Chem 373- Lecture 26: Homonuclear Diatomic Molecules-I

8/3/2019 Chem 373- Lecture 26: Homonuclear Diatomic Molecules-I

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Lecture 26: Homonuclear Diatomic Molecules-I

The material in this lecture covers the following in Atkins.

14 Molecular structure

Molecular Orbital Theory

14.5 The structure of diatomic molecules

(b) bond order

(c) Period 2 diatomic molecules

(d) p-orbitals(e) The overlap integral

Lecture on-lineHomonuclear diatomic molecules (PowerPoint)

Homonuclear diatomic molecules (PDF) Handout for this lecture


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Audio-visuals on-lineShape of molecular orbitals in homonuclear diatomic molecules

(PowerPoint)(From the Wilson Group,***)

Shape of molecular orbitals in homonuclear diatomic molecules(PDF)(From the Wilson Group,***)

Composition of orbitals in homonuclear molecules

(6 MB MBQuick-Time with music)

(A must from the Wilson Group,*****)The Occupation of homonuclear diatomic orbitals

(PowerPoint)(From the Wilson Group,***)

The Occupation of homonuclear diatomic orbitals(PDF)

(From the Wilson Group,***)


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Molecular Orbital Theory Diatomics

Molecular Orbital Theory

We used the orbitals of theone - electron hydrogen to build up

wavefunctions for many - electron

atoms

e shall use the orbitals of

he one - electron H moleculeo describe diatomic molecules

2+

The molecular orbitals are

written as linear combinations

of atomic orbitals

The atomic orbitals are in general those centered on

the atoms of our molecule


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DiatomicsMolecular Orbital Theory

For H we have one 1s orbital on each

hydrogen : 1s (1) = A(1); and 1s (1) = B(1)2 H

A B

With Ee

R

E eR

o

o

energies : EJ+K

(1+S)

E J -K(1- S)

1sH

1sH

+

= +

= +

2

2

4

1

4

1

From these we can form two different molecular orbitals :

+ = + +( ) ( ) [ ( ) ( )]1

1

2 11 1

S A B

=

( )

( )[ ( ) ( )]1

1

2 11 1

SA B

E1sH

H2+


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E1sH

The H2 molecule has two electrons. They

will be in the bonding 1 orbital

H2


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The ground electronicconfiguration of the

hypothetical four-electron

molecule He2 has two

bonding electrons andtwo antibonding electrons.

It has a higher energy

than the separated atoms,

and so is unstable.

The He2 molecule has fourelectrons. They will be in the

bonding 1 orbital and in the

anti - bonding 2 orbital :

1 2

*

( *)2 2

The

n n

bond order is :

b =1

2( )*

n occupied= bonding orb

n occupied* = anti - bonding orb

He2


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2s 2s

In second row elements

we have both 2s and 2p

orbitalsThe 2s orbitals can

form strong overlaps

with each other2p 2p

Weorbitalsalso have two ppointing along

the A -B bond vector

They can overlap with

each other And with 2s

These are the - orbitals, they do not change

sign with rotation around A -B vector

S dvA B=

Second row


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2s 2s

2p 2p

We finally have twosets of p - orbitals

perpendicular to the

A -B bond

vector

They can overlap with

each other in pairs

and

These are the - orbitals, they change

sign with rotation of 180 around A -B vector

S dvA B=


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2s 2s

2p 2p

The - and - orbitalsdo not overlap

S = 0

S = 0

S = 0

S = 0

In all cases positive

and negative contributions

cancel

S dvA B= positive

negative


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Molecular Orbital Theory Diatomics(a) When two orbitals are on

atoms that are far apart, thewavefunctions are small where

they overlap, so Sis small.

(b) When the atoms are closer,

both orbitals have significant

amplitudes where they overlap,

and Smay approach 1. Notethat Swill decrease again as

the two atoms approach more

closely than shown here,

because the region of negativeamplitude of thep orbital starts

to overlap the positive overlap

of the s orbital. When the centres

of the atoms coincide, S= 0.


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The overlap integral, S,

between two H1s orbitals

as a function of their

separation R.


Overlap is 1 when functionscoinside

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Data 1

Zero at infinite

separation


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Molecular Orbital TheoryDiatomics

Consider two orbitals

and on nuclei A and B

of the same energy :

AA

o

A B

o o

+ = ++1

2 1( )[ ]

SABA B

Ee

Ro+= +

o AB

J+K

(1+ S )

2

4

1

They will interact to

form a bonding

orbital of energy E+ +

And the anti - bondingorbital of energy E- -

=

1

2 1( )[ ]

SABA B

Ee

Ro = + o AB

J - K

(1- S )

2

4

1

The interaction intergral K

will be proportional to SAB.

K ~ SAB = A Bdv


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According to molecular orbital theory, orbitals

are built from all orbitals that have the appropriate symmetry.In homonuclear diatomic molecules of Period 2, that means

that two 2s and two 2pzorbitals should be used. From these

four orbitals, four molecular orbitals can be built.

2s 2s

2p 2p


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From two 2s orbitals and two

2p orbitals we can form 4

molecular orbitals :

1 21

21

21

21

2 2

2 2

= +

+ +

c s c s

c p c p

sA A sB B

P PA BA B

2 2

2

2

2

22

22

2 22 2

= ++ +

c s c sc p c p

sA A sB B

P PA BA B

3 23

23

23

23

2 2

2 2

= +

+ +

c s c s

c p c p

sA A sB B

P PA BA B

4 24

24

24

24

2 2

2 2

= +

+ +

c s c s

c p c p

sA A sB B

P PA BA B

2s

2s

2p 2p

1

2

3

4


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To a first approximation

2s and 2p are separated

sufficiently in energy so that :

1 21

212 2= +c s c ssA A sB B

2 22

222 2= +c s c ssA A sB B

We can form two orbitalsmade up of 2s

and two orbitals

made up of 2p

2s 2s

1

2

2p 2p

3

4

3 23

232 2= +c p c pP PA BA B

4 24

24



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Molecular Orbital TheoryDiatomics

A representation of the

composition of bondingand antibonding orbitals

built from the overlap ofp

orbitals. These illustrations

are schematic.

2p 2p

3

4

anti bondingbonding

4 24

242 2= +c p c pP PA BA B 3 2


31

2 12 2=

++

( )[ ]

Sp pA B

Or from symmetry Or from symmetry

41

2 12 2=

( )[ ]

Sp pA B


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2px 2px1x

2x 2py 2py

1y

2y

We also have two p - orbitals perpendicularto the bond - vector

They will form the - orbitals :

1 12 1

2 2

x xA xBS

p p=+

+( )

[ ]

21

2 1

2 2

*

( )

[ ]x xA xBS

p p=

11

2 1 2 2 y yA yBS p p= + +( ) [ ]

21

2 1

2 2

*

( )

[ ]y yA yB

S

p p=


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A schematic

representationof the structure of bonding and

antibondingmolecular orbitals.

orbitals do not change sign onrotation arounf A -B bond vector

orbitals change sign once on

rotation around A -B bond vector


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For oxygen and flourine

where 2p and 2s are well

separated we get

the orbital diagram


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What you must learn from this lecture

. Understand the difference between bonding

and anti - bonding orbitals in diatomic molecules2. Understand the difference between constructiveinterferrence (in bonding orbitals) and destructiveinterferrence in (anti - bonding) orbitals

3. Understand the difference between - orbitalswith complete rotational symmetry around bondvector and - orbitals that change sign on 180rotation.

4. Be able to construct qualitatively themolecular orbitals of the homonucleardiatomic molecules as a linear combinationof atomic orbitals

5. Be able to deduce the bond order for a diatomicmolecule from its electronic configuration

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Chem 373- Lecture 26: Homonuclear Diatomic Molecules-I