Chem 373- Lecture 31: Polyatomic Molecules

8/3/2019 Chem 373- Lecture 31: Polyatomic Molecules

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Lecture 31: Polyatomic Molecules

A course evaluation is scheduled for the last 20

minutes of the lecture on Monday March 27

The material in this lecture covers the following in Atkins.

14 Molecular orbitals for polyatomic systems

14.8 Walsh diagrams

(a) The Walsh diagram for H2X

Lecture on-line

Polyatomic Molecules (PowerPoint)Polyatomic Molecules (PDF)

Handouts for this lecture


2/21

C H WS

i = 1,n k = 1,n

k ik ikk=1

k=n = 0

i

ik k

k=1

k=nC p

k = 1,n ; i = 1,n

=

Polyatomic MoleculesWe shall in the following

develop a simplified modelfor AH and AH moleculesbased on molecular orbitaltheory

2 3

A

H H

H

A

H

H

A key point will be to understandhow the optimal bond anglechanges with the number of

valence electronsBeH H

=180

Se

H H

=90

We shall be using linearvariation theory to calculateenergies

..express molecularorbitals as a linearcombination of atomicorbitals (LCAO)


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Polyatomic MoleculesAH2

H1H2

1sA

H1H2

2sA

H1H2

2pb2

1H2

2pb1

A

1sH1

The atomic orbitals are :

A

1sH2

The 1s and 2s are toolow in energy to participate

in the bonding with 1s(core orbitals). They will go

unchanged from A over intoAH each holding 2 electrons

A A

H

2

H1 H2

2pa1

This is a simplification(approximation)

in the case of 2sA


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H1H2

2pb2

1H2

2pb1

A

1sH1


A

1sH2

The molecular orbitalswill be linear combinationsof atomic orbitals.

Only atomic orbitalson different centersthat overlap will mix

To make use of this

we make two newcombinations of thehydrogen 1s orbitals

A

1sa1

A

1sb2

H1 H2

2pa1


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H1 H2

2pb2

1H2

2pb1


A

1sa1

A

1sb2

H1

H2

2pa1

Inspection indicates that2p will overlap (interact)

with 1s

a

a

1

1

1sH(a1)

2pa1

A

1sb2

2pb2

2p with 1sb2 b2

2p will not interactb1


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Heteronuclear diatomic molecules Linear variation theory

A

B

E

+

E

+ = ++ +

C CA A B B

- = + C CA A B B

This is an in - phasebonding orbital withthe largest contributionfrom of lowest energyA

This is an out - of-phase anti - bondingorbital withthe largestcontribution from

of highest energy

B


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The interaction between 2p

and 1s will give rise toa

a

1

1

A

1sa1H1H2

2pa1

2a1

..anti - bondingorbital 2a1

..bondingorbital 1a 1

1a1

1a a a1 1 1p s= +1

2

21

2

1

2a a a1 1 1p s= +1

22

1

21

The orbital energies are :

1a1 = + o cos( / )2

2a1= o cos( / )2

The interaction large forsmall . It is zero for = 180


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A

1sb2

H1H2

2pb2


The interaction between 2pand 1s will give rise to

b

b2

2

A

1b2

..anti - bondingorbital 2b2..bondingorbital 1b 2

A

2b2

1b b b2 2p s= +1

2

21

2

12

2b b b2 2p s= +1

22

1

21 2

The orbital energies are :

1b2 = + o sin( / )2

2b22= o sin( / )

The interaction small forsmall . It is max. for = 180


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1b2= + o sin( / )2

1a1= + o cos( / )2


Correlation diagram AH2BeH2 and BH2+

Configuration (1b2)2

= 180 H A H

BH , AlH (1b a2 2 2 1) ( )2 11

BH 131 127

AlH 120 127

exp theor

2

2

A

1b2

A

2b2

2a1

1a1

180 90

H1

H2

1b1

A

1b2

H1 H2

1b1

1a1

2a1

A

2 b 2


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1b2= + o sin( / )2

1a1= + o cos( / )2


Correlation diagram AH2

SiH BH (1b a2 2- 2 1, ) ( )2 21

SiH 92 90

BH 102 90

exp

2

2-

Theor

Configuration (1b a b2 12

1) ( )2 1 1

NH PH AsH92 91

H O CH H

99 93

2 2 2

2+

2-

2+

exp

exp

103

111

SS

tthheeoorr = 90

A

1b2

A

2b2

2a1

1a1

180 90

H1 H2

1b1

A

1b2

H1 H2

1b1

1a1

2a1

A2 b 2


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1b2= + o sin( / )2

1a1 = + o cos( / )2

Polyatomic Molecules AH2Correlation diagram AH 2

Configuration (1b a b2 12

1) ( )2 1 1

tthheeoorr

= 90

OH SH SeH92 91

H F NH104

2 2 2

2 + 2-

exp

exp

105

118

Excited statesAH Config

NH (1b a b 144 127

PH (1b a b 123 127

CH (1b a b 136 127

SiH (1b a b 123 127

2 exp theo

2 2 11

1

2 2 1 1 1

2 2 11

1

2 2 1

1

1

) ( )

) ( )

) ( )

) ( )

2 2

2 2

2 1

2 1

1 1

1 1

1 1

1 1

A

1b2

A

2b2

2a1

1a1

180 90

H1 H2

1b1

A

1b2

H1 H2

1b1

1a1

2a1

A2 b 2


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A

1b2

A

2b2

2a1

1a1

180 90

H1 H2

1b1

A

1b2

H1 H2

1b1

1a1

2a1

A

2 b2


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Polyatomic Molecules

=120

trigonal planar

AH3

=10990trigonal pyramidal


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2pa2pex 2pey

1sa 1sex 1sey

Polyatomic Molecules AH3


Interactions are possible

between (2p 1s(2p 1s ; (2p 1s

a aex ex ey ey

, );, ) , )


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120 90

1a

2a

1ex

2ex

1ey

2ey

2a

1a

2ex

1ex

1ey

2ey

Polyatomic Molecules AH3

BH AlH : (1e)

;3 3

4

theo exp

;

= =120 120

(1e)AH

CH 120 109SiH 110 109

PH 113 109

4

3 exp theo

3

33+

1 1aa

(1e)

AHNH 108 90PH 93 90AsH 92 90

SbH 91 90

4

3 exp theo3

3

3

3

1 2aa


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Polyatomic Molecules The fragment approach

Organic molecules are made up of sp,sp and sp carbon centers2 3

H

C C

C

C

H

sp3 hybrides

sp2 hybrides

sp hybrides


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Alternatively, organic molecules are made upof CR (sp),CR ( sp ) and CR (sp ) fragments2

23

3

H

C C

C

C

H

H C

1

1x 1y 2

bonds

bond


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23

3

H

C C

C

C

H

bonds

bond

b2

1a1

1b1


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23

3

H

C C

C

C

H

bond

1a1

1ex 1ey


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What you must learn from this lecture

1. For EH (n = 2,3) you must be able to constructthe molecular orbitals as linear combinations ofthe p - orbitals on the main - group element Eand linear combinations of the 1s orbitals on

hydrogen

n

2. Be able to account for the variation in

the orbital energies of EH a functionof the HEH bond angle, and its influenceon the structure of EH as a function of thenumber of valence electrons.

n

n

as

3. Be able to account for the bonding inorganic hydrocarbons in terms of thefrontier orbitals of CR, CR , and CR2 3

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Chem 373- Lecture 31: Polyatomic Molecules