Symmetry

Edward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

04/19/23

Symmetry Effects

• Simplifies the amount of work needed to solve a problem• reduces it by a factor of 2, 3 or more.

04/19/23

Symmetry Effects

Symmetric atoms in a moleculeare energetically equivalent.

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cyclopentadienide ionC5H5

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Simplifies the appearance of spectra(the symmetric bonds absorb energyat identical energies): nmr, ir, etc.

Simplifies crystallography(fewer unique atomshave to be located).

Simplifies chemistry(symmetric atoms in a molecule react the same way).

04/19/23

Elements of Symmetry

• Look at diagrams or models of the following molecules• What is symmetric about each?• Are they symmetric in the same way?• Are some more symmetric than others?

H2O

HCN

HCCH

CH2Cl2

NH3

BF3 C6H6

PtCl42-

04/19/23

Rotational Symmetry

OH H

How many equivalentpositions are there?

C2

What is therotational orderfor each molecule?

Rotation about an axis producestwo or more equivalent structures.

H2O

HCN

HCCH

CH2Cl2

NH3

BF3 C6H6

PtCl42-

04/19/23

Rotational Symmetry

Can a moleculehave more thanone rotation axis?

Rotation about an axis producestwo or more equivalent structures.

H2O

HCN

HCCH

CH2Cl2

NH3

BF3 C6H6

PtCl42-

04/19/23

Rotational Symmetry

HCCHCan a moleculehave more thanone rotation axis?

Rotation about an axis producestwo or more equivalent structures.

C6

C2

C2’

∞C2

C∞

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Reflection Symmetry

OH H

How many mirrorplanes are there?

v

How manymirror planes doeseach molecule have?

A mirror plane reflects one half of a moleculeinto the other half of the molecule.

v’

H2O

HCN

HCCH

CH2Cl2

NH3

BF3 C6H6

PtCl42-

04/19/23

v

Reflection Symmetry

How many ofeach type of mirrorplane are there?

Are there different kinds of mirror planes?

v’

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Reflection Symmetry

How many mirrorplanes are there?

Are there different kinds of mirror planes?

h

Which of thesemolecules havedifferent types ofmirror planes?

H2O

HCN

HCCH

CH2Cl2

NH3

BF3 C6H6

PtCl42-

04/19/23

Alternate Diagram of Atom Positions

atom above the plane

atom below the plane

atom on the plane

CH4 What is the order of themajor rotation axis?Where are the mirror planes?Are there C2

axes?

04/19/23

Inversion Symmetry

Which of thesemolecules has acenter of inversion?

Every position in a molecule can pass through thecenter of the molecule to give an equivalent position.

trans-dibromodichlorocuprate(II) ionCu ClCl Br

Br 2-

H2O

HCN

HCCH

CH2Cl2

NH3

BF3 C6H6

PtCl42-

i

04/19/23

Improper Rotation Symmetry

Rotation about an n-fold (improper axis)followed by reflection through a perpendicular plane

gives an equivalent structure.

CH4

S4

atom above the plane

atom below the plane

atom on the plane

04/19/23

Improper Rotation Symmetry

Rotation about an n-fold (improper axis)followed by reflection through a perpendicular plane

gives an equivalent structure.

C6H12 (chair)

S8

C2H6 (staggered)

What is the order of theimproper rotation axisin each of these molecules?

Combination of Symmetry Operations

The combination of a two-fold rotationfollowed by a horizontal reflectionis equivalent to whatsymmetry operation?

hC2

04/19/23