CHEM 2060 Lecture 2: Symmetry L2-1 Lecture 2: Molecular Symmetry

• We now start to look at SYMMETRY in molecules.

• You will be expected to understand the symmetry concepts we learn in this

course and apply them in the following courses: Biochemistry 19-2580, 3560, 3570 Structure & Spectroscopy 19-2070 Symmetry & Spectroscopy 19-3870 Chemistry of the Elements 19-3640, 3650 Organic II & III 19-3750, 3760 NANO [DEF] Symmetry is the property of remaining invariant under certain changes (as of orientation in space, for example).

Also: Beauty of form arising from balanced proportions.

Source: Webster’s 9th New Collegiate Dictionary.

CHEM 2060 Lecture 2: Symmetry L2-2 Why is symmetry important? How Symmetry works for us… Example 1. LASERS: Ruby Laser:

Cr3+ (~0.05%) doped in Al2O3 • The Cr3+ ions sit in octahedral sites…more

accurately, distorted octahedral (C3, not Oh)

• The surrounding environment of the alumina provides the symmetry to the Cr3+ ions, which MAKES THE RUBY LASE!

http://hyperphysics.phy-astr.gsu.edu/hbase/optmod/lassol.html

CHEM 2060 Lecture 2: Symmetry L2-3 Example 2. Recognition of DNA Sequences

a man a plan a canal panama “Palindromic” DNA Sequences Binding of Enzymes to DNA Double Helix Endonucleases (a) EcoRI (b) EcoRV CLEVAGE SITES

• Two Fold Symmetry Axis (see later)

5’-G-A-A-T-T-C-3’ 5’-G-A-T-A-T-C-3’

3’-C-T-T-A-A-G-5’ 3’-C-T-A-T-A-G-5’

... ... ...... .

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. ... ... .

.

. ...... .

.

. ...

CHEM 2060 Lecture 2: Symmetry L2-4 Example 3. Chemical reactivity “Diels – Alder Reactions” e.g.

SYMMETRY CONTROLS PRODUCTS !

C

C

C

CC

C

C

O

+

C

C

C

C

C

C

C

O

CHEM 2060 Lecture 2: Symmetry L2-5 An Introduction To Symmetry Analysis There are web tutorials on symmetry analysis: http://symmetry.otterbein.edu/ http://www.reciprocalnet.org/edumodules/symmetry/ • Let’s learn to define the symmetry of molecules in a precise manner. • In order to do this we need to develop a notational scheme that conveys the

symmetry of a molecule (or object). • This notation is universally used by chemists. In other words, it is a form of

language. • It will become second nature as you use it in more advanced courses. First we need to familiarize ourselves with Symmetry Operations and Symmetry Elements.

CHEM 2060 Lecture 2: Symmetry L2-6 Symmetry Operations [DEF] A symmetry operation is an action that leaves the molecule apparently unchanged. A rotation is an example of a symmetry operation. Example: a rotation operation performed on a molecule of water, H2O.

Rotate by 180° C2 axis The dashed line represents the axis of rotation. We can rotate the H2O molecule by (multiples of) 180° about this axis without apparent change to its position in space.

OH H

OH H

CHEM 2060 Lecture 2: Symmetry L2-7 Symmetry Elements And Operations [DEF] A symmetry element is the point, line or plane in the molecule about which the symmetry operation occurs. • 5 symmetry elements are needed to fully describe the symmetry of the

molecule NOTE: Not all 5 are always present!

Element Symbol Operation

Identity E Leaves in original position n-fold proper axis

Cn Rotation about axis by (360/n)° (or multiples thereof)

Plane σ Reflection in the plane Inversion centre

i Inversion through centre

n-fold improper axis

Sn Rotation by (360/n)° (or multiple) followed by reflection in plane perpendicular to axis.

CHEM 2060 Lecture 2: Symmetry L2-8

Identity, E • This is the simplest operation: nothing moves! • All objects have symmetry element E. • Let’s do an example…just to say we did… Water, H2O: E operation

CHEM 2060 Lecture 2: Symmetry L2-9

2-Fold proper rotation, C2 • This is the simplest example of an n-fold rotation. Water, H2O: C2 rotation The water molecule may be rotated through any angle about the bisector of the H-O-H bond angle… …but only a rotation of (a multiple of) 180° (C2) leaves its position unchanged in space.

CHEM 2060 Lecture 2: Symmetry L2-10

3-Fold proper rotation, C3 • A rotation by 120° is one third of a complete circle (360/3)° = C3 • 2 x 120° = 240° is two thirds of a circle 2(360/3)° = C3

2 Ammonia NH3: C3 and C3

2 rotation

A 3-fold rotation is possible about and the C3 axis (drawn looking down the axis from above). There are 2 rotations associated with this axis: C3 and C3

2. Question: Is C3

3 a valid symmetry operator?

CHEM 2060 Lecture 2: Symmetry L2-11

4-Fold proper rotation, C4 • Rotation by 90° = (360/4)° is C4 • Rotation by 2 x 90° = 180° is C2 !!! not C4

2 !!! • Rotation by 3 x 90° = 270° is C4

3 Iodine pentafluoride IF5: C4 , C2 and C4

3 rotation The C4 axis and C2 axis share the same position.

CHEM 2060 Lecture 2: Symmetry L2-12

Can rotation axes have different positions? YES! Higher symmetry molecules can have multiple rotation axes. Tetrachloroplatinate [PtCl4]2- (Note that VSEPR is not enough to predict the geometry…see later in Chem 3650)

Axes that are perpendicular (⊥) to the principle axis are labeled with primes (' ) and (" ).

CHEM 2060 Lecture 2: Symmetry L2-13

Mirror planes, σ Note that there are 3 possible subscripts for a σ plane:

v (vertical), h (horizonal), d (dihedral) σv (v = vertical; it is a mirror plane collinear with the principle rotation axis) Water, H2O: σv and σv' mirror plane There are two vertical mirror planes in H2O. They are ⊥ to one another. One cuts all the atoms in half. One cuts the O atom in half but reflects the H atoms into one another.

CHEM 2060 Lecture 2: Symmetry L2-14

Boric Acid, B(OH)3 : σh mirror plane • Note that for the purpose of this example, we are going to draw

B(OH)3 in one possible configuration, but remember that rotation about the B-O bonds is possible.

In this configuration, there is a C3 axis through the boron atom. The only mirror plane present is ⊥ to this axis. Therefore, it is called a horizontal mirror plane. HOMEWORK FOR TUTORIAL: Identify all the mirror planes in [PtCl4]2-.