chem 373- lecture 35: symmetry groups

8/3/2019 Chem 373- Lecture 35: Symmetry Groups

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Lecture 35: Symmetry Groups

The material in this lecture covers the following in Atkins.

15 Molecular Symmetry

15.2 Symmetry classification of molecules(d) The groups Sn

(e) The cubic groups

(f) The full rotation group

15.3 Some immediate consequences of symmetry

(a) Polarity

(b)Chirality

Lecture on-line

Symmetry Groups (PowerPoint)

Symmetry Groups (PDF)

Handout for this lecture


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The Symmetry Classification of Molecules Sn

S4

Posesses the inproper rotation axis Sn

S C S

S C

4 2 43

42

2

: , ,S4

=

S2 same as Ci

HO H

COOH

OHHOOC

H

Meso-tartaric

acid

S4 S6S8

C C i S S3 32

65

6, , , ,S C S C

S C S

2 4 83

2

85

43

87

; ; ,

, ,


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The Symmetry Classification of Molecules Cubic groups

These groups have more than one principle axis

C3

C3

C3

C3Td

C2 S4

d


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S4


F

SF F

FF

F

Oh

C4

C3d S6

C2


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The relation of an icosahedron

to a cube.The buckminsterfullerene

molecule (15)

is related to this objectby cutting

off each apex to form a

regular pentagon.


I

C5

C3


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Shapes corresponding to the point

groups (a) T.

The presence of thewindmill-like structures

reduces the

symmetry of the object from Td.

C3

C2

T


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Shapes corresponding to the

point groups (b) O.

The presence of the windmill-like

structures reduces the

symmetry of the object from Oh.

O

C4

C2

C3


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Th

The shape of an object

belonging to the group Th.


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Molecule

Linear ?

i ?ND h C v

N

Twoor morec

nn>2 ?

i ?

Td

N

C5 NIn Oh

N

The SymmetryClassificationof Molecules

C O

N N

C ON N


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n ?

N

N

?

Ni?

s

i 1

Select C withhighest n; than,

are the nC

to C ?

n

2

n

perpendicular

NY

The SymmetryClassification

of MoleculesI

F

ClBr

HO H

COOH

OH

HOOC

H

Meso-tartaricacid

N

Quinoline

N

Quinoline

I

F

ClBr

HO H

COOH

OH

HOOC

H

Meso-tartaricacid


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n ?

N

N

?

Ni?

s

i 1

N

h ?Dnh

Y

Y

N

n d ?YDnd N Dn


of Molecules


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C v3NH3

n ?

N

Select C withhighest n; than,

are the nC

to C ?

n

2

n

perpendicular

N


N

h

?Cnh

n v ?CnvS n2 ?

N

S n2

CnB

O

OO

H

H

H

B(OH)3S4

O O

H H

C2

H2O2


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(a) A molecule with a

Cn axis cannot have a dipole

perpendicular to the axis,


Dipole moments

(but (b) it may have one

parallel to theaxis.

The arrows represent local contributions to the overall

electric dipole, such as may arise from bonds between pairs of

neighbouring atoms with different electronegativities.

r s s s

= ( )r rdr


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of Molecules

Dipole moments

I

F

ClBr

HO H

COOH

OH

HOOC

H

Meso-tartaricacid

N

Quinoline

O O

H H

C2

H2O2

C

C

Cl H

H Cl

Trans CHCl=CHCl

B

O

OO

H

H

H

B(OH)3

0 = 0

inversion

0

in plane

= 0

hsymmetry

0along C2

0

along C2

0

along C3 = 0inversion


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of Molecules

Chirality

A chiral molecule is a moleculethat can not be superimposed

on its mirror image

O O

H H

C2

O O

H H

C2

HOOH Mirror image

Canaxis

only contain a Cn

COOH

H2N H

H

Not chiral

COOH

H2N H

CH3

chiral


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A mathematical group, G = {G,}, consists of a set of

elements G = {E, A,B,C,D,....}

A binary relation, called group multiplication is defined such

That:

(a) The product of any two elements A and B in the group

is another element in the group, i.e., we write AB G.

(b) If A, B, C are any three elements in the group then(AB)C = A(BC). Therefore, group multiplication

is associative, and frequently, we omit the brackets.

Groups and group multiplications


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(c) There is a unique element E in G such that

EA=AE=A, for every element A in G.

The element E is called the identity element.

(d) For every element A in G, there is a unique element X in G

, such that XA = AX = E.

The element X is referred to as the inverse of A and is denoted A-1.



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x

y

z

ClCl

C

H

A B

A BH

A B

AB

B

AB

A

H

C

Cl Cl

HH

C2

ClCl

H

C

C

ClClA B

A BHH

C

ClClB

ABHH

A

(yz)

A B

A B

B

B

A

C

ClCl

HH

C

ClCl

HH

(xz)A



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A B

A B

B

B

A

AHH

(xz)C2

H

C

H

C

ClCl ClCl

x

y

z

ClCl

C

H

A B

A BH

(yz)

A B

A B

B

B

A

C

ClCl

HH

C

ClCl

HHA

(yz)(xz)

C2

C

ClClA B

A B

ClCl B

B

A

AHH

(yz)C2

H

C

H

(xz)


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C2v E C2 (xz) (yz)

E E C2 (xz) (yz)

C2 C2 E (yz) (xz)

(xz) (xz) (yz) E C2

(yz) (yz) (xz) C2 E


This table contains all theinformation

about the group and its

structure.

The name of this molecular

point group is C2v.

There are some observations to

makeabout this table.

1. In each row and each column,each operation appears once

and only once

(2) We can identify smaller

groups within the larger one.

For example, {E,C2} is a group.

There are two others;what are they?

(3) In this particular table, we

observe that the group productis commutative.

This is not necessarily true for

other groups.


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Diatomics

The parity of an orbital is even (g) if its wavefunction

is unchanged under inversion in the centre of symmetry

of the molecule, but odd (u) if the wavefunction changes sign.

Heteronuclear diatomic molecules do not have a centre ofinversion, so for them the g,u classification is irrelevant.

Parity of orbitals

The Symmetry

Classification

of orbitals


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Diatomics

The parity of an orbital is even (g) if its wavefunction

is unchanged under inversion in the centre of symmetry

of the molecule, but odd (u) if the wavefunction changes sign.

Heteronuclear diatomic molecules do not have a centre of

inversion, so for them the g,u classification is irrelevant.

Parity of orbitals

The Symmetry

Classification

of orbitals


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Diatomics

The in a term symbol refers

to the symmetry of an orbital

when it is reflected in a plane

containing the two nuclei.

g

= 1

= 1

Reflection index

u

u

g

= 1

u g

= 1

The Symmetry

Classification

of orbitals


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In the language introduced in the next lecture, the

characters of the C2 rotation are +1 and -1 for the and

orbitals, respectively.

A rotation through 180

about the internuclear axis

leaves the sign of a orbital

unchanged

but the sign of a orbital is

changed.

The Symmetry

Classification

of orbitals


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What you should learn from this lecture

1. For a given molecule be able to identify all the symmetry

elements

2. From the list of elements be able to identify the point groupUsing a provided flow chart similar to that given by Atkins


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of Molecules

Dipole moments

O

H H

Water has local dipoles alongeach bond

+

+

r

OH1

r

OH2

Or

O

H H

r

OHx2

r

OH

y2

They can be decomposedinto x and y components

r

OH

x

1

r

OH

y1

x

y

The

and are

OH

OH

x

x

components

equal in

magnetudebut opposite in sign as

they are related by arotation around C2

r

r

1

2

O

H H

C2

r

OHx1

C2

=r

OHx2

Only dipole alongprinciple axis possible

chem 373- lecture 35: symmetry groups

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