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Announcements

n ne ass gnments First online assessment on cha 2 and 3

started, and will be until Wednesday Jan 30 at11.59 pm

You have one hour to answer 10 quiz

questions picked randomly in a larger set ofques ons

Next two classes taught by Laura Pavelka

1

Office hours on Thursday cancelled.

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4. S mmetr and

group point

Inor anic chemistr : Main rou

CHEM 281

2

r. u rey . oores

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CHEM 201-281: II. Symmetry elements and operation of symmetry

. Inversion (i): Each point ends up in an opposite position

respective to the centre of symmetry (which must be center

of the molecule)E.g.: benzene vs methane

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CHEM 201-281: II. Symmetry elements and operation of symmetry

. Rotation-reflection operation (Sn)= improper rotation

It is a com osite transformation: Sn o Cn

Sn is a rotation about an Cn axis followed by a reflectionthrough a perpendicular plane

. .

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and then another. The second operation is done first, then comes the

first. It is like a multiplication.

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CHEM 201-281: III. Point groups: group of symmetry of operations

.Def:A group is a mathematical object. It contains some operations of

s mmetr and the com osition and obe s 4 rules described below

The composition of two elements of the group is also an element ofthe group

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Application: multiplication table

o E C2 v v

E

C2

E C2 v v

C2 E v v

4 Associative ro ert : A o B o C = A o B o C

vv v

v v C2 E

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

The collection of the symmetry operations of a molecule(+ o) = symmetry group of the molecule. These groupsare given names.

E.g.:

Water molecule C2v C2, v, v, E associated with o

Starwars Sk walker

Springfield Simpson

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

C1: Group containing E only (no symmetry)

C : E + 1 reflection

C : E + inversion center

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Cn (n>1): E + (n-1) rotations about an axis Cn

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o e: a mo ecu e as one ax s n, en n, n n- are ro a ons a a

belong to the group. Thus we say that the group possesses (n-1) Cn

rotations. E.g.: C3 and C32 C3 group => The group has 2C3

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III.3) Symmetry groups nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Cnv (n>1): E + (n-1) rotations Cn + n vertical reflections

C (n>1): E + (n-1) rotations C + 1 horizontal reflection

Cv: E + rotations of any angle about an axis C+

infinite number of vertical planes

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Dn (n>1): E + (n-1) rotations Cn (principal axis) + nrotations C2 (the C2 axes are perpendicular to Cn

Dnh (n>1): E + (n-1) rotations Cn (principal axis) + n C2

inversion when n is even Sn when n3

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Dnd (n>1): E + 2 improper rotations S2n + (n-1) Cnrotations + n C2 rotations + n vertical reflections

nvers on w en n s uneven

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Dh: E + rotations of any angle + number of vertical

planes + horizontal plane + i + number of C2 rotations +

Reminder: Cv:

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Sn (n even): E + 2 improper rotations Sn, 2 Cn/2 + iif n/2 is uneven

See Molwave software

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Oh (octahedron): E + 4C3 + 6C2 + 3C4 + i + 3S4 +4S6 + 3 h + 6 d

http://www.mathsisfun.com/geometry/octahedron-model.html

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Ih (Icosahedron): E + 6S5 + 6C5 + 10 C3 + 15 C2 +i + 6 S10 + 10 S6 + 15

htt ://www.mathsisfun.com/ eometr /icosahedron-model.html

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III.3 S mmetr rou s nomenclature

CHEM 201-281: III. Point groups: group of symmetry of operations

Point group assignment tree You can find it on myCourses

To assign the point group of a molecule, we

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cons er so e y epos on o e a oms an nothe lone pairs, the orbitals