chem 373- lecture 34: symmetry elements

8/3/2019 Chem 373- Lecture 34: Symmetry Elements

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Lecture 34: Symmetry Elements

The material in this lecture covers the following in

Atkins.

15 Molecular SymmetryThe symmetry elements of objects

15.1 Operations and symmetry elements

15.2 Symmetry classification of molecules

(a) The groups C1,Ci, and Cs

(b) The groups Cn,Cnv, and Cnh

(c) The groups Dn,Dnh, and Dnd

Lecture on-lineSymmetry Elements (PowerPoint)

Symmetry Elements (PDF)

Handout for this lecture



Some of the symmetry elements of a cube.The twofold, threefold, and fourfold axes

are labelled with the conventional symbols.

Symmetry elements

The systematic discussion ofsymmetry is calledSome objects are moresymmetrical than others

Any rotation of spherearound axis throughcenter brings sphere

over into itself Only some rotations of spherebrings cube into itself



(b) an H2O

molecule has a twofold (C2) axis.

Both have other symmetry

elements too.

Symmetry elements

(a) An NH3 molecule has a

threefold (C3) axis

NHO

3 has more rotationsymmetry than H

2



Operators Symmetryand elements

The classification of objects according tosymmetry elements corrsponding tooperations that leave at least one commonpoint unchanged gives rise to the :

There are five kinds of symmetryoperations and correspondingsymmetry elements

I

F

Cl

Br

1. The identity E Consists of doing nothing

Only element for CFClBrI




(b) an H2Omolecule has a twofold (C2) axis.C and C3 3-1

C6

C ; C ; C

and C ; C

6 3 2

6-1

3-1

C5The principle rotation axis

is the axis of the higest fold




The OH moleculehas two mirror

planes. They areboth vertical(that is containthe vertical axis)

and as so aredenoted

and

2

v vσ σ'



Benzene has onemirror plane

perpendicular

to the principleC - axis (6 hσ )


C2

C2

C2

C6

Dihedral mirror planes ( bisect

the C axis perpendicular to theprinciple axis

d

2

σ )



A regular octahedron has a centre of inversion (i).




(a). A CH4 molecule

has a fourfold improperrotation axis (S4):

the molecule is indistinguishable

after a 90° rotation followed by

a reflection across the horizontalplane, but neither operation

alone is a symmetry operation.


C4

σ



(b) The staggered form of ethane has an S6 axis

composed of a 60°

rotation followed by

a reflection.




The Symmetry Classification of Molecules

The Schoenflies system

Hermann Mauguin−




The groups C , C , C1 i s

A molecule belongs to C if it

has only the identitity E

1 I

F

ClBr


has only the identitity E and ii

HO H

COOH

OH

HOOC

H

Meso-tartaric

acid

N

Quinoline

A molecule belongs to Cs if ithas only the identity and a mirrorplane

C , C , C1 i s




The groups C C , and Cn nv nh,


has a C axis and the identitity E onlyn

n

O O

H H

C2

H2O2

C2 C3

C4C5

C6

Cn




The groups C C , and Cn nv nh,A molecule belongs to C if it

has a C axis and n vertical

mirror planes

nv

n

C v2C v3

C v4C v5 C v6

C v∞

cone

CO

Heteronucleardiatomics areC v∞

Cnv

H O2 C v2

C v3

NH3




The groups C C , and Cn nv nh,A molecule belongs to C if it

has a C axis and a horizontal

mirror plane

nh

n

C h2C h3 C h4

C h5C h6

C

C

Cl H

H Cl

Trans CHCl=CHCl

B

O

OO

H

H

H

B(OH)3

Cnh



The presence of a twofold axis and a horizontal mirror plane

jointly imply the presence of a centre of inversion in the

molecule.


The groups C C , and Cn nv nh

,

Cnh

C2

σ

i




The groups D D , and Dn nv nh

,

A molecule belongs to D if ithas a C axis and n two fold axes(C ) perpendicular to C .

n

n

2 n

A molecule with n twofold rotation axes perpendicular to an

n-fold rotation axis belongs to the group Dn.

Dn

Pt

NN

N

NN

N

D3





,

D2 D3D4 D5

D6

Dn





,

A molecule belongs to D if it

has a C axis and n two fold axes

(C ) perpendicular to C as well as

a horizontal mirror plane.

nh

n

2 n

A molecule

with a

Mirror plane

perpendicularto a Cn axis,

and with n

twofold axes in

the plane, belongsto the group

Dnh.

Dnh





,

A molecule belongs to D if ithas a C axis and n two fold axes(C ) perpendicular to C as well as


nh

n

2 n

Dnh

D h2 D h3

D h4 D h5 D h6

C

C

H H

H H

C4

C2

C2

σh

D2h

Cl

Cl ClAu

Cl

C4

C2

C2

C'2

C2

σh

D4h





,

A molecule belongs to D if it

has a C axis and n two fold axes

(C ) perpendicular to C as well as


nh

n

2 n

E , C , 3C ,3C'6 2 2 h, σ

B

F

FF

E , C , 3C3 2 h, σ

Dnh



The Symmetry Classification of Molecules Dnh

F P

F

F

F

F

C3

C2

C2

C2

σh


,

D h3

Th S Cl ifi i f M l l




The groups D D , and Dn nv nh,

A molecule belongs to D if in addition to the elements of D it posesses n dihedral mirror

planes

nd

n

Dnd

D d2 D d3 D d4D

d5D

d6

C C C C2

C2

C2

D d2



What you must learn from this lecture

1. Given a molecule, you should be able to identify the different

symmetry elements (Cn,σv,σh,σd,i,Sn, etc. )

2. Having identified the symmetry elements of a molecule,

you should be able to establish the point group to which

the molecule belong

chem 373- lecture 34: symmetry elements

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