CHEMICAL BONDING

(1)

MODULE-II

CHEMICAL BONDING

Chemistry

CHY-101

By: Dr. Himanshu Arora

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Covalent Bond; sigma and pi bond; single, double and triple bonds;

Ionic Bond;

Octet stability,

Lewis dot structure,

VSEPR Theory

,

Valence Bond Theory,

LCAO-MO; H

₂

; CO

Periodic trends of chemical properties,

Inter-molecular and Intra-molecular bonding (Hydrogen Bonding, Van

Der Waals forces, London Forces, etc); dipole moment; polarizibility

of molecules;

Band theory of solids; conductors; semiconductors; insulators;

Crystal Systems; Examples on property variations based on lattice

structure.

I o n i c B o n d i n g

R e s o n a n c e S t r u c t u r e s

V S E P R

B a s i c S h a p e s

3 - D N o t a t i o n

H y b r i d i z a t i o n ( L a b )

M o l e c u l a r G e o m e t r i e s

O c t e t R u l e

P o l a r M o l e c u l e s

L e w i s S t r u c t u r e s

C o v a l e n t B o n d i n g

T y p e s o f B o n d s

CHEMICAL

BONDING

CHEMICAL

_BONDING

CHEMICAL

_BONDING

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• _{Chemical bond}

_{: attractive force holding two or more}

atoms together.

• _{Covalent bond results from sharing electrons between}

the atoms. Usually found between nonmetals.

• Ionic bond results from the transfer of electrons from a

metal to a nonmetal.

• _{Metallic bond}

_{: attractive force holding pure metals}

together.

CHEMICAL BONDS, LEWIS SYMBOLS, AND THE

OCTET RULE

CHEMICAL BONDS, LEWIS SYMBOLS, AND THE

_{OCTET RULE}

CHEMICAL BONDS, LEWIS SYMBOLS, AND THE

_{OCTET RULE}

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IONIC BONDING

_{IONIC BONDING}

COVALENT

BONDING

COVALENT

_BONDING

COVALENT

_BONDING

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

Metallic bonding



Occurs between

like

atoms of a metal in the free state



Valence e- are mobile (move freely among all metal atoms)



Positive ions in a sea of electrons



Metallic characteristics



High mp temps, ductile, malleable, shiny



Hard substances



Good conductors of heat and electricity as (s) and (l

)

It’s the

mobile electrons

that enable me

-

tals to

(7)

ION

IC

BONDING



e

lectrons are

transferred

between

valence shells

of atoms



ionic compounds are

made of ions

Ionic compounds are called

Salts

or

Crystals

NOT MOLECULES



Always

formed between metals and non-metals

[METALS ]

+

_{[NON-METALS ]}

-Lost e

(8)

-

Electronegativity difference

> 2.0



_{Look up e-neg of the atoms in the bond and subtract}

NaCl

CaCl

₂



Compounds

with

polyatomic ions

NaNO

₃

ION

IC

BONDING

PROPERTIES OF

IONIC

COMPOUNDS



hard solid @ 22

o

C



high mp temperatures



non

conductors of electricity in

solid

phase



good

conductors in liquid phase or

dissolved in water (aq)

(9)

PROPERTIES OF MOLECULAR

SUBSTANCES



Low m.p. temp and b.p. temps



relatively

soft solids

as compared to ionic compounds



nonconductors

of electricity in any phase

Covalent bonding 

Pairs

of e- are

shared

between

non-metal

atoms



electronegativity

difference < 2.0



forms polyatomic ions

COVALENT

BONDING

(10)

Characteristics of Ionic Bond



_{Solids at room temperature}



High melting point



_{Hard and brittle}



Soluble in water



Conductors of electricity



_{Do not exhibit isomerism}

(11)

Characteristics of Covalent Bond



Gases, liquids or solids at room temperature



Low melting points and boiling points



_{Neither hard nor brittle}



Soluble in non-polar organic solvents



Non-conductors of electricity



Exhibit isomerism

(12)

Characteristics of Metallic Bond



_{Luster or Reflectivity}



Electric conductivity



Heat conductivity



_{Ductility and Malleability}

(13)

Bond Type Single

Double

Triple

# of e’s

2

4

6 Notation

—

=



Bond order 1

2

3 Bond

strength

Increases from Single to Triple

Bond length

Decreases from Single to Triple

CHEMICAL

BONDS

CHEMICAL

_BONDS

CHEMICAL

_BONDS

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AVERAGE BOND ENTHALPIES

(KJ/MOL)

AVERAGE BOND ENTHALPIES

_(KJ/MOL)

AVERAGE BOND ENTHALPIES

_(KJ/MOL)

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STRENGTH OF COVALENT

BONDS

STRENGTH OF COVALENT

_BONDS

STRENGTH OF COVALENT

_BONDS

AVERAGE BOND LENGTHS FOR SOME SINGLE, DOUBLE, AND

TRIPLE BONDS

AVERAGE BOND LENGTHS FOR SOME SINGLE, DOUBLE, AND

_{TRIPLE BONDS}

AVERAGE BOND LENGTHS FOR SOME SINGLE, DOUBLE, AND

_{TRIPLE BONDS}

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Octet Rule

• All noble gases except He has an

s

2

_p

6

_{configuration.}

• _{Octet rule:}

_{atoms tend to gain, lose, or share electrons until they are surrounded}

by 8 valence electrons (4 electron pairs).

• _Caution

_{: there are many exceptions to the octet rule.}

CHEMICAL BONDS, LEWIS SYMBOLS, AND THE

OCTET RULE

CHEMICAL BONDS, LEWIS SYMBOLS, AND THE

OCTET RULE

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• Electronegativity:

The ability of one atoms

in a

molecule

to attract electrons to itself.

• Pauling set electronegativities on a scale from 0.7 (

Cs

) to

4.0 (

F

).

• Electronegativity increases

across a period and but decreases

down a group

BOND POLARITY AND

ELECTRONEGATIVITY

BOND POLARITY AND

_{ELECTRONEGATIVITY}

BOND POLARITY AND

_{ELECTRONEGATIVITY}

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• There is no sharp distinction between bonding types.

• The positive end (or pole) in a polar bond is represented



+ and the negative pole



-.

BOND POLARITY AND

ELECTRONEGATIVITY

BOND POLARITY AND

_{ELECTRONEGATIVITY}

BOND POLARITY AND

_{ELECTRONEGATIVITY}

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Follow Step by Step Method

1. Total all valence electrons. [Consider Charge]

2. Write symbols for the atoms and guess skeleton structure [ define a central

atom ].

3. Place a pair of electrons in each bond.

4. Complete octets of surrounding atoms. [ H = 2 only ]

5. Place leftover electrons in pairs on the central atom.

6. If there are not enough electrons to give the central atom an octet, look for

multiple bonds by transferring electrons until each atom has eight electrons

around it.

DRAWING LEWIS

STRUCTURES

DRAWING LEWIS

_STRUCTURES

DRAWING LEWIS

_STRUCTURES

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H

₂

O

8e

-

H O H

2 bond pairs 2 lone pairs

X E

AX₂E₂

CO

₂

16e

-

_O

C

O

2 bond pairs

X

O C O AX₂

LEWIS

STRUCTURES

LEWIS

_STRUCTURES

LEWIS

_STRUCTURES

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Central Atoms Having Less than an Octet

• _{Relatively rare.}

• Molecules with less than an octet are typical for compounds of

Groups 1A, 2A, and 3A.

• Most typical example is BF

₃

.

• Formal charges indicate that the Lewis structure with an

incomplete octet is more important than the ones with double

bonds.

BF

₃

24e

-

F B F

F

EXCEPTION TO THE OCTET

RULE

EXCEPTION TO THE OCTET

_RULE

EXCEPTION TO THE OCTET

_RULE

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Central Atoms Having More than an Octet

• _{This is the largest class of exceptions.}

• _{Atoms from the 3}

rd

_{period onwards can accommodate more than}

an octet.

• Beyond the third period, the

d

-orbitals are low enough in energy

to participate in bonding and accept the extra electron density.

PF

₅

_40e

-F

P

_F

F

EXCEPTION TO THE OCTET

RULE

EXCEPTION TO THE OCTET

_RULE

EXCEPTION TO THE OCTET

_RULE

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There are three fundamental geometries for molecular shape:

on the plane

into plane

out of plane

MOLECULAR SHAPES – 3D

NOTATIONS

MOLECULAR SHAPES – 3D

_NOTATIONS

MOLECULAR SHAPES – 3D

_NOTATIONS

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MOLECULAR

SHAPES

MOLECULAR

_SHAPES

MOLECULAR

_SHAPES

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e-pairs

Notation

Name of VSEPR shape Examples

2 AX₂ Linear HgCl₂ , ZnI₂ , CS₂ , CO₂

3 AX₃ Trigonal planar BF₃ , GaI₃

AX₂E Non-linear (Bent) SO₂ , SnCl₂

4 AX₄ Tetrahedral CCl₄ , CH₄ , BF₄

-AX₃E (Trigonal) Pyramidal NH₃ , OH₃

-AX₂E₂ Non-Linear (Bent) H₂O , SeCl₂

5 AX₅ Trigonal bipyramidal PCl₅ , PF₅

AX₄E Distorted tetrahedral

(see-sawed)

TeCl₄ , SF₄

AX₃E₂ T-Shaped ClF₃ , BrF₃

AX₂E₃ Linear I₃-_{, ICl}

2

-6 AX₆ Octahedral SF₆ , PF₆

-AX₅E Square Pyramidal IF₅ , BrF₅

AX₄E₂ Square Planar ICl₄-_{, BrF}

4

-SUMMARY OF VSEPR MOLECULAR

SUMMARY OF VSEPR MOLECULAR

SHAPES

SUMMARY OF VSEPR MOLECULAR

_SHAPES

SUMMARY OF VSEPR MOLECULAR

_SHAPES

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How do we determine the shapes of molecules and ions?

What does VSEPR stand for?

Valence Shell Electron Pair Repulsion

Why is this important to know?

It explains how molecules and ions behave.

For example:

It explains why water molecules are so good at

dissolving ionic

substances even though water does not have an ionic bond.

Another example: Use it to clean up greasy hands from working

on your car or sprucing up your nails between manicures!

Another example:

It explains why

part of a soap molecule attracts water

while

the

other part attracts grease and oils.

VSEPR

THEORY

VSEPR

_THEORY

VSEPR

_THEORY

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1)

Determine the central atom

(usually the atom with the lowest

subscript and/or the atom capable of forming the most bonds).

2)

Draw the electron dot structure and bar diagram

3)

Determine the molecular geometry using ALL electron pairs

AND atoms around the central atom.

4)

Modify the geometry to determine the molecular shape if

non-bonding electron pairs exist by ignoring them,

BUT LEAVE

THE ATOMS OF BONDED PAIRS WHERE THEY ARE.

This is done because even if the electrons have no atom

attached, these unbounded electron pairs still affect the shape

of the structure.

VSEPR THEORY: BASIC PROCEDURE

_{VSEPR THEORY: BASIC PROCEDURE}

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

Central Atom?

Be

(only 1 atom)



Electron Dot?



Bar Diagram?



Geometry? Hint: What is the furthest apart you can spread two

atoms attached to a central atoms?



Shape? Ignore any unbonded pairs of electrons —not

necessary in this case.

 LINEAR

Be

H

Be

H

Be

H

Note that Be violates the octet

rule—this is an exception!

VSEPR THEORY: EXAMPLE:

BEH

VSEPR THEORY: EXAMPLE:

_BEH

VSEPR THEORY: EXAMPLE:

_BEH

₂₂

2

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

Central Atom?



B

(only 1 atom)



Electron Dot?



Bar Diagram?



Geometry? Hint: What is the furthest apart you can

spread three atoms attached to a central atom?



Shape? Ignore any unbonded pairs of electrons —not

necessary in this case.



trigonal planar

F B F

F

F—B—F

F

Note that B violates the octet rule—

this is an exception!

B

F

VSEPR THEORY: EXAMPLE:

BF

VSEPR THEORY: EXAMPLE:

_BF

VSEPR THEORY: EXAMPLE:

_BF

₃₃ 3

3 ₂₂

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

Central Atom?

C

(only 1 atom)



Electron Dot?



Bar Diagram?



Geometry? Hint: What is the furthest apart you can spread four atoms

attached to a central atom? Think in 3D!



Shape? Ignore any unbounded pairs of electrons —not necessary in this

case.



tetrahedral

C H H H H C H H H H

C

H

VSEPR THEORY: EXAMPLE:

CH

VSEPR THEORY: EXAMPLE:

_CH

VSEPR THEORY: EXAMPLE:

_CH

₄₄

(31)



Central Atom?



N (only 1 atom)



Electron Dot?



Bar Diagram?



Geometry? Hint: What is the furthest apart you

can spread three atoms plus one unbounded pair

of electrons attached to a central atom? Think in

3D!



Shape? Ignore any unbonded pairs of electrons

—it is necessary in this case.



trigonal pyramidal

H

N

H

~109.5

o

N

H

N

H

VSEPR THEORY: EXAMPLE:

NH

VSEPR THEORY: EXAMPLE:

_NH

VSEPR THEORY: EXAMPLE:

_NH

₃₃

(32)



Central Atom?



O

(only 1 atom)



Electron Dot?



Bar Diagram?



Geometry? Hint: What is the furthest apart you can

spread two atoms plus two unbonded pairs of electrons

attached to a central atom? Think in 3D!



Shape? Ignore any unbonded pairs of electrons —it is

necessary

in this case.



bent

O H

H

O H

H

O

H

~109.5

o

VSEPR THEORY: EXAMPLE:

H

VSEPR THEORY: EXAMPLE:

_H

VSEPR THEORY: EXAMPLE:

_H

₂₂

O

2

O

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In conclusion:



Since water (also called the universal solvent) is bent it

is able to dissolve ionic substances:

O side tends to be –

(the electron pairs

hybridize into one

group)

O

H

H sides tend to be +

This negative side

tends to attract

positive ions

H

O

H

These positive ends

tend to attract

negative ions

VSEPR

THEORY

VSEPR

_THEORY

VSEPR

_THEORY

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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

104.5

O

107

O

N

H

C

H

109.5

O

H

Shapes of Larger Molecules

• In acetic acid, CH

₃

COOH, there are three central atoms

VSEPR

MODEL

VSEPR

_MODEL

VSEPR

_MODEL

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MOLECULAR SHAPE AND MOLECULAR

POLARITY

MOLECULAR SHAPE AND MOLECULAR

_POLARITY

MOLECULAR SHAPE AND MOLECULAR

_POLARITY

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MOLECULAR SHAPE AND MOLECULAR

POLARITY

MOLECULAR SHAPE AND MOLECULAR

_POLARITY

MOLECULAR SHAPE AND MOLECULAR

_POLARITY

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• _{Lewis structures and VSEPR do not explain why a bond}

forms.

• How do we account for shape in terms of quantum

mechanics?

• What are the orbitals that are involved in bonding?

• We use Valence Bond Theory:

• Bonds form when orbitals on atoms overlap.

• There are two electrons of opposite spin in the orbital overlap.

COVALENT BONDING AND ORBITAL

OVERLAP

COVALENT BONDING AND ORBITAL

_OVERLAP

COVALENT BONDING AND ORBITAL

_OVERLAP

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ELECTRON-DOMAIN GEOMETRIES AS A

FUNCTION OF THE NUMBER OF ELECTRON

DOMAINS

ELECTRON-DOMAIN GEOMETRIES AS A

FUNCTION OF THE NUMBER OF ELECTRON

DOMAINS

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• To determine the electron pair geometry:

• draw the Lewis structure,

• count the total number of electron pairs around the central atom,

• arrange the electron pairs in one of the above geometries to minimize e_-e

repulsion, and count multiple bonds as one bonding pair.

VSEPR

MODEL

VSEPR

_MODEL

VSEPR

_MODEL

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VSEPR

MODEL

VSEPR

_MODEL

VSEPR

_MODEL

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Formal Charge

• Consider:

• For

C

:

• _{There are 4 valence electrons (from periodic table).}

• _{In the Lewis structure there are 2 nonbonding electrons and 3 from the triple} bond. There are 5 electrons from the Lewis structure.

• _{Formal charge: 4 - 5 = -1.}

• For

N

:

• _{There are 5 valence electrons.}

• _{In the Lewis structure there are 2 nonbonding electrons and 3 from the} _triple bond. There are 5 electrons from the Lewis structure.

• _{Formal charge = 5 - 5 = 0.}

C

N

C

N

DRAWING LEWIS

STRUCTURE

DRAWING LEWIS

_STRUCTURE

DRAWING LEWIS

_STRUCTURE

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Linus Pauling stated valence bond theory

Overlap of Atomic Orbitals

The sharing of electrons between atoms is viewed as an overlap

of atomic orbitals of the bonding atoms.

VALENCE BOND

THEORY

VALENCE BOND

_THEORY

VALENCE BOND

_THEORY

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When H – H distance = 74 pm, Repulsion = Attraction

 strongest bond

 optimal overlap

 lowest energy

74 pm

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At H – H distance > 74 pm, Repulsion < Attraction

 weaker bond

 too little overlap

 atoms come closer

74 pm

> 74 pm

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At H – H distance < 74 pm, Repulsion > Attraction

 weaker bond

 too much overlap

 atoms get further apart

74 pm

< 74 pm

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Because of orbital overlap, the bonding electrons

localize

in the region between the bonding nuclei

such that

There is a

high probability

of finding the electrons in the

region between the bonding nuclei.

Overlap of two

half-filled

orbitals leads to the formation

of a covalent bond.

1s



1s



1s-1s overlap gives a H – H single bond

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(50)



1s

H

_F

_

2s

2p



1s-2p overlap gives a H – F single bond

F

_

2s

2p



1s

H

Non-bonding electrons

22

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(51)

F

_

2s

2p



Non-bonding electrons

F

_

2s

2p



Each F atom has three pairs of non-bonding electrons

F

_

2s

2p



_F

_

2s

2p



The 2p-2p overlap gives a F – F single bond

22

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S

a

m

ple

fo

o

te

(52)

Each O atom has two pairs of non-bonding electrons

O

_

_

2s

2p



O

_

_

2s

2p



Non-bonding electrons

O

_

_

2s

2p



O

_

_

2s

2p



Identify the non-bonding electrons in O

₂

molecules

Two 2p-2p overlaps give a O=O double bond

22

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(53)

O

Represented by an arrow



pointing from the electron

pair

donor

to the electron pair

acceptor

.

N H

H

+

N

H

Overlap of an

empty orbital

with a

fully-filled orbital

leads to the formation of a

co-ordinate covalent bond

or

dative bond

N O

O O

F

₃

B

₊

NH

₃

F

₃

B NH

₃

22

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a

m

ple

fo

o

te

(54)

By VB

Theory

N





2s

2p



_3H



_H

+

1s

(a) NH

₄₄++

By Lewis model, the structure is

4 single bonds are formed, one of them is a dative bond

N H

H

INTERTRETATION OF THE FORMATION OF

COVALENT BONDS IN TERMS OF VALENCE

BOND THEORY

INTERTRETATION OF THE FORMATION OF

COVALENT BONDS IN TERMS OF VALENCE

BOND THEORY

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By VB Theory

One 2s(fully-filled)-1s(vacant) overlap

leads to the

formation of one N



H dative bond.

N





2s

2p



_3H



_H

+

1s

N H

H

+

N

H

N

H

Three 2p-1s(half-filled) overlaps

lead to the

formation of three N – H single bonds.

22 S_ep

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(56)

By VB Theory

C



Only 2 single bonds can be formed



Promotion of a 2s electron to a 2p orbital





2s

2p

C*

_

2s

2p



(b) HCN

By Lewis model, the structure is H-C



N



one H-C single bond and

one C



N triple bond.

22

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a

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fo

o

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(57)



The 2s electrons on N are non-bonding

electrons



The energy released by forming a stronger triple bond

outweighs

the

energy required for promoting an electron from a 2s orbital to a 2p

orbital.

C*



2s

2p



N





2s

2p



H



1s

H

C

N

C*



2s

2p



N





2s

2p



H



1s



**The overlap of one orbital (?) of C* with an 1s orbital of H**

gives the

C-H single bond

.



**Overlaps of three orbitals (???) of C* with three 2p**

orbitals of N

give the

C



N triple bond

.

(58)

(c) SO

₂

By Lewis model, the three possible structures are

O



S=O, O=S



O, O=S=O

Most stable



no separation of opposite formal charges

By VB Theory



Only two single bonds can be formed



One 3p electron has to be promoted to a 3d orbital



Expansion of Octet

S





3s

3p



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a

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fo

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(59)

By VB Theory

S





3s

3p



S*

_

_

3s

3p



3d

octet expansion

The energy released by forming of two stronger double

bonds

outweighs

the energy required for promoting an

electron from a 3p orbital to a 3d orbital.

22

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fo

o

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(60)



**Overlaps of two half-filled orbitals (??) of S* with two half-filled 2p**

orbitals of an oxygen atom give a S=O double bond.



A total of two S=O bonds are formed with two O atoms

2O

_

_

2s

2p



S*

_

_

3s

3p



3d

O

S

O

2O





2s

2p



S*





3s

3p



3d

O

S

O

Non-bonding electrons: S* 3s

2

; O 2s

2

and 2p

2

22

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a

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fo

o

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(61)

According to VB theory, the two less stable structures of SO

₂

,

O



S=O and O=S



O do

‘

exist’

.

Each of these structures contributes in certain extent to the real

structure of SO

₂

.

If represents the wave function of the real structure

of SO

₂

SO

molecules, then

2



O S O O

S O O

S O

SO



a



 



b



 



c



 



2

where



_O__S__O



_O__S__O



_O__S__O

are the wave functions of the three possible structures and

a > b = c > 0

THE CONCEPT OF

RESONANCE

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(62)

S





3s

3p



O





2s

2p



O*



2s

2p

A S=O double bond is formed by

3p(half-filled)-2p(half-filled)

overlaps between S and O.

O=S



O

In other words, the real structure of SO

₂

is the

resonance hydrid

of the three possible structures.

O=S=O



O



S=O



O=S



O

More contribution

Less contribution

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(63)

S





3s

3p



O





2s

2p



_O*



2s

2p

O=S



O

A O



S dative bond is formed by

3p(fully-filled)-2p(empty)

overlap between S and O*

Formation of dative bond is

not favourable because the two

unpaired 2p electrons in O are forced to pair up to give O*

O





2s

2p



_O*



2s

2p

S





3s

3p



O=S



O

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a

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fo

o

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(64)

By VB

Theory

Only two S-F single bonds can be formed by 3p-2p overlaps

between one S atom and two F atoms



SF

₂

is formed.

S





3s

3p



_F



2s

2p



F-S-F

(d) SF

₂

, SF

₄

, SF

₆

To form four S-F single bonds in SF

₄

, a 3p electron in S has to be

promoted to a 3d orbital.

S*

_

_

3s

3p



3d

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a

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fo

o

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(65)

By VB

Theory

To form six S-F single bonds in SF

₆

**, a 3s electron in S* has to be**

promoted to a 3d orbital.

S**

_

3s

3p



3d



S

F

S

F

The energy released by forming more single bonds outweighs the

energy required for promoting 3s and 3p electrons to 3d orbitals.

S





3s

3p



22

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(66)

By VB Theory

To form two Xe-F bonds in XeF

₂

, a 5p electron in Xe has to be

promoted to a 5d orbital.

Xe



5s

5p



_F



2s

2p



Xe*

_

5s

5p



5d

(e) XeF

₂

, XeF

₄

, XeF

₆

F-Xe-F

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(67)

By VB Theory

To form four Xe-F bonds in XeF

₄

**, a 5p electron in Xe* has to be**

promoted to a 5d orbital.

Xe*

_

5s

5p



5d

Xe**

_

_

5s

5p



5d



Xe

F

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(68)

By VB Theory

To form six Xe-F bonds in XeF

₆

, a 5p electron in Xe has to be**

promoted to a 5d orbital.

Xe**

_

_

5s

5p



5d



Xe***

_

_

5s

5p



5d



Xe

F

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(69)

By VB Theory

Xe**

_

_

5s

5p



5d



Xe***

_

_

5s

5p



5d



The energy released by forming more single bonds outweighs

the energy required for promoting 5p electrons to 5d orbitals.

22

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a

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fo

o

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(70)

The localized models for bonding we have examined (Lewis and VBT)

assume that all electrons are restricted to specific bonds between atoms or

in “lone pairs”. In contrast, the delocalized approach to bonding places the

electrons in Molecular Orbitals (MO’s) - orbitals that encompass the entire

molecule and are not associated with any particular bond between two

atoms. In most cases, MO theory provides us with a more accurate picture

of the electronic structure of molecules and it gives us more information

about their chemistry (reactivity).

Two (sp-1s) Be-H  bonds.

Be H

H

sp 1s Localized Bonding ₁ ₂ Delocalized Bonding

MO diagram for BeH₂

The two  bonding MO’s in

BeH₂

THE DELOCALIZED APPROACH TO BONDING:

MOLECULAR ORBITAL THEORY

THE DELOCALIZED APPROACH TO BONDING:

MOLECULAR ORBITAL THEORY

(71)

Molecular orbitals are constructed from the available atomic orbitals in a molecule. This is done in a manner similar to the way we made hybrid orbitals from atomic orbitals in VBT. That is, we will make the MO’s for a molecule from Linear

Combinations of Atomic Orbitals (LCAO). In contrast to VBT, in MO theory the atomic orbitals will come from several or all of the atoms in the molecule. Once we have constructed the MO’s, we can build an MO diagram (an energy level diagram) for the molecule and fill the MO’s with electrons using the Aufbau principle.

Some basic rules for making MO’s using the LCAO method:

1) n atomic orbitals must produce n molecular orbitals

(e.g. 8 AO’s must produce 8 MO’s)

.

2) To combine, the atomic orbitals must be of the appropriate symmetry.

3) To combine, the atomic orbitals must be of similar energy.

4) Each MO must be normal and must be orthogonal to every other MO.

+

₁

H 1s Be 2s H 1s

MOLECULAR ORBITAL

THEORY

MOLECULAR ORBITAL

_THEORY

MOLECULAR ORBITAL

_THEORY

₂₂

S

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(72)

This produces an MO over the molecule with a node between the atoms (it is also symmetrical about the H-H axis). This is known as an

antibonding MO and is given the label _u* because of its symmetry. The star indicates antibonding.

Diatomic molecules: The bonding in H

₂

H

A

H

B

Each H atom has only a 1s orbital, so to obtain MO’s for the H

₂

molecule,

we must make linear combinations of these two 1s orbitals.

Consider the addition of the two 1s functions (with the same phase):

1s

_A

1s

_B

+

This produces an MO around both H atoms and has the same phase everywhere and is symmetrical about the H-H axis. This is known as a

bonding MO and is given the label _g because of its

symmetry.

Consider the subtraction of the two 1s functions (with the same phase):

1s

_A

1s

_B

-Remember that:

-

is equivalent to:

+



_g

=



0.5 (1s

_A

+ 1s

_B

)



_u

* =



0.5 (1s

_A

- 1s

_B

)

MOLECULAR ORBITAL

THEORY

MOLECULAR ORBITAL

_THEORY

MOLECULAR ORBITAL

_THEORY

₂₂

(73)

Diatomic molecules: The bonding in H

₂

H

A

H

B You may ask … Why is _g called “bonding” and _u* “antibonding”? What does this mean? How do you know the relative energy ordering of these MO’s?

Remember that each 1s orbital is an atomic wavefunction (_1s) and each MO is also a wave function,



, so we can also write LCAO’s like this:

Remember that the square of a wavefunction gives us a probability density function, so the density functions for each MO are:

_g =



₁ = 0.5 (_1sA + _1sB) u* =



2 = 0.5 (1sA - 1sB)

(₁)2_{= 0.5 [(}

1sA 1sA) + 2(1sA 1sB) +(1sB 1sB)]

(₂)2_{= 0.5 [(}

1sA 1sA) - 2(1sA 1sB) +(1sB 1sB)]

and

The only difference between the two probablility functions is in the cross term (in bold), which is attributable to the kind and amount of overlap between the two 1s atomic

wavefunctions (the integral (_1sA_1sB)  is known as the “overlap integral”, S). In-phase overlap makes bonding orbitals and out-of-phase overlap makes antibonding

orbitals…why?

MOLECULAR ORBITAL

THEORY

MOLECULAR ORBITAL

_THEORY

MOLECULAR ORBITAL

_THEORY

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(₁)2_{= 0.5 [(}

1sA 1sA) + 2(1sA 1sB) +(1sB 1sB)]

(₂)2_{= 0.5 [(}

1sA 1sA) - 2(1sA 1sB) +(1sB 1sB)]

Diatomic molecules: The bonding in H

₂

H

A

H

B

Consider the electron density between the two nuclei: the red curve is the probability density for H_A by itself, the blue curve is for H_B by itself and the brown curve is the density you would get for _1sA + _1sB without any overlap: it is just (_1sA)2_{+ (}

1sB)2 {the

factor of ½ is to put it on the same scale as the normalized functions}.

The increase of electron density between the nuclei from the in-phase overlap reduces the amount of repulsion between the positive charges. This means that a bonding MO will be lower in energy (more stable) than the corresponding antibonding MO or two non-bonded H atoms.

The function (₁)2_{is shown in}_green

and has an extra + 2 (_1sA_1sB) of electron density than the situation where overlap is neglected.

The function (₂)2_{is shown in}_pink

and has less electron density between the nuclei {- 2(_1sA_1sB)} than the situation where overlap is neglected.

MOLECULAR ORBITAL

THEORY

MOLECULAR ORBITAL

_THEORY

MOLECULAR ORBITAL

_THEORY

(75)

Diatomic molecules: The bonding in H

₂

H

A

H

B So now that we know that the  bonding MO is more stable than the atoms by themselves and the _u* antibonding MO, we can construct the MO diagram.

H E ne rg y H H₂ 1s 1s _g _u*

To clearly identify the symmetry of the different MO’s, we add the appropriate subscripts g (symmetric with respect to the inversion center) and u

(anti-symmetric with respect to the inversion center) to the labels of each MO.

The electrons are then added to the MO diagram using the Aufbau principle.

Note:

The amount of stabilization of the _g MO (indicated by the red arrow) is slightly less than the amount of destabilization of the _u* MO (indicated by the blue arrow) because of the pairing of the electrons. For H₂, the stabilization energy is 432 kJ/mol and the bond

order is 1.

B o n d O r d e r = ( # o f e ' s i n b o n d i n g M O ' s ) - ( # o f e ' s i n a n t i b o n d i n g M O ' s ) 2

-

-MOLECULAR ORBITAL

MOLECULAR ORBITAL

THEORY

MOLECULAR ORBITAL

_THEORY

MOLECULAR ORBITAL

_THEORY

(76)

Diatomic molecules: The bonding in He

₂

He also has only 1s AO, so the MO diagram for the molecule He₂ can be formed in an identical way, except that there are two electrons in the 1s AO on He.

He E ne rg y He He₂ 1s 1s _g _u*

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

of the electronic structure of any hypothetical molecule that we can

imagine.

The bond order in He₂ is (2-2)/2 = 0, so the molecule will not exist.

However the cation [He₂]+_{, in which one}

of the electrons in the _u* MO is

removed, would have a bond order of (2-1)/2 = ½, so such a cation might be predicted to exist. The electron

configuration for this cation can be written in the same way as we write those for atoms except with the MO labels replacing the AO labels:

CHEMICAL BONDING

MODULE-II