lecture 1 - symmetry elements and operations

Symmetry and Shape in Inorganic Chemistry

Prof. Phil Gale

Office 30:4028

philip.gale@soton.ac.uk

Topics to be covered

•Symmetry elements and operations in molecular and ionic species

•Predictions of molecular shape

•Valence Shell Electron Pair Repulsion Theory

• Isoelectronic principle

• Isomerisation

Outcomes for this component of the course

• Identify the symmetry elements present in a particular structure.

•Use VSEPR theory to rationalize a particular molecular shape.

•Use VSEPR theory to predict the shape of a simple species.

•Sketch the possible geometric isomers of a molecule or ion.

By the end of this component of the course you should be able to:

Resources

• In addition to the lectures, a workshop will be held in week 3, at which time there will be an opportunity to consolidate your learning, and to discuss any problems with the tutors.

•All the lecture material for this component of the course is contained within the standard text (“Inorganic Chemistry” - Shriver and Atkins) but this book deals with some topics in more detail than is required at this stage. See Chapter 7 Section 7.1 S&E 4th Edition p196

Web resources

•There are numerous websites that cover molecular symmetry and shape. Some good ones are:

• http://symmetry.otterbein.edu/jmol/index.html

• http://winter.group.shef.ac.uk/vsepr/

Symmetry elements and operations in molecules

• Proper Axis of Rotation: Symbol Cn

• Plane of Symmetry: σ

• Centre of Symmetry: i

• Rotation-Reflection (or Improper Rotation) axis: Sn

• The Identity: E

A symmetry element is a feature which permits a symmetry operation to be performed.

i.e. a symmetry operation is an action that leaves the molecule unchanged. A symmetry element is a point or line or plane through which an operation is performed.

There are five types of symmetry element in discrete molecules:

Proper axis of Rotation Cn

•Element: n-fold rotation axis

•Operation: rotation by 360˚/n

•Symbol: Cn H

O

H

180˚

C2

C3

A

C3

A120˚

C3

A120˚

A

C3

A120˚

A

120˚

C3

A

A120˚

A

120˚

Cn: n = 4, 5, 6

90˚ 72˚ 60˚

Mirror Plane: σ

•Element: mirror plane

•Operation: reflection

•Symbol: σ

Mirror Plane: σ

•σv vertical, i.e. parallel to the rotational axis

•σh horizontal, i.e. perpendicular to rotational axis

•σd dihedral, i.e. additional planes parallel to the rotational axis

e.g. Hexagon

e.g. Hexagon

C6

e.g. Hexagon

e.g. Hexagonσv

σv

σv

σv

e.g. Hexagonσv

e.g. Hexagonσvσh

e.g. Hexagon

σh

e.g. Hexagon

e.g. Hexagonσd

σd

σd

e.g. Hexagon

e.g. Hexagon

σh

σv

e.g. Hexagon

σh

σv

σd

Centre of symmetry: i

•Element: centre or point

•Operation: inversion through centre

•Symbol: i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: i

i

Centre of symmetry: iSo for a point on a Cartesian set of axes with a centre of

symmtery at the origin the inversion operation will translate it from (x, y, z) to (-x, -y, -z)

Axis of Improper Rotation: Sn

•Element: n-fold axis of improper rotation

•Operation: Rotation by 360˚/n followed by a reflection perpendicular to the rotation axis

•Symbol: Sn

S4 axis in CH4

The Identity: E

•Don’t do anything!

•The identity operation does nothing to an object - it is necessary for mathematical completeness as you will see in the second year when you do group theory...

Some examples...

Examples of shapes or molecules which contain a

centre of symmetry

H Z X

Examples of shapes or molecules which contain a

centre of symmetryCO2 staggered-ethane

Location of the symmetry elements in:

H2O NH3 CH2Cl2

Location of the symmetry elements in:

XeOF4

A methodical route for identifying symmetry elements

•Step 1: Look for proper axes of rotation....symbol Cn

remember that it is not uncommon to find more than one axis rotation.

•Step 2: Select the highest order axis. The direction of this axis defines ‘vertical’.

A methodical route for identifying symmetry elements

•Step 3: Look for planes. These will be ‘horizontal’ or ‘vertical’ depending on their relationship to the highest order axis. A plane of symmetry which is perpendicular to the highest order axis(sometimes called the principal axis) is a horizontal plane. A plane of symmetry which contains the highest order axis is a vertical plane.

A methodical route for identifying symmetry elements

•Step 4: What else could be present?

• (a) is there a centre of symmetry?

• (b) are there any rotation-reflection axes? (symbol Sn) These are the hardest symmetry elements to spot. If present, they are likely to be co-incident with one of the Cn axes - usually the principal axis. Remember that the rotation - reflection operation does two things: the rotation and the reflection

•Step 5 Finally there is always the identity E.

Worked examples.

Molecules with an ‘infinity-fold’ axis: C∞

•Linear molecules such as carbon dioxide, nitrous oxide or acetylene (ethyne) have an internuclear axis around which rotation by any angle generates an equivalent position.

•Mathematically, an equivalent position is generated by rotation through an infinity of infinitesimally small angles. The axis defines ‘vertical’ and there are an infinite number of vertical planes of type σv.

O C O C∞

Molecules with no symmetry•Many molecules have little or no symmetry apart

from the identity E.

This is the structure found, for example in CHFClBr

Octahedron•Can you work out all the symmetry elements

present in an octahedron?

Ni2+

OH2

OH2H2O OH2

H2O OH2

C4, C2, S4

C3, S6

C3, S6

σh

σdi

C2

C2