpaired electrons
present in π*2px and π*2py, so oxygen
molecule is paramagnetic in nature.

Homonuclear period 2 Diatomics
• s2s s2s* s2pz  2px = 2py *2px *2pys2pz*.
(O2 and higher)
• s2s s2s*  2px = 2py  s2pz *2px *2pys2pz*.
(Up to N2)

Energy levels of first-row homonuclear diatomic
Molecules Li2, Be2, B2,C2 and N2
have π(2p) lower in energy than σ(2p)
Molecules O2, and F2 have π(2p) higher
in energy than σ(2p)
crossover point

83
Heteronuclear diatomic molecule
In heteronuclear diatomic molecule, the atomic orbital have different
energy and hence their contribution to MO will be unequal.
The AO closer in energy to a MO contribute more to that MO and its coefficient is large.

For example, in HF, ψ = cH1sH + cF2pzF
The bonding orbital has principally F2pz character, and the antibonding orbital, H1s. The
bond will be polar with a partial negative charge on F.
Bonding character
Antibonding
character
HF molecule
B.O = 1

85
Molecular orbital diagram of CO
Total no. of electrons = 14 (isoelectronic to N2)
Total valence electrons = 10
So the electronic configuration is:
(σ2s)2 (σ*2s)2 (π2px)2 = (π2py)2 (σ2pz)2
Oxygen has more
electronegativity, so the
atomic orbitals are lower
lying compared to carbon.
B.O = 3

86
Q. Draw the MO diagram for NO. Find out the B.O.? Predict the
magnetism in it.

Chapter 2 chemical_bonding_final

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